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Games, Theory and Applications by L. C. Thomas (Dover) Unabridged and slightly corrected republication of the 1986 paperback edition of the work originally published by Ellis Horwood/John Wiley, Chichester, London, 1984. 31 figures. 6 tables.

Anyone with a knowledge of basic mathematics will find this an accessible and informative introduction to the fundamentals and applications of game theory. It opens with the theory of two-person zero-sum games, two-person non-zero-sum games, and n-person games, at a level between nonmathematical introductory books and technical mathematical game theory books.  

Succeeding sections focus on a variety of applications—including introductory explanations of gaming and metagames—that offer non-specialists information about new areas of game theory at a compre­hensible level. Numerous exercises appear with full solutions, in addition to an extensive bibliography, 80 problems with worked solutions, and more than 30 illustrations useful for the theory of non-zero and n-person games.  

All readers involved in game theory will find this book of value, as will those interested in the applications of mathematics and in game theory's potential role in matters of economics, operational research, business theory, accounting, marketing, advertising, and related fields.

The Mathematics of Juggling by Burkard Polster (Springer Verlag) Learn to juggle numbers! This book is the first comprehensive account of the mathematical techniques and results used in the modelling of juggling patterns. This includes all known and many new results about juggling sequences and matrices, the mathematical skeletons of juggling patterns.
Many useful and entertaining tips and tricks spice up the mathematical menu presented in this book. There are detailed descriptions of jugglable and attractive juggling sequences, easy zero-gravity juggling, robot juggling, as well as fun juggling of words, anti-balls, and irrational numbers.

The book also includes novel, or at least not very well known connections with topics such as bell ringing, knot theory, and the many body problem. In fact, the chapter on mathematical bell ringing has been expanded into the most comprehensive survey in the literature of the mathematics used by bell ringers.

Accessible at all levels of mathematical sophistication, this is a book for mathematically wired jugglers, mathematical bell ringers, combinatorists, mathematics educators, and just about anybody interested in beautiful and unusual applications of mathematics.

Contents: Juggling-an Introduction * Simple Juggling * Multiplex Juggling * Multihand Juggling * Practical Juggling * Jingling, or, Ringing the Changes * Juggling Loose Ends * Appendix A: Stereograms of Hamiltonian Cycles * References * Index  

Mathematical Journeys by Peter Schumer (John Wiley) The world of mathematics abounds with fascinating, unusual ideas—ideas and concepts that even seasoned mathematicians often wonder about. Mathematical Journeys  takes readers on a grand tour of the best of modern math—it's most elegant solutions, most clever discoveries, most mind-bending propositions, and most impressive personalities. Writing in an easily accessible format while still incorporating real mathematics, author Peter Schumer introduces the history of mathematics, number theory, combinatorics, geometry, graph theory, and "recreational mathematics."  

Requiring only high school mathematics and a healthy curiosity, this book explores all those aspects that mathematicians themselves find most delightful, from brilliant, sometimes quirky and humorous tidbits to profiles of great thinkers like Paul Erdos and Leonhard Euler that provide glimpses into the minds that gave birth to the math. Each chapter of the book focuses on some interesting dimension of mathematics, providing the history and requisite mathematic background, the solution of a problem or two, and some indication of natural generalization and related areas of study.

Mathematical Amusements Contained Within Mathematical Journeys Include:

•  The green chicken contest

•  The Josephus problem—Please choose me last

• Nim and Wythoff's game: or how to get others to pay your bar bill

•  Mersenne primes, perfect numbers, and amicable pairs

• Tic-tac-toe, magic squares, and Latin squares

• Clever twists on rolling dice

• Episodes in the calculation of pi

• Pizza slicing, map coloring, pointillism, and jack-in-box

•  Choosing stamps to mail a letter

• Pascal potpourri

Whether you are a mathematics lover, or simply a novice curious to learn what your calculus class omitted, Mathematical Journeys offers a colorful tour through the intriguing world of mathematics.  

Speed Mathematics : Secrets Skills for Quick Calculation by Bill Handley (John Wiley) Is it true that some people are born with a mathematical mind? Do some people have an advantage over others? And, conversely, are some people at a disadvantage when they have to solve mathematical problems?

The difference between high achievers and low achievers is not the brain they were born with but how they learn to use it. High achievers use better strategies than low achievers.

Speed Mathematics will teach you better strategies. These methods are easier than those you have learned in the past so you will solve prob­lems more quickly and make fewer mistakes.

Imagine there are two students sitting in class and the teacher gives them a math problem. Student A says, "This is hard. The teacher hasn't taught us how to do this. So how am I supposed to work it out? Dumb teacher, dumb school."

Student B says, "This is hard. The teacher hasn't taught us how to do this. So how am I supposed to work it out? He knows what we know and what we can do so we must have been taught enough to work this out for ourselves. Where can I start?"

Which student is more likely to solve the problem? Obviously, it is student B.

What happens the next time the class is given a similar problem? Student A says, "I can't do this. This is like the last problem we had. It's too hard. I am no good at these problems. Why can't they give us something easy?"

Student B says, "This is similar to the last problem. I can solve this. I am good at these kinds of problems. They aren't easy, but I can dc them. How do I begin with this problem?"

Both students have commenced a pattern; one of failure, the other, success. Has it anything to do with their intelligence? Perhaps, but not necessarily. They could be of equal intelligence. It has more to d( with attitude, and their attitude could depend on what they have been told in the past, as well as their previous successes or failures. It is not enough to tell people to change their attitude. That make: them annoyed. I prefer to tell them they can do better and I will shove them how. Let success change their attitude. People's faces light up a they exclaim, "Hey, I can do that!"

Here is my first rule of mathematics:

The easier the method you use to solve a problem, the faster you will solve it with less chance of making a mistake.

The more complicated the method you use, the longer you take to solve a problem and the greater the chance of making an error. People, who use better methods are faster at getting the answer and make fewer mistakes, while those who use poor methods are slower at get­ting the answer and make more mistakes. It doesn't have much to do with intelligence or having a "mathematical brain."

Speed Mathematics is written as a non-technical book that anyone can comprehend. By the end of this book, you will understand mathematics as never before, you will marvel that math can be so easy, and you will enjoy mathematics in a way you never thought possible.

Each chapter contains a number of examples. Try them, rather than just read them. You will find that the examples are not difficult. By trying the examples, you will really learn the strategies and principles and you will be genuinely motivated. It is only by trying the examples that you will discover how easy the methods really are.

I encourage you to take your time and practice the examples, both by writing them down and by calculating the answers mentally. By working your way through this book, you will be amazed at your new math skills.  

Statistics

Stochastic Models in Queueing Theory, 2nd edition by Jyotiprasad Medhi (Academic Press) Medhi's second edition provides clear, comprehensive coverage of stochastic queueing models and their most recent innovations. Among its features are a wealth of compelling and relevant examples and exercises. These along with numerous discussions help readers understand queueing theory and demonstrate its wide applicability in several areas of modern technology. Generous updated reference lists follow each chapter to give readers ample and convenient opportunities for further investigation in this ever-growing field.
 
This is a graduate level textbook that covers the fundamental topics in queuing theory. The book has a broad coverage of methods to calculate important probabilities, and gives attention to proving the general theorems. It includes many recent topics, such as server-vacation models, diffusion approximations and optimal operating policies, and more about bulk-arrival and bull-service models than other general texts.

• Current, clear and comprehensive coverage
• A wealth of interesting and relevant examples and exercises to reinforce concepts
• Reference lists provided after each chapter for further investigation

The study of queueing models has been of considerable active interest ever since the birth of queueing theory at the beginning of the last century. Queue­ing theory continues to be one of the most extensive theories of stochastic models. Its progress and development, both in methodology and in applica­tions, are ever growing. Innovative analytic treatments toward its theoretical development are being advanced, and newer areas of application are emerging.

There is a large and growing audience interested in the study of queueing models. The level of background and preparation among them varies a great deal, along with their requirements for depth of coverage. The audience is composed of advanced undergraduate and graduate students from a number of disciplines. In addition to students of standard graduate courses, there are many researchers, professionals, and industry analysts who require an in-depth knowledge of the subject.

There are, of course, some excellent advanced works, monographs, and texts on the subject as well. The rapid development of the subject demands updated texts, especially for the type of audience aimed at. Furthermore, the style of presentation and the approach of individual authors appeal to different sections of this large and varied audience.

The author feels that there is sufficient scope and material to warrant ad­ditional texts, especially at the graduate level, in this ever-growing subject area. This book has grown out of the author's long experience of teaching and research in India , the United States , and Canada . A reviewer's glowing compli­ment (in American Mathematical Monthly) on the author's first book Stochastic Processes (Wiley Eastern, and Halsted Wiley 1982) inspired the author to under­take preparation of a book on queueing models in a similar readable style.

Organization of the book

The book is divided into eight chapters. Chapter 1 is a summary of basic results in stochastic processes. This should be helpful to users in eliminating the need to refer frequently to other books on stochastic processes just for basic results. Chapter 2, which is devoted to general concepts, contains some discussions on concepts such as PASTA, superposition of arrival processes, and customer and time averages. Chapters 3 and 4 deal with birth-and-death queueing models and non-birth-and-death systems, respectively. Transient behavior and busy period analysis have been discussed at some length, and a uniformity of ap­proach is emphasized. Some models of bulk queues have also been included because of their importance in transportation science. Chapter 5 is devoted to networks of queues and Chapter 6 to certain non-Markovian queueing sys­tems. In Chapter 7, systems with both general arrival and service patterns are discussed. Chapter 8 covers miscellaneous topics such as asymptotic methods and queues with vacations, with a brief excursion into the design and control of queues. Diffusion approximations, which have emerged as powerful tools, have been discussed in some detail. We believe this chapter will be especially useful to researchers and professionals who wish to have a broad, general idea of the diffusion approximation methods.

Each of the chapters (except Chapter 2) contains a number of worked exam­ples and problems, and all the chapters include extensive and recent references. The problems contain some materials that have been discussed, keeping in mind researchers and those who wish to pursue the subject further.

In order to facilitate use of the second edition by those who are already familiar with the first edition, a drastic change in the basic structure has been avoided. The number of chapters has been kept at eight, with considerable additions in the broad topics mainly based on recent developments during the intervening years. Apart from inclusion of new topics (including some emerging during the past few years), new examples, and new problems, topical discussions have been expanded through notes, remarks, and so on. References have been updated. These have been supplemented by related works of interest for further reading. Chapters 3, 6, and 8, in particular, contain many new topics. Some of the new matters address finite input source and finite buffer models, advanced vacation models, retrial queueing systems, and a newly emerging trend in teletraffic processes and their analyses. My sincere hope is that the book will be found useful as a graduate text and also as a reference book by professionals and researchers in this subject area.

In addition to mathematics and statistics, the book could be used for a one or two-semester course at the advanced undergraduate or graduate level in science, systems science, branches of engineering, telecommunications, economics, management, and business (with programs focused on quantitative methods).

Course coverage: The prerequisites for using this book are a course on applied probability and a course on advanced calculus.

Teachers would be the best judges of topics to be covered in a course. The following suggestions are for their consideration: For a two-semester course: The whole book.

For a one-semester course: Sections 1.1 through 1.5; 1.7 through 1.9; Sections 2.1 through 2.7; Sections 3.1 through 3.8 and 3.11; Sections 4.2 and 4.3; Sections 5.1 through 5.4; Sections 6.1 through 6.4; 6.7, 6.9 and 6.10; and Sections 7.1 and 8.1

Exercises are to be selected from problems and complements.  

An Introduction to Multivariate Statistical Analysis, 3rd edition by T. W. Anderson (Wiley-Interscience) Text provides a basic knowledge of multivariate statistical analysis. Updated to include new advances in the field and a new chapter on patterns of dependence and graphical models. For graduate students of multivariate statistics. A classic comprehensive sourcebook, now fully updated

For more than four decades An Introduction to Multivariate Statistical Analysis has been an invaluable text for students and a resource for professionals wishing to acquire a basic knowledge of multivariate statistical analysis. Since the previous edition, the field has grown significantly. This updated and improved Third Edition familiarizes readers with these new advances, elucidating several aspects that are particularly relevant to methodology and comprehension.

The Third Edition features new or more extensive coverage of:

•  Patterns of Dependence and Graphical Models–a new chapter

• Measures of correlation and tests of independence

• Reduced rank regression, including the limited-information maximum-likelihood estimator of an equation in a simultaneous equations model

• Elliptically contoured distributions

Incorporation of the advice and comments of the readers of the first two editions as well as extensively classroom-tested techniques and calculations makes An Introduction to Multivariate Statistical Analysis, Third Edition, more valuable than ever for both professional statisticians and students of multivariate statistics.

For some forty years the first and second editions of An Introduction to Multivariate Statistical Analysis have been used by students to acquire a basic knowledge of the theory and methods of multivariate statistical analysis. The book has also served a wider community of statisticians in furthering their understanding and proficiency in this field. Since the second edition was published, multivariate analysis has been developed and extended in many directions. Rather than attempting to cover, or even survey, the enlarged scope, Anderson elected to elucidate several aspects that are particularly interesting and useful for methodology and comprehension.

Earlier editions included some methods that could be carried out on an adding machine! In the twenty-first century, however, computational techniques have become so highly developed and improvements come so rapidly that it is impossible to include all of the relevant methods in a volume on the general mathematical theory. Some aspects of statistics exploit computational power such as the resampling technologies; these are not covered here.

The definition of multivariate statistics implies the treatment of variables that are interrelated. Several chapters are devoted to measures of correlation and tests of independence. A new chapter, "Patterns of Dependence; Graphical Models" has been added. A so-called graphical model is a set of vertices or nodes identifying observed variables together with a new set of edges suggesting dependences between variables. The algebra of such graphs is an outgrowth and development of path analysis and the study of causal chains. A graph may represent a sequence in time or logic and may suggest causation of one set of variables by another set.

Another new topic systematically presented in the third edition is that of elliptically contoured distributions. The multivariate normal distribution, which is characterized by the mean vector and covariance matrix, has a limitation that the fourth-order moments of the variables are determined by the first- and second-order moments. The class of elliptically contoured distribution relaxes this restriction. A density in this class has contours of equal density which are ellipsoids as does a normal density, but the set of fourth-order moments has one further degree of freedom. This topic is expounded by the addition of sections to appropriate chapters.

Reduced rank regression developed in Chapters 12 and 13 provides a method of reducing the number of regression coefficients to be estimated in the regression of one set of variables to another. This approach includes the limited-information maximum-likelihood estimator of an equation in a simultaneous equations model.

Choosing and Using Statistics: A Biologist's Guide by Calvin Dytham (Blackwell) A handbook for any student or professional biologist who wants to process data using a statistical package on a computer, to select appropriate methods, and to extract important information from the often confusing output produced. Stresses the importance of experimental design, measurement of data, and interpretation of results. Emphasis is on actual use of the most popular statistics packages (SPSS, MINITAB, and Microsoft Excel), rather than how they work or how to do the calculations. This is a great, practical book for ecological and evolutionary researchers. Dytham walks you through the choosing and using of different common statistical applications. If you can't find it in here, you probably have an advanced question that requires a mathematical answer, in which case it's time to dust off that heavy textbook. For most questions, this will save you time and frustration.  

Statistical Analysis of Gene Expression Microarray Data edited by T. P. Speed (Chapman & Hall/CRC) Written by pre-eminent world authorities in the field, this book will be the definitive reference guide for the statistical analysis of genetic microarray data. Starting from the first steps of genetic microarray data analysis, the book covers the most important topics and common methodologies for analyzing gene expression data, including preprocessing issues, experiment design, and classification and clustering. These discussions provide the tools and guidance needed by biologists, geneticists, and statisticians working in the analysis of genetic data. The presentation level is appropriate for a quantitative biologist and geneticist, as well as for computer scientists working in the area.
The field of microarray data analysis is less than a decade old, but it is already occupy­ing the time and energies of a large and growing number of statisticians and others. It appears clear to us that large-scale gene expression studies are not a passing fashion, but are instead one aspect of a new mode of biological experimentation, one involving large-scale, high throughput assays. Themes here include parallel approaches to the collection of very large amounts of data (by biological standards), quite sophisticated instrumentation that needs understanding by statisticians, data where the systematic features are at least as important as the random ones, and a general sense that we are dealing more with industrial scale than the traditional single-investigator lab research, with data compiled in a notebook. Furthermore, this kind of research often involves many different kinds of data, including clinical, genetic, and molecular, as well as the basic assay data, and so topics of data integration and the use of databases readily arise.

Although the details of the technologies will undoubtedly change over time, the oppor­tunities for serious statistical engagement will remain. We hope our readers will find this field as interesting as we do, and join us. More than enough datasets and problems are available to go around.  

Elementary Statistics in Social Research (9th Edition) by Jack Levin, James Alan Fox (Allyn & Bacon) provides an introduction to statistics for students in sociology and related fields, including criminal justice, political science, and social work. This book is not a comprehensive reference work on statistical methods. On the contrary, our first and foremost objective is to be understandable to a broad range of students, particularly to those who may not have a strong background in mathematics.

Like its predecessors, the ninth edition contains a number of pedagogical features. Most notably, detailed step-by-step illustrations of statistical procedures continue to be located at important points throughout the text. We have again provided clear and logical explanations for the rationale and use of statistical methods in social research. And we have again included a large number of end-of-chapter questions and problems, almost all of which are answered at the end of the book. Finally, we have ended each part of the text with a section entitled "Looking at the Larger Picture," which carries the student through the entire research process based on a hypothetical survey of smoking and drinking among high school students.

This latest revision contains a number of improvements and enhancements. Most important, all numerical exercises and illustrations have been painstakingly checked and verified to minimize the frustrations that students feel when they encounter computational errors. Because perfection is something to strive for, we  enhancements include conceptual problems at the end of each chapter, updated examples and illustrations, new material on box plots, and a simplified coverage of nonparametric measures.

Following a detailed overview in Chapter 1, the text is divided into five parts. Part I (Chapters 2 to 4) introduces the student to the most common methods for describing and comparing data. Part II (Chapters 5 and 6) serves a transitional purpose. Beginning with a discussion of the basic concepts of probability, it leads the student from the topic of the normal curve as an important descriptive device to the use of the normal curve as a basis for generalizing from samples to populations. Continuing with this decision-making focus, Part III (Chapters 7 to 9) contains several well-known tests of significance. Part IV (Chapters 10 to 12) includes procedures for obtaining correlation coefficients, and an intro­duction to regression analysis. Finally, Part V consists of an important chapter in which stu­dents learn, through example, the conditions for applying statistical procedures to research problems.

The text provides students with background material for the study of statistics. A review of basic mathematics, statistical tables, a list of formulas, and a glossary of terms are included.  

Numerical Issues in Statistical Computing for the Social Scientist by Micah Altman, Jeff Gill, Michael P. McDonald (Wiley-Interscience) This book is intended to serve multiple purposes. In one sense it is a pure research book in the traditional manner: new principles, new algorithms, and new solu­tions. But perhaps more generally it is a guidebook like those used by naturalists to identify wild species. Our "species" are various methods of estimation requir­ing advanced statistical computing: maximum likelihood, Markov chain Monte Carlo, ecological inference, nonparametrics, and so on. Only a few are wild; most are reasonably domesticated.

A great many empirical researchers in the social sciences take computational factors for granted: "For the social scientist, software is a tool, not an end in itself— (MacKie-Mason 1992). Although an extensive literature exists on statis­tical computing in statistics, applied mathematics, and embedded within various natural science fields, there is currently no such guide tailored to the needs of the social sciences. Although an abundance of package-specific literature and a small amount of work at the basic, introductory level exists, a text is lacking that provides social scientists with modern tools, tricks, and advice, yet remains accessible through explanation and example.

The overall purpose of this work is to address what we see as a serious defi­ciency in statistical work in the social and behavioral sciences, broadly defined. Quantitative researchers in these fields rely on statistical and mathematical com­putation as much as any of their colleagues in the natural sciences, yet there is less appreciation for the problems and issues in numerical computation. This book seeks to rectify this discrepancy by providing a rich set of interrelated chapters on important aspects of social science statistical computing that will guide empirical social scientists past the traps and mines of modern statistical computing.

The lack of a bridging work between standard statistical texts, which, at most, touch on numerical computing issues, and the comprehensive work in statisti­cal computing has hindered research in a number of social science fields. There are two pathologies that can result. In one instance, the statistical computing process fails and the user gives up and finds less sophisticated means of answering research questions. Alternatively, something disastrous happens during the numerical calculations, yet seemingly reasonable output results. This is much worse, because there are no indications that something has failed, and incorrect statistical output becomes a component of the larger project.

Fortunately, many of the most common problems are easy to describe and easier still to avoid. We focus here to a great extent on problems that can occur in maximum likelihood estimation and nonlinear regression because these are. with the exception of simple linear models, the methods most widely used by social scientists. False convergence, numerical instability, and problematic like­lihood surfaces can he diagnosed without much agony by most interested social scientists if they have specific advice about how to do so. Straightforward com­putational techniques such as data resealing, changes of starting values, function reparameterization, and proper use of analytic derivatives can then he used to reduce or eliminate many numerical problems. Other important and recent statistical approaches that we discuss are ecological inference, logistic regression, Markey chain Monte Carlo , and spatial analysis.

Starters

In this book we introduce the basic principles of numerical computation, outlines the optimization process, and provides specific tools to assess the sensitivity of the subsequent results to problems with these data or model. The reader is not required to have an extensive background in mathematical statistics, advanced matrix algebra, or computer science In general, the reader should have at least a year of statistics training, including maximum likelihood estimation, modest matrix algebra, and some basic calculus. In addition, rudimentary programming knowledge in a statistical package or compiled language is required to understand and implement the ideas herein.

Some excellent sources for addressing these preliminaries can be found in the following sources.

• Introductory statistics. A basic introductory statistics course, along the lines of such texts as: Moore and McCabe's Introduction to the Practice of Statis­tics (2002), Moore's The Basic Practice of Statistics (1999), Basic Statistics fur the Social and Behavioral Sciences by Diekhoff (1996), Blalock's well-worn Social Statistics (1979), Freedman et al.'s Statistics (1997), Ame­miya's Introduction to Statistics and Econometrics (1994), or Statistics find the Social Sciences by Sirkin (1999).

• Elementary matrix algebra. Some knowledge of matrix algebra, roughly at the level of Greene's (2003) introductory appendix, or the first half of the undergraduate texts by either Axler (1997) or Anton and Rorres (2000). It will not be necessary for readers to have an extensive knowledge of linear algebra or experience with detailed calculations. Instead, knowledge of the structure of matrices, matrix and vector manipulation, and essential symbology will be assumed. Having said that, two wonderful reference books that we advise owning are the theory book by Lax (1997), and the aptly entitled book by Harville (1997), Matrix Algebra from a Statisticians Perspective.

• Basic calculus. Elementary knowledge of calculus is important. Helpful, basic, and inexpensive basic texts include Kleppner and Ramsey (1985). Bleau (1994), Thompson and Gardner (1998), and for a very basic intro­duction, see Downing (1996). Although we avoid extensive derivations, this material is occasionally helpful.

Programming

Although knowledge of programming is not required, most readers of this book are, or should he, programmers. We do not mean necessarily in the sense of generating hundreds of lines of FORTRAN code between seminars. By program­ming we mean working with statistical languages: writing likelihood functions in Gauss, R, or perhaps even Shaba , coding solutions in WinBUGS, or manip­ulating procedures in SAS. If all available social science statistical solutions were available as point-and-click solutions in SP SS, there would not be very many truly interesting models in print.

There are two, essentially diametric views on programming among academic practitioners in the social sciences. One is emblemized by a well-known quote from Hoare (1969, p. 576): "Computer programming is an exact science in that all the properties of a program and all the consequences of executing it in any given environment call, in principle, be found out from the text of the program itself by means of purely deductive reasoning." A second is by Knuth (1973): "It can be an aesthetic experience much like composing poetry or music." Our per­spective on programming agrees with both experts; programming is a rigorous and exacting process, but it should also be creative and fun. It is a reward­ing activity because practitioners can almost instantly see the fruits of their labor. We give extensive guidance here about the practice of statistical pro­gramming because it is important for doing advanced work and for generating high-quality work.

There are two basic sections to this book. The first comprises four chapters and focuses on general issues and concerns in statistical computing. The goal in this section is to review important aspects of numerical maximum likelihood and related estimation procedures while identifying specific problems. The second section is a series of six chapters outlining specific problems that center on problems that originate in different disciplines but are not necessarily contained within. Given the extensive methodological cross-fertilization that occurs in the social sciences, these chapters should have more than a narrow appeal. The last chapter provides a summary of recommendations from previous chapters and an extended discussion of methods for ensuring the general replicability of one's research.

The book is organized as a single-semester assignment accompanying text. Obviously, this means that some topics are treated with less detail than in a including bibliographies, discussion-lists, benchmark data, high-precision libraries, and optimization software.

In addition, the Web site includes links to all of the code and data used in this book and not otherwise described in detail, in order to assist other scholars in carrying out similar analyses on other datasets. However, there is a sufficient set of references to lead interested readers into more detailed works.

A general format is followed within each chapter in this work, despite widely varying topics. A specific motivation is given for the material, followed by a detailed exposition of the tool (mode finding, El, logit estimation, MCMC, etc.). The main numerical estimation issues are outlined along with various means of avoiding specific common problems. Each point is illustrated using data that social scientists care about and can relate to. This last point is not trivial; a great many books in overlapping areas focus on examples from biostatistics, and the result is often to reduce reader interest and perceived applicability in the social sciences. Therefore, every example is taken from the social and behavioral sciences, including: economics, marketing, psychology, public policy, sociology, political science, and anthropology.

Many researchers in quantitative social science will simply read this book from beginning to end. Researchers who are already familiar with the basics of statistical computation may wish to skim the first several chapters and pay particular attention to Chapters 4, 5, 6, and I I, as well as chapters specific to the methods being investigated.

Because of the diversity of topics and difficulty levels, we have taken pains to ensure that large sections of the book are approachable by other audiences. Recommend for those who do not have the time or training to read the entire book, the following:         

• Undergraduates in courses on statistics or research methodology, will find a gentle introduction to statistical computation and its importance in Section 1.1 and Chapter 2. These may be read without prerequisites.
• Graduate students doing any type of quantitative research will wish to read the introductory chapters as well, and will find Chapters 3 and 11 useful and approachable. Graduate students using more advanced statistical models should also read Chapters 5 and 8, although these require more some mathematical background.
• Practitioners may prefer to skip the introduction, and start with Chapters 3, 4, and 11, as well as other chapters specific to the methods they are using (e.g., nonlinear models, MCMC, ecological inference, spatial methods).

However, we hope readers will enjoy the entire work. This is intended to be a research work as well as a reference work, so presumably experienced researchers in this area will still find some interesting new points and views within. Web Site Accompanying this book is a Web site.

Non-Self-Adjoin Boundary Eigenvalue Problems by Reinhard Mennicken, Manfred Moller (North-Holland Mathematics Studies, No 192: North-Holland) The purpose of this book is the study of non-self-adjoint boundary eigenvalue problems for first order systems of ordinary differential equations and n-th or-der scalar differential equations. The coefficients of the differential equations as well as the boundary conditions are allowed to depend polynomially, holomor­phically or asymptotically on the eigenvalue parameter. The boundary conditions may contain infinitely many interior points and an integral term. With the bound­ary eigenvalue problem a bounded operator function is associated which consists of two components, the differential operator function and the boundary operator function. These operator functions depend in general nonlinearly on the eigen­value parameter.

Various eigenfunction expansions are proved by the contour integral method under regularity conditions which originally were introduced by Birkoff and Stone in case of A-independent boundary conditions. The calculation of the Fourier coefficients of these expansions is based on the theory of the inverses of holomorphic Fredholm operator valued functions which for the sake of complete­ness is included in this book. An important aspect of this theory is the representa­tion of the principal parts of the inverses of these functions at their poles by root functions (eigenvectors and associated vectors) of the given operator functions and their adjoints. The proofs of the eigenfunction expansions are based on sharp asymptotic estimates of the resolvents (Green's functions) for large values of the eigenvalue parameter.

Our approach is based on functional analytic methods. The reader should be familiar with basic concepts of Banach spaces and Lebesgue integration and should have some knowledge about distributions. Whenever we use these ba­sic results we give references so that the reader unfamiliar with these concepts can easily find them. Our main references to the basic topics are the monograph of T. Kato for Banach spaces, the monograph [HS] of E. Hewitt and K. Stromgberg for the theory of Lebesgue integration, and the monograph [H02] of L. Hormander for the theory of distributions.

Each chapter ends with a short section containing historical notes.

Chapters I and II are concerned with preparations from functional analysis and Sobolev space theory. In Chapters III–V first order systems are considered, followed by n-th order equations in Chapters VI—IX. Since n-th order equations are reduced to first order systems, some of the results of Chapters III—V are needed

in Chapters VI–IX. Chapter X contains applications to problems from physics and engineering.

The literature for n-th order linear differential equations and first order sys­tems is vast, and the bibliography is only a selection of publications in this field. The list of notations and the index should help the reader to navigate through the text.

Chapter I deals with spectral theory for holomorphic Fredholm valued oper­ator functions, in particular, the principal parts of their inverses at the poles are investigated. It is shown that these principal parts can be written in terms of eigen­vectors and associated vectors of the operator function and its adjoint. One-to-one connections between biorthogonal systems of eigenvectors and associated vectors and the principal parts of the inverse operator functions are established. Special attention is paid to the case of A-linear problems.

Chapter II contains the prerequisites for the study of differential operators. Sobolev spaces on intervals are introduced and their properties are investigated. These results are essentially well-known but, in general, are stated and proved for subsets of 1R" . The one dimensional case is easier and gives some additional prop­erties. Therefore, and to make the monograph more self-contained, this chapter is included. Also, some basic results for differential equations are stated.

Chapter III starts with the definition of boundary eigenvalue problems for first order systems. The adjoint and the inverse are calculated, and their relations to the "classical" adjoint and inverse for the differential operator considered in Lp spaces are discussed. Some examples show the difficulties which arise if one considers the classical adjoint. The inverse is an extension of the classical inverse, which is an integral operator whose kernel is the Green's matrix function.

Chapter IV is devoted to the estimate of the Green's matrix function. To this end, Birkhoff regularity is introduced for systems which are asymptotically linear in the eigenvalue parameter, and necessary and sufficient conditions for Birkhoff regularity are given. The characteristic determinant is estimated below away from its zeros, which are the eigenvalues of the given boundary eigenvalue problem. Then the Green's matrix function and finally the resolvent of the boundary eigenvalue operator functions are estimated on suitable circles in the complex plane tending to infinity.

In Chapter V the estimates of the previous chapter are used to prove expansion theorems for first order systems which are linear in the parameter; the boundary conditions are still allowed to depend polynomially on the parameter. Not only Birkhoff regularity is considered but also Stone regularity. Whereas all functions in Lp(a,b), 1 < p < 00, are expandable in eigenfunctions and associated functions if the problem is Birkhoff regular, the expandable functions must be sufficiently smooth and must satisfy certain auxiliary boundary conditions if the problem is Stone regular. Also uniform convergence is investigated, where even for Birkhoff regular problems the expandable functions have to satisfy certain regularity con­ditions and some boundary conditions.

Chapter VI is concerned with n-th order differential equations. Here the cor­responding results of Chapter III are obtained for an n-th order differential equa­tion, where also the equivalence of this problem to one for a first order system is established.

Chapter VII deals with boundary value problems for differential equations whose equivalent first order system can be linearized asymptotically. Using the estimates of Chapter IV, expansion theorems are proved.

Chapter VIII is concerned with regular two-point boundary eigenvalue prob­lems for the differential equation , where K and H are differential operators such that K is of higher order than H. The structures of the fundamen­tal system, its adjoint, and the Green's function are investigated more thoroughly. However, the estimates of Chapter IV can still be used. Some applications to problems from mechanics are given, to which the results of Chapter VII are not directly applicable.

In Chapter IX problems depending polynomially on the eigenvalue parameter A are linearized with respect to A. The corresponding convergence theorems for first order systems lead to n-fold expansions for the original problem. Complete­ness and minimality for these problems are considered.

Chapter X contains further examples dealing with problems from mechanics like elastic bars and control of beams, fluid mechanics, magnetohydrodynamics, and meteorology.

Appendix A deals with estimates of exponential sums. They are needed for the estimate of the characteristic determinant in Chapter IV.  

Precalculus

Precalculus, Second Edition by Robert F. Blitzer (Prentice Hall)  is designed and written to help students make the transition into calculus. The book has three fundamental goals:

To help students acquire a solid foundation in algebra and trigonometry, preparing them for calculus; To show students how algebra and trigonometry can model and solve authentic real-world problems; To enable students to develop problem-solving skills, fostering critical thinking within a varied and interesting setting.

Precalculus is not simply a condensed version of my Algebra and Trigonometry book. Precalculus students are different from algebra and trigonometry students, and this text reflects those differences. Here are a few specific examples:

Factorizations involving fractional and negative exponents, as well as simplifying the kinds of fractional expressions that students encounter in calculus, have been added to Chapter P. Chapter 1 includes applications that are traditional calculus problems and that can be approached algebraically. Chapter 2 includes discussions of difference quotients, average rate of change, average velocity, and composite functions in calculus. Chapter 3 introduces an optimization strategy for solving word problems within the context of quadratic functions. Students will be able to use this strategy in calculus when solving similar problems with the derivative. Chapter 5 develops trigonometry from the perspective of the unit circle. Liberal arts applications are often replaced by more scientific applications. For example, Einstein's relativity models are discussed in Chapter 1, and Newton 's Law of Cooling is developed in Chapter 4. Chapter 12, entitled "Introduction to Calculus," takes the student into calculus with discussions of limits, continuity, and derivatives.

A source of frustration for me and my colleagues is that very few students read their textbook. When I ask students why they do not take full advantage of the text, their responses generally fall into two categories:

"I cannot follow the explanations." "The applications are not interesting."

I thought about both of these objections in writing every page of this book.

"I can't follow the explanations." For many of my students, textbook explanations are too compressed. The chapters in Precalculus have been written to make them extremely accessible. Every section contains a range of simple, intermediate, and challenging examples. Voice balloons allow for specific annotations in examples, further clarifying procedures and concepts.

"The applications are not interesting." One of the things I enjoy most about teaching in a large urban community college is the diversity of who my students; are and what interests them. Real-world data that celebrate this variety are used to bring relevance to examples, discussions, and applications. I selected all updated real-world data to be interesting and intriguing to students. By connecting; precalculus to the whole spectrum of their interests, it is my intent to show students that their world is profoundly mathematical and, indeed, pi is in the sky. Student Supplements

Student Solutions Manual (0-13-028654-0); (2865D-2). Includes fully worked out. solutions to most of the odd-numbered exercises in the text as well as all exercises in chapter tests and all review exercises.

MathPak Integrated Learning Environment (0-13-028247-2); (28246-5). Contains the College Algebra MathPro 4.0 along with a passcode-protected Website: specifically designed to accompany this text. This product combines the series' key' supplements into a comprehensive, easy-to-navigate package. Materials on the Website include but are not limited to: Section-bysection reading quizzes, Section-by-Section Powerpoint downloads, additional chapter projects, Chapter Quizzes and Tests, Student Solutions Manuals presented by chapter (exactly what is in the print version), Chapter Destinations and to interesting math Websites, and Graphing Calculator Manuals for the full line of TI's, Sharp, HP, and Casio Calculators.

Review Videos (0-13-028240-5); (2824K-6). Section-by-section videos written by and highlighting Jacquelyn White of St. Leo College . Each segment covers approximately 20 minutes of the key concepts and examples for each section. Each set of videos comes with a permissions letter allowing the school to duplicate for specific campus needs.

Precalculus Investigations/Simundza, et. (0-13-010954-1); (1095D-6). A three year NSFfunded project integrates an applied approach to the topics in the Precalculus curriculum via applied projects. The investigations reflect the AMATYC and NCTM Standards in both curriculum content and pedagogy.

Companion Website (prenhall/blitzer). This CW address will lead to the bridge page for all of the Blitzer titles. On the CW sites (which are different than the MathPak sites) are the following: Chapter Quizzes, Chapter Tests, Projects, Graphing Calculator Manual, Destinations, and PowerPoints.

WebCT/Blackboard. Contains all the materials from the MathPak website (i.e., no MathPro) plus testing materials. Can be made available in Blackboard on adoption. Instructor Supplements

Instructor's Resource Manual (0-13-028656-7) (2865F-7). IRM contains the full solutions to the even-numbered exercises in the text.

TestGen-EQ WIN/MAC CD (0-13-028249-9) (2824J-8). New to Prentice Hall Mathematics is the use of TestGen EQ for our mathematics testing. TestGen-EQ is a fully algorithmic, easy-to-use software program written and based on the section objectives in the text.

Test Item File (0-13-028676-1) (2867F-5). A hard copy version of materials derived from the TestGen-EQ program. To the Student

I've written this book so that you can learn about the power of algebra and trigonometry and how it relates directly to your life outside the classroom. All

concepts are carefully explained, important definitions and procedures are set off in boxes, and worked-out examples that present solutions in a step-by-step manner appear in every section. Each example is followed by a similar matched problem, called a Check Point, for you to try so that you can actively participate in the learning process as you read the book. (Answers to all Check Points appear in the back of the book.) Study Tips offer hints and suggestions and often point out common errors to avoid. A great deal of attention has been given to applying algebra and trigonometry to your life to make your learning experience both interesting and relevant. As you begin your studies, I would like to offer some specific suggestions for using this book and for being successful in this course:

Attend all lectures. No book is intended to be a substitute for valuable insights and interactions that occur in the classroom. In addition to arriving for lecture on time and being prepared, you will find it useful to read the section before it is covered in lecture. This will give you a clear idea of the new material that will be discussed. Read the book. Read each section with pen (or pencil) in hand. Move through the illustrative examples with great care. These worked-out examples provide a model for doing exercises in the exercise sets. As you proceed through the reading, do not give up if you do not understand every single word. Things will become clearer as you read on and see how various procedures are applied to specific worked-out examples. Work problems every day and check your answers. The way to learn mathematics is by doing mathematics, which means working the Check Points and assigned exercises in the exercise sets. The more exercises you work, the better you will understand the material. Prepare for chapter exams. After completing a chapter, study the summary, work the exercises in the Chapter Review, and work the exercises in the Chapter Test. Answers to all these exercises are given in the back of the book. Use the supplements available with this book. A solutions manual containing worked-out solutions to the book's odd-numbered exercises and all review exercises, a dynamic web page, and video tapes created for every section of the book are among the supplements created to help you tap into the power of mathematics. Ask your instructor or bookstore what supplements are available and where you can find them.

It is my hope that that you will enjoy the pages of this book as you empower yourself with the algebra and trigonometry needed to succeed in calculus, your career, and in your life.

A Graphical Approach to Precalculus, Third Edition by John Hornsby, Margaret L. Lial, Gary K. Rockswold (Addison-Wesley) The third edition of this text reflects our ongoing commitment to teaching precalculus mathematics using graphing technology. Our journey began in 1993 when initial drafts of the first edition were developed and class-tested at the University of New Orleans . Two editions and some 10 years later, we remain true to our approach, based on the premise that students use graphing calculators from the first day of class throughout the course. In this third edition, we have polished presentations, developed new fea­tures, added an attractive design, and incorporated many helpful suggestions, com­ments, and ideas from both instructors and students. Gary Rockswold joins us as co-author-we are pleased to add his expertise with applications and the benefits of his classroom teaching experience.

Our Approach

It is our desire that these books provide instructors with the best possible methods of teaching with a graphing calculator and students with the easiest way to make con­nections between graphs of functions and their associated equations and inequalities. Using linear functions as the basis of the presentation in Chapter 1, we introduce a four-step process for the study of functions in subsequent chapters. After introducing a class of function:

• We first examine the nature of its graph.

• Next we solve equations analytically and use graphing calculators to find and support solutions using the x-intercept method or the intersection-of-graphs method.

• We then solve the associated inequalities analytically and graphically.

• Finally, we apply analytic and graphical methods to modeling and traditional applications.

By using this unifying approach consistently with each class of function, we hope that students will better understand, connect, and ultimately apply concepts and skills.

Because technology is ever-changing, we have not in the past nor do we try in this edition to teach students how to use specific models of graphing calculators. Unlike many texts that use artistic renderings of calculator screens, we use actual graphing calculator screens that can be duplicated using the Texas Instruments TI-83 Plus graphing calculator. In addition, the Graphing Calculator Manual that accompanies the text provides students with keystroke operations for many of the more popular models of graphing calculators.

Content Changes

We have worked hard to fine-tune and polish presentations of topics throughout the text based on user and reviewer feedback. Some of the content changes you may notice include the following:

• Chapter 1 has been streamlined and reorganized for improved continuity.

• The material on graphs of rational functions in Chapter 4 is now covered in two sections.

• Power functions are included in Section 4.4.

• Inverse functions, previously covered in Chapter 4, have been moved to Chapter 5.

• Harmonic motion is covered in new Section 8.8.

• Sum and difference identities are covered in Section 9.2, and Section 9.3 includes double-number and half-number identities as well as new coverage of product-to­sum and sum-to-product identities.

• Parametric equations with trigonometric functions and applications of parametricequations are presented in new Section 10.7.

• Three new appendices on vectors in space, polar form of conic sections, and rotation of axes are included at the back of the text.

New and Enhanced Features

We believe students and instructors will welcome the following new and enhanced features.

Function Capsules This special feature provides a comprehensive, visual introduc­tion to each class of function and also serves as an excellent resource for student ref­erence and review throughout the course. Each function capsule includes traditional and calculator graphs and a calculator table of values, as well as the domain, range, and other specific information about the function. Abbreviated versions of all function capsules are given on the inside back cover of the text.

New Real-Life Applications We have provided many new or updated applied prob­lems that focus on real-life applications of mathematics. Since today's students are more visually oriented than ever, new photos and additional figures, diagrams, and tables have been included to enhance applications in examples and exercises. All ap­plications are titled, and an Index of Applications is included at the back of the text.

Increased Emphasis on Modeling Many of the new applications feature mathe­matical models based on real data or real data in table form, thereby providing students with increased opportunities to use, construct, and analyze models. Curve fit­ting using linear, quadratic, polynomial, exponential, logarithmic, and trigonometric models is also covered.

Dual Solution Format To connect analytic methods for solving problems with graphical methods of solution or support, selected examples now provide a graphing calculator solution alongside the traditional analytic solution. The side-by-side format visually unifies the two solution methods for students.

What Went Wrong? Using graphing technology to study mathematics opens up a whole new area of error analysis. In anticipation of typical errors, this popular feature from previous editions allows students and instructors to discuss such errors. Answers are now included. (We still do not know the name of the reviewer who suggested this feature several years ago. To this person, we say thank you. Please contact us if you are reading this.)

Multivariable Mathematics, Fourth Edition by Richard E. Williamson, Hale F. Trotter (Prentice Hall) explores the standard problem-solving techniques of multivariable mathematics — integrating vector algebra ideas with multivariable calculus and differential equations. Unique coverage including, the introduction of vector geometry and matrix algrebra, the early introduction of the gradient vector as the key to differentiability, optional numerical methods. For any reader interested in learning more about this discipline. Intended for courses in second-year calculus, linear calculus and differential equations, this text explores the standard problem-solving techniques of multivariable mathematics - integrating vector algebra ideas with multivariable calculus and differential equations. A textbook for a course in basic calculus, vector calculus, or differential equations, depending on what material is used and in what order. Covers the algebra and geometry of vectors and matrices, multivariable and vector calculus, and differential equations including systems. Emphasizes basic problem solving in pure and applied contexts; and encourages geometric thinking in two, three, and arbitrary dimensions. Assumes a previous first course in one-variable calculus.

Calculus

Thomas' Calculus, Early Transcendentals Updated 10th  Edition by Ross L. Finney (Addison Wesley) Throughout its illustrious history, Thomas' Calculus has been used to support a va­riety of courses and teaching methods, from traditional to experimental. This tenth edition is a substantial revision, yet it retains the traditional strengths of the text: sound mathematics, relevant and important applications to the sciences and engi­neering, and excellent exercises. This flexible and modern text contains all the ele­ments needed to teach the many different kinds of courses that exist today.

A book does not make a course; the instructor and the students do. This text is a resource to support your course. With this in mind, we have added a number of fea­tures to the tenth edition making it even more flexible and useful, both for teaching and learning calculus.

Features of the Tenth Edition: For the first time, this classic text is available in both standard and Early Transcendentals versions. The new Annotated Instructor's Edition contains suggestions for the incor­poration of technology, highlighting how the Web site and CD-ROM can be used to enhance the presentation of chapter topics.             As always, this text continues to be easy to read, conversational, and mathe­matically rich. Each new topic is motivated by clear, easy-to-understand ex­amples and is then reinforced by its application to real-world problems of immediate interest to students. Each section now begins with a list of subsection headings, making key concept readily apparent. Within the tenth edition is an increased emphasis on modeling and applica­tions using real data. As a result, there is an improved balance of graphical, numerical, and analytic methods and techniques, accomplished without compromising the mathematical integrity of the book. Vectors and projectile motion in the plane are now covered separately from vectors in space, concluding the treatment of single-variable calcu­lus. Three-dimensional vectors are then treated in conjunction with multivariable calculus. Exercise sets continue to be grouped within appropriate headings. Titles that indicate the content or application have been added for most word problems, and those requiring the use of a graphing utility are identified throughout the text by the icon ©. Computer Algebra System (CAS) exercises also appear in every chapter and are grouped in special subsections labeled "Computer Explorations." Together, the CD-ROM and Web site provide students and instructors with even more support: A collection of Maple® and Mathematica® modules, videos, and Java applets are available to help students visualize key calculus concepts. - Interactive online tutorials help students review precalculus and text­ book-specific material, take practice tests, and receive diagnostic feedback on their performance. Chapter-by-chapter quizzes are also provided. These quizzes can be administered and graded online for skills-based mastery assessment. - Downloadable technology resources are provided for specific com­puter algebra systems and graphing calculators. Expanded historical biographies are now on the Web site and CD­-ROM, leaving more room in the margin of the text for notes, obser­vations, and annotations and giving the book a more open look.

With all these changes, the authors have not compromised their belief that the funda­mental goal of calculus is helping prepare students to enter the worlds of mathemat­ics, science, and engineering.

Highlights of New Content Features, by Chapter:

Preliminaries:    All the familiar precalculus functions are covered completely. Parametric equations are introduced. Inverses of familiar functions, including inverse trigonometric functions, are also covered. Mathematical modeling, with modeling exercises, is introduced. New examples and exercises employ real data and regression analysis using a calculator.

Chapter 1 Limits and Continuity: Limits are introduced by way of rates of change, with a concluding section on tangent lines to connect and complete the initial discussion. All the fundamental ideas on limits are now together in a single chapter, including finite limits, infinite limits, asymp­totes, and limit rules.

Both informal and precise definitions of the limit concept are given, but there is less emphasis on using the precise de­finition to prove theorems.

Chapter 2 Derivatives: The derivative as a rate of change is presented earlier to stress its importance in studying motion along a line in mod­eling real-world phenomena. Differentiation rules are presented in two sections to enhance the clarity and flow of the presentation. First and second derivatives for parametric equations are included as an application of the Chain Rule. The Early Transcendentals version of this Chapter differs from the standard edition in that it has two additional se­tions, the first devoted to the derivatives of inverse trigonometric functions, and the second to derivatives of exponen­tial and logarithmic functions.     With exponential and logarithmic functions now available, we study exponential change and verify the derivative power rule for arbitrary real powers.

Chapter 3 Applications of Derivatives: The availability of the derivatives of inverse trigonometric, exponential, and logarithmic functions enriches the exam­ples, exercises, and applications in this chapter. The treatment of using the first and second derivatives to determine the shape of a graph is more focused and streamlined. A new section on using the first and second derivative to produce graphical solutions to autonomous first-order differ­ential equations acts as a graphical prelude to Chapters 4 and 6. The new section includes an introduction to population modeling.

Chapter 4 Integration: As before, indefinite integrals are presented first, stressing their importance for solving elementary differential equa­tions. The rules for antiderivatives and the substitution method follow next. The list of available integrable funtions now includes exponential functions and functions leading to logarithmic and inverse trigonometric functions. We no longer have to wait until Chapter 6, as in the standard edition, to integrate the tangent and cotangent functions. As in the previous edition, estimating with finite sums in a variety of application settings motivates the ideas of Rie­mann sums and definite integrals. Students see the definite integral early as more than just a tool for finding area. The section defining the definite integral as a limit of Riemann sums has been streamlined and now focuses on contin­uous functions. Piecewise-continuous functions are treated in the Additional Exercises at the end of the chapter. All the material on single integral area calculations (including areas between curves) is now treated in this chapter.

Chapter 5 Applications of Integrals: The treatment of volumes has been combined from three into two sections. Arc length formulas are developed for both explicit function and parametric curves in the plane. Surface area has been moved to Chapter 13, where it is needed for surface integrals. There, it is treated in a unified fashion rather than as a special case of surfaces of revolution. The availability of exponential and logarithmic functions makes it possible to treat applications of separable first-order dif­ferential equations here instead of waiting until the next chapter as in the standard edition. Among the applications are mod­eling growth and decay, heat transfer, falling with resistance proportional to velocity, coasting to a stop, and torricelli's law. The important applications to springs, pumping and lifting, fluid forces, and moments have all been retained from the previous edition.

Chapter 6 Transcendental Functions and Differential Equations: With so much of the standard material on transcendental functions now in earlier chapters, this chapter is considerably shorter than its standard-edition counterpart. It still begins with defining the natural logarithm as an integral, however, then defining the natural exponential function as its inverse and reconfirming the laws and differentiation rules derived at the end of Chapter 2.  Linear first-order differential equations follow, modeling mixture problems and RL circuits. Euler's method and the improved Euler's method are combined with additional material on population models, illustrating graphical, numerical, and analytic solution methods. This chapter concludes with a short treatment of hyperbolic and inverse hyperbolic functions.

Chapter 7 Integration Techniques, L'Hopital's Rule, and Improper Integrals: Monte Carlo integration is now included with the use of integral tables or computer algebra systems (CAS) to find integrals. L'Hopital's Rule is covered in this chapter just prior to its use for calculating some improper integrals and limits of se­quences (in Chapter 8).

Chapter 8 Infinite Series: The basic ideas concerning sequences of numbers and their limits are covered in the first section. The next section, which is optional, treats the more theoretical ideas involving subsequences and bounded monotonic sequences. Most of the important series convergence tests are presented together in a single, streamlined section. Two new optional sections at the end of the chapter cover the basics of Fourier series. This inclusion allows for an ear­lier introduction to these important concepts for students requiring their use right away in their applied science and en­gineering courses. Completing the elementary introduction to series, these sections illustrate important representations of functions by series other than power series.

Chapter 9 Vectors in the Plane and Polar Functions: This is a new chapter on vectors and projectile motion in the plane, with two sections at the end covering polar coordi­nates and graphs and the calculus of polar curves to prepare students for their use in multivariable calculus. It permits an earlier self-contained treatment of planar vectors, if desired. The chapter can be covered any time after the cover­age of the integral and the calculus of exponential and logarithmic functions. Chapters 7 through 9 now form a complete package treating the ideas of single variable calculus. Three-dimensional vectors are presented independently along with multivariable calculus, beginning in Chapter 10. Vector ideas are motivated by their application to studying paths, velocities, accelerations, and forces associated with bodies moving along planar paths. The detailed analytic geometry of conic sections and quadratic equations has been eliminated. These ideas are thor­oughly covered in high school and precalculus courses, but we nevertheless review many of the basics throughout the text as needed. Parametrizations of plane curves has been moved to earlier chapters.

Chapter 10 Vectors and Motion in Space: Three-dimensional vectors, the geometry of space, and vector-valued functions defining space curves are now orga­nized together in this single chapter with fresh introductions and examples. This chapter now constitutes, and clearly delineates, the entry point for the multivariable calculus. Letters representing vectors have been changed from uppercase letters to the now more standard lowercase letters. Vectors in the plane are reviewed along with the development of the algebra and geometry of three-dimensional vec­tors to help students bridge any possible gap between Calculus H and Calculus III courses. The logical treatment and organization of motion along space curves and the TNB frame has been retained from the previous edition.

Chapter 11 Multivariable Functions and Their Derivatives: The chapter has been reorganized to improve efficiency and flow. The treatment of partial derivatives with constrained variables has been moved toward the end of the chapter to follow the introduction to Lagrange multipliers. The treat­ment of linearization and differentials now follows the treatment of directional derivatives, gradient vectors, and tan­gent planes. The treatment of gradients and tangent planes is shorter and more direct. A new introduction to extreme values and saddle points compares and contrasts the multivariable case with the single ­variable case. The exercise sets have been streamlined and all applications exercises labeled for quick identification.

Chapter 12 Multiple Integrals: The treatment of the calculation of masses, moments, and centers of mass with multiple integrals is now self­-contained. It no longer assumes previous exposure to the single-integral calculations in Chapter 5, which may now be bypassed entirely. Again, the practice of titling exercises makes them noticeably easier to select than before.

Chapter 13 Integration in Vector Fields:  In the treatment of Green's Theorem in the plane, circulation density at a point is introduced as the k-component of a more general circulation vector called the curl, which is treated in detail in the later section on Stokes' Theorem. This arrangement resolves the apparent inconsistency of having circulation in the plane represented by a scalar while circu­lation in space is represented by a vector.  

Brief Calculus and Its Applications, 10th Edition by Larry J. Goldstein, David I. Schneider, David C. Lay (Prentice Hall) We have been very pleased with the enthusiastic response to the first nine editions of Calculus 6 Its Applications by teachers and students alike. The present work incorporates many of the suggestions they have put forward.

Although there are many changes, we have preserved the approach and the flavor. Our goals remain the same: to begin the calculus as soon as possible; to present calculus in an intuitive yet intellectually satisfying way; and to illus­trate the many applications of calculus to the biological, social, and management sciences.

The distinctive order of topics has proven over the years to be successful  easier for students to learn, and more interesting because students see significant applications early. For instance, the derivative is explained geometrically before the analytic material on limits is presented. To reach the applications in Chapter 2 quickly, we present only the differentiation rules and the curve sketching needed for those applications. Advanced topics come later when they are needed. Other aspects of this student-oriented approach follow below.

Applications

We provide realistic applications that illustrate the uses of calculus in other disciplines. See the Index of Applications on the inside cover. Wherever possible, we have attempted to use applications to motivate the mathematics.

The text includes many more worked examples than is customary. Furthermore, we have included computational details to enhance readability.

The exercises comprise about one-quarter of the text-the most important part of the text in our opinion. The exercises at the ends of the sections are usually arranged in the order in which the text proceeds, so that the homework assign­ments may easily be made after only part of a section is discussed. Interesting applications and more challenging problems tend to be located near the ends of the exercise sets. Supplementary exercises at the end of each chapter expand the other exercise sets and include problems that require skills from earlier chapters.

The practice problems have proven to be a popular and useful feature. Practice Problems are carefully selected questions located at the end of each section, just before the exercise set. Complete solutions are given following the exercise set. The practice problems often focus on points that are potentially confusing or are likely to be overlooked. We recommend that the reader work the practice problems and study their solutions before moving on to the exercises. In effect, the practice problems constitute a built-in workbook.

In Chapter 0, we review those concepts that the reader needs to study calculus. Some important topics, such as the laws of exponents, are reviewed again when they are used in a later chapter. Section 0.6 prepares students for applies problems that appear throughout the text. A reader familiar with the content of Chapter 0 should begin with Chapter 1 and use Chapter 0 as a reference whenever needed.

New in this Edition

Among the many changes in this edition, the following are the most significant:

1. Additional Exercises. We have added and revised about 400 exercises. Many new exercises from business, medicine, life and social sciences, are based on current real-world data. At the beginning of more challenging sections, such as Section 2.6, we added straightforward exercises, designed to aid students with limited math background. We also added more exercises with figures. These exercises challenge the students' ability to read graphs and examine their grasp of fundamental concepts such as rates of change, the chain rule, and areas under a graph. We introduced a new genre of problems designed to test the students' understanding of mathematical formulas and abstract concepts (see for example, Sec. 3.1, # 39-44, Sec. 3.2 #21-26, and # 61-64.).

2. Additional Art. We have added many new graphs to enhance examples and exercises. We also added new graphs in more challenging sections to help visualize solutions of optimization problems (Section 2.6), and understand more difficult concepts such as elasticity of demand (Section 5.3).

3. Revision of some sections.

a. The topics of Section 2.6 have been reordered and a detailed example and figures were added to allow an easier access to the inventory control problem from business.

b. Worked examples and figures were added to Section 5.3 to provide a clearer and more accessible discussion of the topic of elasticity of demand from economics.

c. The topics of Section 7.6 on nonlinear regression have been reordered. The Pareto distribution is used as an example of a power regression function to model the distribution of income of the U.S. male population in 2001. Deductions from this model are compared to actual statistical data.

This edition contains more material than can be covered in most two-semester courses. Optional sections are starred in the table of contents. In addition, the level of theoretical material may be adjusted to the needs of the students. For instance, only the first two pages of Section 1.4 are required in order to introduce the limit notation.

A Study Guide for students containing detailed explanations and solutions for every sixth exercise is available. The Study Guide also includes helpful hints and strategies for studying that will help students improve their performance in the course. In addition, the Study Guide contains a copy of Visual Calculus, the popular, easy-to-use software for IBM compatible computers. Visual Calculus contains over 20 routines that provide additional insights into the topics discussed in the text. Also, instructors find the software valuable for constructing graphs for exams.  

Calculus and Its Applications, 10th Edition by Larry J. Goldstein, David I. Schneider, David C. Lay (Prentice Hall) Among the many changes in this edition, the following are the most significant:

1. Additional Exercises. We have added and revised over 400 exercises. These include 90 new problems on differential equations and their applications. Many new exercises from business, medicine, life and social sciences, are based on current real-world data. At the beginning of more challenging sections, such as Section 2.6, we added straightforward exercises, designed to aid students with limited math background. We also added more exercises with figures. These exercises challenge the students' ability to read graphs and examine their grasp of fundamental concepts such as rates of change, the chain rule, and areas under a graph. We introduced a new genre of problems designed to test the students' understanding of mathematical formulas and abstract concepts (see for example, Sec. 3.1, # 39-44, Sec. 3.2 #21-26, and # 61-64.).

2. Additional Art. We have added over 80 new graphs to enhance examples and exercises. We also added new graphs in more challenging sections to help visualize solutions of optimization problems (Section 2.6), and understand more difficult concepts such as elasticity of demand (Section 5.3).

3. Revision of some sections.  

a. The topics of Section 2.6 have been reordered and a detailed example and figures were added to allow an easier access to the inventory control problem from business.  

b. Worked examples and figures were added to Section 5.3 to provide a clearer and more accessible discussion of the topic of elasticity of demand from economics.

c. The topics of Section 7.6 on nonlinear regression have been reordered. The Pareto distribution is used as an example of a power regression function to model the distribution of income of the U.S. male population in 2001. Deductions from this model are compared to actual statistical data.  

d. Section 10.1 now includes the topic of slope fields and the geometric in­terpretation of a differential equation. The section emphasizes a graphical approach to differential equations and their real-life applications.  

e. Section 10.3 on numerical solutions of differential equations is now Section 10.7, at the end of Chapter 10.

4. Two new sections on differential equations.

a. Section 10.3 contains several worked examples and figures that provide a smooth and very accessible presentation of the technique of integrating factor for solving first-order linear differential equations. This section contains 40 exercises that vary in difficulty from straightforward to more challenging.

b. Section 10.4 presents useful real-life applications, including investment accounts, paying off car loans, home mortgages, Newton's law of cooling, population models with migration, along with problems from medicine that include kidney dialysis, determining the therapeutic level of drugs, and studying morphine infusions. Most applications are based on real data. Over 30 examples and exercises are carefully crafted to teach mod­eling techniques in addition to solving differential equations. Many prob­lems stress the use of differential equations to study their solutions.

This edition contains more material than can be covered in most two-semester courses. Optional sections are starred in the table of contents. In addition, the level of theoretical material may be adjusted to the needs of the students. For instance, only the first two pages of Section 1.4 are required in order to introduce the limit notation.

A Study Guide for students containing detailed explanations and solutions for every sixth exercise is available. The Study Guide also includes helpful hints and strategies for studying that will help students improve their performance in the course. In addition, the Study Guide contains a copy of Visual Calculus, the popular, easy-to-use software for IBM compatible computers. Visual Calculus contains over 20 routines that provide additional insights into the topics discussed in the text. Also, instructors find the software valuable for constructing graphs for exams.

An Instructor's Solutions Manual contains worked solutions to every exercise. TestGen provides nearly 1000 suggested test questions, keyed to chapter and section. TestGen is a text-specific testing program networkable for administering tests and capturing grades online. Edit and add your own questions, or use the new "Function Plotter" to create a nearly unlimited number of tests and drill worksheets.

Designed to complement and expand upon the text, the text Web site of­fers a variety of interactive teaching and learning tools. Since many of the text projects use real-life data, we made the data easier to use by making it avail­able in Excel spreadsheets on the Web site. The Web site also includes links to related Web sites, quizzes, Syllabus Builder, and more. For more information, visit www. prenhall. com/goldstein or contact your local Prentice Hall representative.

Calculus for Biology and Medicine, Second Edition by Claudia Neuhauser (Prentice Hall) teaches calculus in the biology context without compromising the level of regular calculus. The material is organized in the standard way and explains how the different concepts are logically related. Each new concept is typically introduced with a biological example; the concept is then developed without the biological context and then the concept is tied into additional biological examples. This allows readers to first see why a certain concept is important, then lets them focus on how to use the concepts without getting distracted by applications, and then, once readers feel more comfortable with the concepts, it revisits the biological applications to make sure that they can apply the concepts. The book features exceptionally detailed, step-by-step, worked-out examples and a variety of problems, including an unusually large number of word problems. The volume begins with a preview and review and moves into discrete time models, sequences, and difference equations, limits and continuity, differentiation, applications of differentiation, integration techniques and computational methods, differential equations, linear algebra and analytic geometry, multivariable calculus, systems of differential equations and probability and statistics.

Differential Analysis

The Theory of Differential Equations: Classical & Qualitative by Walter Kelley, Allan Peterson (Prentice Hall) Differential equations first appeared in the late seventeenth century in the work of Isaac Newton, Gottfried Wilhelm Leibniz, and the Bernoulli broth­ers, Jakob and Johann. They occurred as a natural consequence of the efforts of these great scientists to apply the new ideas of the calculus to certain problems in mechanics, such as the paths of motion of celestial bod­ies and the brachistochrone problem, which asks along which path from point P to point Q a frictionless object would descend in the least time. For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. Their importance has motivated generations of mathematicians and other scien­tists to develop methods of studying properties of their solutions, ranging from the early techniques of finding exact solutions in terms of elementary functions to modern methods of analytic and numerical approximation. Moreover, they have played a central role in the development of mathe­matics itself since questions about differential equations have spawned new areas of mathematics and advances in analysis, topology, algebra, and ge­ometry have often offered new perspectives for differential equations.

This book provides an introduction to many of the important topics associated with ordinary differential equations. The material in the first six chapters is accessible to readers who are familiar with the basics of cal­culus, while some undergraduate analysis is needed for the more theoretical subjects covered in the final two chapters. The needed concepts from linear algebra are introduced with examples, as needed. Previous experience with differential equations is helpful but not required. Consequently, this book can be used either for a second course in ordinary differential equations or as an introductory course for well-prepared students.

The first chapter contains some basic concepts and solution methods that will be used throughout the book. Since the discussion is limited to first-order equations, the ideas can be presented in a geometrically simple setting. For example, dynamics for a first-order equation can be described in a one-dimensional space. Many essential topics make an appearance here: existence, uniqueness, intervals of existence, variation of parame­ters, equilibria, stability, phase space, and bifurcations. Since proofs of existence-uniqueness theorems tend to be quite technical, they are reserved for the last chapter.

Systems of linear equations are the major topic of the second chapter. An unusual feature is the use of the Putzer algorithm to provide a con­structive method for solving linear systems with constant coefficients. The study of stability for linear systems serves as a foundation for nonlinear systems in the next chapter. The important case of linear systems with periodic coefficients (Floquet theory) is included in this chapter.

Chapter 3, on autonomous systems, is really the heart of the subject and the foundation for studying differential equations from a dynamical viewpoint. The discussion of phase plane diagrams for two-dimensional systems contains many useful geometric ideas. Stability of equilibria is in­vestigated by both Liapunov's direct method and the method of lineariza­tion. The most important methods for studying limit cycles, the Poincare­Bendixson theorem and the Hopf bifurcation theorem, are included here. The chapter also contains a brief look at complicated behavior in three dimensions and at the use of Mathematica for graphing solutions of differ­ential equations. We give proofs of many of the results to illustrate why these methods work, but the more intricate verifications have been omitted in order to keep the chapter to a reasonable length and level of difficulty.

Perturbation methods, which are among the most powerful techniques for finding approximations of solutions of differential equations, are intro­duced in Chapter 4. The discussion includes singular perturbation prob­lems, an important topic that is usually not covered in undergraduate texts.

The next two chapters return to linear equations and present a rich mix of classical subjects, such as self-adjointness, disconjugacy, Green's functions, Riccati equations, and the calculus of variations.

Since many applications involve the values of a solution at different input values, boundary value problems are studied in Chapter 7. The contraction mapping theorem and continuity methods are used to examine issues of existence, uniqueness, and approximation of solutions of nonlinear boundary value problems.

The final chapter contains a thorough discussion of the theoretical ideas that provide a foundation for the subject of differential equations. Here we state and prove the classical theorems that answer the following questions about solutions of initial value problems: Under what conditions does a solution exist, is it unique, what type of domain does a solution have, and what changes occur in a solution if we vary the initial condition or the value of a parameter? This chapter is at a higher level than the first six chapters of the book.

There are many examples and exercises throughout the book. A sig­nificant number of these involve differential equations that arise in applica­tions to physics, biology, chemistry, engineering, and other areas. To avoid lengthy digressions, we have derived these equations from basic principles only in the simplest cases.

Harmonic Analysis

Classical and Modern Fourier Analysis by Loukas Grafakos (Prentice Hall) An ideal refresher or introduction to contemporary Fourier Analysis, this book starts from the beginning and assumes no specific background. Readers gain a solid foundation in basic concepts and rigorous mathematics through detailed, user-friendly explanations and worked-out examples, acquire deeper understanding by working through a variety of exercises, and broaden their applied perspective by reading about recent developments and advances in the subject. Features over 550 exercises with hints (ranging from simple calculations to challenging problems), illustrations, and a detailed proof of the Carleson-Hunt theorem on almost everywhere convergence of Fourier series and integrals of Lp functions—one of the most difficult and celebrated theorems in Fourier Analysis. A complete Appendix contains a variety of miscellaneous formulae. Lp Spaces and Interpolation. Maximal Functions, Fourier transforms, and Distributions. Fourier Analysis on the Torus. Singular Integrals of Convolution Type. Littlewood-Paley Theory and Multipliers. Smoothness and Function Spaces. BMO and Carleson Measures. Singular Integrals of Nonconvolution Type. Weighted Inequalities. Boundedness and Convergence of Fourier Integrals. For mathematicians interested in harmonic analysis.

The word analysis comes from the Greek, which means "dissolving into pieces." This is usually the first step of a process that leads to a careful study and understanding of an object or phenomenon. The antithetical process, called synthesis, is equally significant as it assembles the analyzed pieces after they have been individually examined. This procedure is the heart of Fourier analysis. Through its aorta, this heart disseminates information to a variety of applications. Fourier analysis is therefore a prism that diffracts ideas into a rainbow of uses and applications, making the subject one of the richest and most far-reaching in mathematics.

The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables.

The choice of the material in the text reflects a measure of personal taste; however, a certain effort has been made to include a variety of topics of general interest. Much attention is given to details, which are designed to facilitate the understanding of first-time readers. Based on my personal experience, I felt a need to include details related to topics that articles often omit, leaving beginners to struggle through without explanation. Although it will behoove many readers to skim through the more technical aspects of the presentation and concentrate on the flow of ideas, the mere fact that details are here for reference will be comforting to some. I hope that students will profit from this comprehensive presentation and learn how to do mathematics rigorously. Unfortunately, including so many details has led to the large size of the book. But as one's maturity and familiarity with the subject increases, topics slowly become natural and reading is significantly accelerated.

The exercises that follow each section enrich the material of the corresponding section and provide an opportunity to develop additional intuition 'and deeper com­prehension. Some of them are rather rudimentary and require minimal skill, while others are more interesting and challenging. Only a few exercises are considered difficult, but these are given with hints. A special effort has been made to prepare the exercises, which unfortunately did not double, but almost tripled, the amount of time and effort it took to complete this text. I hope that the reader will find this extra effort beneficial.

The historical notes given at the end of each chapter are intended to provide an accurate account of past research but also to suggest directions for further inves­tigation. This book was partly written with the purpose of attracting students to research. Many of the topics in Chapter 10 lead to open problems that have bewil­dered mathematicians for decades. It is hoped that many students will be fascinated by the easy statements, yet the delicate complexity of some of these problems, and pursue a deeper understanding.

The text is completely self-contained as the appendix includes the miscellaneous material needed throughout. Certain user-friendly conventions have been adopted to facilitate searching. For instance, theorems, propositions, definitions, lemmas, remarks, and examples are numbered according to the order in which they appear in each section. Exercises are numbered similarly and can be easily located.

As this book is intended for a three-course sequence on the subject, I would like to suggest a slowly paced initial breakdown of the material, flexible enough to accommodate adjustments: Semester I: Chapters 1, 2, 3, and 4. Semester II: Chapters 5, 6, 7, and 9. Semester III: Chapters 8, 10, and other topics. Sections or subsections marked by a star would normally be omitted in a yearly course.

I am solely responsible for any misprints, mistakes, and historical omissions in this book. Please contact me directly (loukas@math.missouri.edu) if you have any comments, suggestions, improvements, or corrections. Instructors are also wel­come to contact me to obtain further hints on the existing exercises in the text. Suggestions for other exercises are also welcome. A list of current errata with ac­knowledgements will be kept at the following URL: http://math.missouri.edu/~loukas/Fourier-Analysis  

Algebra

Algebra: A Combined Approach, 2nd edition by K. Elayn Martin-Gay (Prentice Hall) is intended for a two se­mester course in introductory and intermediate algebra. It was written to pro­vide a solid foundation in algebra for students who might have had no previous experience in algebra. Specific care was taken to ensure that students have the most up-to-date relevant text preparation for their next mathematics course or for nonmathematical courses that require an understanding of algebraic fundamentals. I have tried to achieve this by writing a user-friendly text that is keyed to objectives and contains many worked-out examples. As suggested by the AMATYC Crossroads Document and the NCTM Standards (plus Addenda), real-life and real-data applications, data interpretation, conceptu­al understanding, problem solving, writing, cooperative learning, appropriate use of technology, mental mathematics, number sense, critical thinking, and geometric concepts are emphasized and integrated throughout the book.

The many factors that contributed to the success of the first edition have been retained. In preparing the Second Edition, I considered comments and suggestions of colleagues, students, and many users of the prior edition throughout the country.

Algebra: A Combined Approach, 2nd edition is part of a series of texts that can include Basic College Mathematics, Second Edition; Prealgebra, Third Edition; Introductory Algebra, Second Edition; and Intermediate Algebra, Second Edition. Throughout the series pedagogical features are designed to develop student proficiency in algebra and problem solving, and to prepare students for future courses.

Experiencing Intermediate Algebra (2nd Edition) by Joanne Thomasson, Bob Pesut (Prentice Hall) continues to embrace the goal of promoting a new approach to teaching and learn­ing developmental mathematics. This approach combines a traditional model with the reform movements presented in the National Council of Teach­ers of Mathematics (NCTM) and American Mathematical Association of Two­Year Colleges (AMATYC) standards. The NCTM goals state that in our present technological society, students should learn to value mathematics, rea­son and communicate mathematically, become confident of their mathemat­ical abilities, and become mathematical problem solvers. The AMATYC standards for intellectual development state that students will model real­world situations, connect mathematics with other disciplines, and use appro­priate technology.

In this second edition, we have incorporated recommendations and suggestions from instructors and reviewers of the text. Instructors who currently use the text valued the real-world application feature and encouraged us to expand it. At the same time, they recommended that the text be streamlined to reduce its volume. The content of this edition is still organized by families of functions, according to the AMATYC standards. Consequently, the first five chapters, Chapters 0 through 4, focus on linear expressions, equations, and functions. Chapters 5 through 8 focus on polynomial expressions, equa­tions, and functions. Chapters 9 presents rational expressions, equations, and functions. Radical expressions, equations, and functions are discussed in Chapter 10. Chapter 11 features exponential and logarithmic expressions, equations, and functions.

We have streamlined the discussion of the complex number system that was formerly Chapter 1 and rewritten it as a review of the real-number system (prealgebra material), calling it Chapter 0. Imaginary numbers and the complex number system are now presented in Chapter 10 after the study.

In the previous edition, exponents and polynomials were presented together with factoring, all within one chapter. We have now separated this material into two chapters. The first of the two, Chapter 5, focuses on expo­nents and polynomial operations. We have added more material on polyno­mial division that presents polynomial long division in greater detail.

Feedback from reviewers indicated a need for expanding and strengthening the discussion of factoring, so, we have created a separate chapter on the subject, Chapter 7. In this chapter, we offer more examples, more exercises, and a different ordering of topics.

The first part of the text presents a balanced discussion of algebraic, numerical, and graphical methods for solving linear equations, so that stu­dents have a solid understanding of what the concepts represent. However, as we progress further into the second part, the emphasis increasingly focuses on algebraic methods. Numerical and graphical methods are used only for checking solutions rather than for obtaining solutions. This way of teaching the topics will strengthen the students' algebraic skills for their sub­sequent math courses.

The new feature in the second edition is the inclusion of a project at the end of each chapter. The project enriches the study of the material presented in the chapter and provides connections to other areas of mathematics and other disciplines. Students may be asked to research the history of mathe­matical topics, collect and interpret data for use in their mathematical modeling activities, and build on the applications they have studied. The Companion Web site provides support for those instructors who need to access data.  

Elementary Algebra Early Graphing, Second Edition by Allen R. Angel (Prentice Hall) An emphasis on the practical applications of algebra motivates readers and encourages them to see algebra as an important part of their daily lives. Strongly emphasizes good problem-solving skills, uses real-world applications. For anyone interested in Algebra.

This book was written for college students and other adults who have never been exposed to al­gebra or those who have been exposed but need a re­fresher course. My primary goal was to write a book that students can read, understand, and enjoy. To achieve this goal I have used short sentences, clear ex­planations, and many detailed, worked-out examples. I have tried to make the book relevant to college stu­dents by using practical applications of algebra throughout the text.

Features of the Text

Full-Color Format Color is used pedagogically in the following ways:

• Important definitions and procedures are color screened.

• Color screening or color type is used to make other important items stand out.

• Artwork is enhanced and clarified with use of mul­tiple colors.

• The full-color format allows for easy identification of important features by students.

• The full-color format makes the text more appeal­ing and interesting to students.

Readability One of the most important features of the text is its readability. The book is very readable, even for those with weak reading skills. Short, clear sentences are used and more easily recognized, and easy-to-understand language is used whenever possible.

Accuracy Accuracy in a mathematics text is essen­tial. To ensure accuracy in this book, mathematicians from around the country have read the pages careful­ly for typographical errors and have checked all the answers.

Connections Many of our students do not thor­oughly grasp new concepts the first time they are pre­sented. In this text we encourage students to make connections. That is, we introduce a concept, then later in the text briefly reintroduce it and build upon it.

Often an important concept is used in many sections of the text. Students are reminded where the material was seen before, or where it will be used again. This also serves to emphasize the importance of the concept. Im­portant concepts are also reinforced throughout the text in the Cumulative Review Exercises and Cumu­lative Review Tests.

Chapter Opening Application Each chapter begins with a real-life application related to the material cov­ered in the chapter. By the time students complete the chapter, they should have the knowledge to work the problem.

A Look Ahead This feature at the beginning of each chapter gives students a preview of the chapter and also indicates where this material will be used again in other chapters of the book. This material helps students see the connections between various topics in the book and the connection to real-world situations.

The Use of Icons At the beginning of each chapter and of each section, a variety of icons are illustrated. These icons are provided to tell students where they may be able to get extra help if needed. There are icons for the Student's Solution Manual, I; the Student's Study Guide, I ;CDs and videotapes, , ; Math Pro 4/5 Software, c ; the Prentice Hall Tutor Center, fib; and the Angel Website, . Each of these items will be discussed shortly.

Keyed Section Objectives Each section opens with a list of skills that the student should learn in that section. The objectives are then keyed to the appropriate portions of the sections with red numbers such as 1.

Problem Solving Polya's five-step problem-solving procedure is discussed in Section 1.2. Throughout the book problem solving and Polya's problem-solving pro­cedure are emphasized.

Practical Applications Practical applications of al­gebra are stressed throughout the text. Students need to learn how to translate application problems into algebraic symbols. The problem-solving approach used throughout this text gives students ample practice in setting up and solving application problems. The use of practical applications motivates students.

Detailed, Worked-Out Examples A wealth of examples have been worked out in a step-by-step, de­tailed manner. Important steps are highlighted in color, and no steps are omitted until after the student has seen a sufficient number of similar examples.

Now Try Exercise In each section, students are asked to work exercises that parallel the examples given in the text. These Now Try Exercises make the students active, rather than passive, learners and they reinforce the concepts as students work the exercises. Through these exercises students have the opportunity to im­mediately apply what they have learned. Now Try Ex­ercises are indicated in green type such as 35, in the exercise sets.

Study Skills Section Many students taking this course have poor study skills in mathematics. Section 1.1, the first section of this text, discusses the study skills need­ed to be successful in mathematics. This section should be very beneficial for your students and should help them to achieve success in mathematics.

Helpful Hints The Helpful Hint boxes offer useful suggestions for problem solving and other varied top­ics. They are set off in a special manner so that students will be sure to read them.

Helpful Hints-Study Tips This is a new feature.

These Helpful Hint-Study Tips boxes offer valuable information on items related to studying and learning the material.

Avoiding Common Errors Errors that students often make are illustrated. The reasons why certain proce­dures are wrong are explained, and the correct proce­dure for working the problem is illustrated. These Avoiding Common Errors boxes will help prevent your students from making those errors we see so often.

Mathematics in Action This new feature stresses the need for and the uses of mathematics in real-life situ­ations. Examples of the use of mathematics in many professions, and how we use mathematics daily without ever giving it much thought, are given. This can be a motivational feature for your students and can give them a better appreciation of mathematics.

Using Your Calculator The Using Your Calculator boxes, placed at appropriate locations in the text, are written to reinforce the algebraic topics presented in the section and to give the student pertinent informa­tion on using a scientific calculator to solve algebraic problems.

Using Your Graphing Calculator Using Your Graphing Calculator boxes are placed at appropriate loca­tions throughout the text. They reinforce the algebraic topics taught and sometimes offer alternate methods of working problems. This book is designed to give the instructor the option of using or not using a graphing calculator in his or her course. Some of the Using Your Graphing Calculator boxes contain graphing calculator exercises, whose answers appear in the answer section of the book. The illustrations shown in the Using Your Graphing Calculator boxes are from a Texas Instru­ments 83 Plus calculator. The Using Your Graphing Calculator boxes are written assuming that the student has no prior graphing calculator experience.  

The exercise sets are broken into three main categories: Concept/Writing Exercises, Practice the Skills, and Problem Solving. Many exercise sets also contain Chal­lenge Problems and/or Group Activities. Each exercise set is graded in difficulty. The early problems help de­velop the student's confidence, and then students are eased gradually into the more difficult problems. A suf­ficient number and variety of examples are given in each section for the student to successfully complete even the more difficult exercises. The number of exercises in each section is more than ample for student assignments and practice.

Concept/Writing Exercises Most exercise sets include exercises that require students to write out the answers in words. These exercises improve students' understanding and comprehension of the material. Many of these exercises involve problem solving and conceptualization and help develop better reasoning and critical thinking skills.

Problem Solving Exercises These exercises have been added to help students become better thinkers and prob­lem solvers. Many of these exercises involve real-life ap­plications of algebra. It is important for students to be able to apply what they learn to real-life situations. Many problem solving exercises help with this.

Challenge Problems These exercises, which are part of many exercise sets, provide a variety of problems. Many were written to stimulate student thinking.

Others provide additional applications of algebra or present material from future sections of the book so that students can see and learn the material on their own before it is covered in class. Others are more challenging than those in the regular exercise set.

Video Icon Exercises The exercises that are worked out in detail on the videotapes are marked with the video icon, ®. This will prove helpful for your students.

Cumulative Review Exercises All exercise sets (after the first two) contain questions from previous sections in the chapter and from previous chapters. These cumulative review exercises will reinforce top­ics that were previously covered and help students re­tain the earlier material, while they are learning the new material. For the students' benefit the Cumulative Review Exercises are keyed to the section where the material is covered, using brackets, such as [3.4].

Group Activities Many exercise sets have group ac­tivity exercises that lead to interesting group discus­sions. Many students learn well in a cooperative learning atmosphere, and these exercises will get stu­dents talking mathematics to one another.

Chapter Summary At the end of each chapter is a chapter summary that includes a glossary and impor­tant chapter facts.

Chapter Review Exercises At the end of each chap­ter are review exercises that cover all types of exercis­es presented in the chapter. The review exercises are keyed, using color numbers and brackets, to the sec­tions where the material was first introduced.

Chapter Practice Tests The comprehensive end-of­chapter practice test will enable the students to see how well they are prepared for the actual class test. The In­structor's Test Manual includes several forms of each chapter test that are similar to the student's practice test. Multiple choice tests are also included in the In­structor's Test Manual.

Cumulative Review Tests These tests, which appear at the end of each chapter after the first, test the stu­dents' knowledge of material from the beginning of the book to the end of that chapter. Students can use these tests for review, as well as for preparation for the final exam. These exams, like the cumulative review exercises, will serve to reinforce topics taught earlier. The answers to the Cumulative Review Test questions directly follow the test so that students can quickly check their work. After each answer, the section and objective numbers where that material was covered are given using brackets, such as.

Answers The odd answers are provided for the ex­ercise sets. All answers are provided for the Using Your Graphing Calculator Exercises, Cumulative Review Exercises, Review Exercises, Practice Tests, and Cu­mulative Review Tests. Answers are not provided for the Group Activity exercises since we want students to reach agreement by themselves on the answers to these exercises.

Recommendations of the Curriculum and Evaluation Standards for School Mathematics, prepared by the Na­tional Council of Teachers of Mathematics (NCTM), and Crossroads in Mathematics: Standards for Intro­ductory College Mathematics Before Calculus, prepared by the American Mathematical Association of Two Year Colleges (AMATYC), are incorporated into this edition.

Prerequisite

This text assumes no prior knowledge of algebra. How­ever, a working knowledge of arithmetic skills is im­portant. Fractions are reviewed early in the text, and decimals are reviewed in Appendix A.

Modes of Instruction

The format and readability of this book lends itself to many different modes of instruction. The constant re­inforcement of concepts will result in greater under­standing and retention of the material by your students.  

Changes in the Second Edition

When I wrote the second edition I considered many letters and reviews I got from students and faculty alike. I would like to thank all of you who made suggestions for improving the second edition. I would also like to thank the many instructors and students who wrote to inform me of how much they enjoyed, appreciated, and learned from the text. Some of the changes made in this edition of the text include:

Chapter 3, Formulas and Applications of Algebra, has been rewritten. Many of the exercises have been shortened and additional explanations have been added where necessary. Section 3.5 has been reor­ganized for greater clarity. The real-life application problems have been updated.

Addition and subtraction of fractions in Chapter 1 have been greatly enhanced.

Solving equations containing fractions is now intro­duced in Chapter 2. Many examples and exercises containing fractions were added.

There is expanded coverage of order of operations with nested parentheses.

The identity properties and inverse properties have been added to this edition.

The Pythagorean Theorem has been moved earlier at the request of many instructors.

Direct and Inverse Variation has been added as the last section in Chapter 8.

There is now an entire section dedicated to Appli­cations of Quadratic Equations.

A greater variety of exercises has been added to ex­ercise sets throughout the book. In general, the ex­ercise sets have been greatly enhanced.

There is more emphasis on geometry than in the previous edition. More sections have examples and exercises that relate to geometry.

In selected sections, more difficult exercises have been added at the end of exercise sets.

Rational numbers have been explained more com­pletely.

A brief introduction to complex numbers has been added to Chapter 10 for those instructors who wish to introduce this topic to their students.

The book has a new design with the purpose of mak­ing the exercise sets flow more smoothly so that ex­ercises will be easy to spot and identify.

The Cumulative Review Tests now have the answers directly following the test so that students can get immediate feedback. In addition, the section and objective numbers where the material was discussed are given after the answer.

A Look Ahead has replaced the Preview and Perspectives. The information provided gives students an overview of the chapter and how it relates to other material in the book and to real-life situations.

A new feature called Mathematics in Action has been added. This feature stresses the need for and the importance of mathematics in real life. This may be motivational for your students.

More and new Helpful Hints and Avoiding Com­mon Errors have been added where appropriate.

Helpful Hint-Study Tips have been added. These reinforce and expand upon the Study Skills for Suc­cess in Mathematics covered in Section 1.1.

Application problems throughout the book have been updated and made more interesting.

Using Your Graphing Calculator boxes now show keystrokes and screens from a Texas Instruments 83 Plus calculator.

A fraction raised to a negative exponent is covered more completely.

The balance bars have been removed from the ex­planations in Chapter 2.

When factoring by grouping, the common factor is now placed on the left for consistency with other factoring problems.

Perpendicular lines are now introduced in the text rather than in the exercise set.

Chapter 9, Roots and Radicals, has been rewritten and reorganized for greater clarity and understand­ing. The material also now flows more smoothly.

Variables other than x and y are used more often in examples and exercises.

More photos have been added to the text to make it more attractive and interesting for students.

The basic colors used in the text have been softened to make the text easier to read.

A brief introduction to metric units of measurement is now presented in the Scientific Notation section.

The format and readability of this book lends itself to many different modes of instruction. The constant reinforcement of concepts will result in greater understanding and retention of the material by your students.

Elementary and Intermediate Algebra, Second Edition by Allen R. Angel (Prentice Hall) The features of the text and the large variety of sup­plements available make this text suitable for many types of instructional modes including:

• lecture
• distance learning
• self-paced instruction
• modified lecture
• cooperative or group study
• learning laboratory

Changes in the Second Edition

When I wrote the second edition I considered many letters and reviews I got from students and faculty alike. I would like to thank all of you who made suggestions for improving the second edition. I would also like to thank the many instructors and students who wrote to inform me of how much they enjoyed, appreciated, and learned from the text. Some of the changes made in the second edition of the text include:

Chapter 3, Formulas and Applications of Algebra, has been rewritten. Many of the exercises have been shortened and additional explanations have been added where necessary. Section 3.5 has been reor­ganized for greater clarity. The real-life application problems have been updated.

Addition and subtraction of fractions in Chapter 1 have been greatly enhanced.

Solving equations containing fractions is now introduced in Chapter 2. Many examples and exercises containing fractions were added.

There is expanded coverage of order of operations with nested parentheses.

The identity properties and inverse properties have been added to this edition.

The Pythagorean Theorem has been moved earlier, to Chapter 6, at the request of many instructors.

There is now an entire section dedicated to Appli­cations of Quadratic Equations.

A greater variety of exercises has been added to ex­ercise sets throughout the book. In general, the exercise sets have been greatly enhanced.

There is more emphasis on geometry than in the previous edition. More sections have examples and exercises that relate to geometry.

In selected sections, more difficult exercises have been added at the end of exercise sets.

Rational numbers have been explained more completely.

Complementary and supplementary angles have been moved from the exercises into the body of the text.

Selected material in the Graphs and Functions chap­ter has been reorganized and rewritten for better understanding by students.

More concept/writing exercises have been added where appropriate.

More material on multiplication of radicals is provided.

The discussion of complex fractions more clearly in­dicates to students when it is advantageous to use each of the methods to simplify complex fractions.

Selected material in the Exponential and Logarithmic Functions chapter has been rewritten for greater clarity.

The basic characteristics of both exponential and log­arithmic graphs are now discussed more completely.

The chapter on Roots, Radicals, and Complex Num­bers has been reorganized and rewritten for greater clarity. The chapter now has a better flow of material.

The number of both examples and exercises in the Exponential and Logarithmic Functions chapter has been increased.

Material on finding the area of an ellipse has been added to the Conic Sections chapter.

Certain definitions in the Sequences, Series, and the Bi­nomial Theorem chapter have been rewritten for great­er clarity and for better understanding by students.

The book has a new design with the purpose of mak­ing the exercise sets flow more smoothly so that ex­ercises will be easy to spot and identify.

The Cumulative Review Tests now have the answers directly following the test so that students can get immediate feedback. In addition, the section and objective numbers where the material was discussed are given after the answer.

A Look Ahead has replaced the Preview and Perspectives. The information provided gives stu­dents an overview of the chapter and how it re­lates to other material in the book and to real-life situations.

A new feature called Mathematics in Action has been added. This feature stresses the need for and the importance of mathematics in real life. This may be motivational for your students.

More and new Helpful Hints and Avoiding Com­mon Errors have been added where appropriate.

Helpful Hint-Study Tips have been added. These reinforce and expand upon the Study Skills for Suc­cess in Mathematics covered in Section 1.1.

Application problems throughout the book have been updated and made more interesting.

Using Your Graphing Calculator boxes now show keystrokes and screens from a Texas Instruments 83 Plus calculator.

A fraction raised to a negative exponent is covered more completely.

The balance bars have been removed from the ex­planations in Chapter 2.

When factoring by grouping, the common factor is now placed on the left for consistency with other factoring problems.

Variables other than x and y are used more often in examples and exercises.

More photos have been added to the text to make it more attractive and interesting for students.

The basic colors used in the text have been softened to make the text easier to read.

A brief introduction to metric units of measurement is now presented in the Scientific Notation section.

Algebra and Trigonometry, Second Edition by Robert Blitzer (Prentice Hall) was written Algebra and Trigonometry, Second Edition do help diverse students, with different backgrounds ant future goals do succeed. The book has three fundamental goals:

1. To help students acquire a solid foundation in algebra ant trigonometry, preparing them for other courses such as calculus, business calculus, ant finite mathematics.

2. To show students how algebra ant trigonometry can motel ant solve authentic real-world problems.

3. To enable students do develop problem-solving skills, while fostering critical thinking, within an interesting setting.  

Intermediate Algebra Functions and Authentic Applications, Second Edition by Jay Lehmann (Prentice Hall) Unique and enthusiastic in its approach, Lehmann's book is a rich combination of important skills, concepts, and applications. This book captivates readers' interest as they use curve fitting to model current, compelling, and authentic situations. The curve fitting approach emphasizes concepts related to functions in a natural, substantial way and encourages readers to view functions graphically, numerically, and symbolically as well as to verbally describe concepts related to functions. The examples in the test demonstrate both how to perform skills and how to investigate concepts. Students learn why they perform skills to solve problems as well as how to solve the problems. Explorations deepen users' understanding as they investigate mathematics with graphing calculator and pencil and paper activities. Topics discussed include linear functions, modeling with linear functions, systems of linear functions, exponential functions, logarithmic functions, polynomial functions, using quadratic functions to model data, rational functions, radical functions, and modeling with sequences and series. For individuals interested in deepening their understanding of algebra.

The question of common sense is always `What is it good for?'-a question which would abolish the rose and be answered triumphantly by the cabbage. -James Russell Lowell, 1819-1891, American poet, editor.

The above quote suggests James Russell Lowell must have taken intermediate algebra. How many times have your students asked, "What is it good for?" After years of responding, "You'll find out in the next course," I began a five-year quest to develop a more satisfying and substantial response to my students' query.  

Curve Fitting Approach

Although there are many ways to center an intermediate algebra course around authen­tic applications, I chose a curve fitting approach for several reasons. A curve fitting approach

• allows great flexibility in choosing interesting, authentic, current situations to model.

• emphasizes concepts related to functions in a natural, substantial way.

• deepens students' understanding of functions because it requires them to describe functions graphically, numerically, symbolically, and verbally.

• serves as a glue to hold together the many diverse topics of a typical intermediate algebra course.

To curve fit, students learn the following four-step modeling process: 1. Examine the data set to determine which type of model, if any, to use. 2. Find an equation for the model. 3. Verify that the model fits the data. 4. Use the model to make estimates and predictions.

This four-step process weaves together topics that are crucial to the course. Students must notice numerical patterns from data displayed in tables, recognize graph­ical patterns in scattergrams, find formulas of functions, graph functions, evaluate func­tions, and solve equations.

Curve fitting not only fosters cohesiveness within a chapter, it also creates a parallel theme for each chapter that introduces and discusses another function. This structure enhances students' abilities to observe similarities and differences between fundamen­tal functions such as linear functions, exponential functions, and quadratic functions. Specifically, this structure has exponential functions directly follow linear functions so that students can easily observe the dual nature of these two functions (comparing the slope addition property to the base multiplier property). Additionally, logarithms can then be studied relatively early in the course, when students still have plenty of energy to learn about an unfamiliar function.

With many intermediate algebra texts, the first third of the course reviews topics typically taught in elementary algebra. For this reason, some students find it hard to stay interested in the course because they have "seen it all before." To address this issue, there is content new to most students in Sections 1.1, 1.4, and 1.6 and throughout most of Chapters 2-11. Section 1.1 sets the tone that this course will be different, interesting, alive, and relevant, inviting students' creativity into the classroom.

Response from math departments using the first edition have been enthusiastic. They feel that their students have learned a great deal from the text. Their students have found the first edition easy to read and the applications very interesting. Instructors have noticed a quantum leap forward in students' participation, morale, and success in the course.

Math departments' enthusiasm notwithstanding, there were requests from review­ers and class testers. In response, I have reorganized content and added some topics for the second edition.  

NEW IN THE SECOND EDITION
Data Sets: About 90% of the data sets have been updated or replaced. Data sets were replaced because of changes in trends or because new data sets were more interesting and/or better illustrated concepts. The number of application exercises has been increased by about 15%.  

New Sections: Many reviewers wanted more discussion about polynomials of degree greater than two. To meet this need, the new Section 6.4 discusses how to factor such polynomials.

There is a new Section 8.7 on direct variation and inverse variation. These topics are discussed within the context of curve fitting, a departure from most other texts that work with models but don't use data.

The new Section 11.5 includes value, interest, and revenue applications. Some re­viewers want these types of word problems included because they require a different form of deductive reasoning than curve fitting applications do. However, the prob­lems in this section are distinct from those in other texts because students use the equations for authentic purposes that lend themselves to concepts that are relevant to functions.

A brief Section A.3 on absolute value has been added.

Revised or Expanded Sections: Section 5.1 on inverse functions has been rewritten. The section has widened its scope from the inverse of a linear function to the inverse of any invertible function. The inverse of a nonlinear invertible function is described in terms of a table and a graph. The section explains how to graph an inverse function by reflecting the graph of an invertible function across the line y = x, setting the stage for graphing logarithmic functions later in the chapter.

The scope of Sections 6.2, 6.4, and 6.5 have been expanded from quadratic expressions and equations to polynomial expressions and equations.

Section 8.4 on complex rational expressions has been expanded to include two methods to simplify these expressions.

The cumulative review sections have been greatly expanded. Some of the chapter review sections have also been expanded.

To offer students more technological support, the number of graphing calculator screen dumps has been increased.

Reorganization

Natural logarithms has been moved from Chapter 11 to Section 5.6 so that all types of logarithms discussed in the text are in one chapter.

Most reviewers do not teach sums and differences of cubes. So, this topic has been moved from Chapter 8 to the Additional Topics Chapter 11.

Factoring by grouping has been moved from Chapter 8 to Section 6.4 to join other factoring techniques discussed in Chapter 6.

Scientific Applications

Hierarchical and Geometrical Methods in Scientific Visualization edited by Gerald E. Farin, B. Hamann, H. Hagen (Springer Verlag) emerged from a Department of Energy/National Science Foundation-sponsored workshop, held in Tahoe City , California , October 2000. About fifty invited participants presented state-of-the-art research on topics such as: terrain modeling - multiresolution subdivision - wavelet-based scientific data compression - topology-based visualization - data structures, data organization and indexing schemes for scientific data visualization.
All invited papers were carefully refereed, resulting in this collection. Hierarchical and Geometrical Methods in Scientific Visualization  will be of great interest to researchers, graduate students and professionals dealing with scientific visualization and its applications.  

Contents: with some abstracts:

• Dataflow and Remapping for Wavelet Compression and View-dependent Optimization of Billion-triangle Isosurfaces by Mark A. Duchaineau, Serban D. Porumbescu, Martin Bertram, Bernd Hamann, and Kenneth I. Joy

Currently, large physics simulations produce 3D discretized field data whose individual isosurfaces, after conventional extraction processes, contain up­wards of hundreds of millions of triangles. Detailed interactive viewing of these surfaces requires (a) powerful compression to minimize storage, and (b) fast view­dependent optimization of display triangulations to most effectively utilize high­performance graphics hardware. In this work, we introduce the first end-to-end multiresolution dataflow strategy that can effectively combine the top performing subdivision-surface wavelet compression and view-dependent optimization methods, thus increasing efficiency by several orders of magnitude over conventional processing pipelines. In addition to the general development and analysis of the dataflow, we present new algorithms at two steps in the pipeline that provide the "glue" that makes an integrated large-scale data visualization approach possible. A shrink-wrapping step converts highly detailed unstructured surfaces of arbitrary topology to the semi-structured meshes needed for wavelet compression. Remapping to triangle bintrees minimizes disturbing "pops" during realtime display­triangulation optimization and provides effective selective-transmission compression for out-of-core and remote access to extremely large surfaces. Overall, this is the first effort to exploit semi-structured surface representations for a complete data visualzation pipeline.

• Extraction of Crack-free Isosurfaces from Adaptive Mesh Refinement Data by Gunther H. Weber, Oliver Kreylos, Terry J. Ligocki, John M. Shalf, Hans Hagen, Bernd Hamann, and Kenneth I. Joy

Adaptive mesh refinement (AMR.) is a numerical simulation technique used in computational fluid dynamics (CFD). This technique permits efficient sim­ulation of phenomena characterized by substantially varying scales in complexity. By using a set of nested grids of different resolutions, AMR combines the simplic­ity of structured rectilinear grids with the possibility to adapt to local changes in complexity within the domain of a numerical simulation that otherwise requires the use of unstructured grids. Without proper interpolation at the boundaries of the nested grids of different levels of a hierarchy, discontinuities can arise. These discontinuities can lead, for example, to cracks in an extracted isosurface. Treating locations of data values given at the cell centers of AMR grids as vertices of a dual grid allows us to use the original data values of the cell-centered AMR data in a marching-cubes (MC) isosurface extraction scheme that expects vertex-centered data. The use of dual grids also induces gaps between grids of different hierarchy levels. We use an index-based tessellation approach to fill these gaps with "stitch cells." By extending the standard MC approach to a finite set of stitch cells, we can define an isosurface extraction scheme that avoids cracks at level boundaries.

• Edgebreaker on a Corner Table: A Simple Technique for Representing and Compressing Triangulated Surfaces by Jarek Rossi,gnac, Alla Safonova, and Andrzej Szymczak

A triangulated surface S with V vertices is sometimes stored as a list of T independent triangles, each described by the 3 floating-point coordinates of its vertices. This representation requires about 576V bits and provides no explicit information regarding the adjacency between neighboring triangles or vertices. A variety of boundary-graph data structures may be derived from such a representa­tion in order to make explicit the various adjacency and incidence relations between triangles, edges, and vertices. These relations are stored to accelerate algorithms that visit the surface in a systematic manner and access the neighbors of each vertex or triangle. Instead of these complex data structures, we advocate a simple Corner Table, which explicitly represents the triangle/vertex incidence and the tri­angle/triangle adjacency of any manifold or pseudo-manifold triangle mesh, as two tables of integers. The Corner Table requires about 12V1og2V hits and must be ac­companied by a vertex table, which requires 96V bits, if Floats are used. The Corner Table may be derived from the list of independent triangles. For meshes homeomor­phic to a sphere, it may be compressed to less that 4V bits by storing the "clers" sequence of triangle-labels from the set {C,L,E,R,S}. Further compression to 3.6V bits may be guaranteed by using context-based codes for the clers symbols. En­tropy codes reduce the storage for large meshes to less than 2V bits. Meshes with more complex topologies may require O(log2V) additional bits per handle or hole. We present here a publicly available, simple, state-machine implementation of the Edgebreaker compression, which traverses the corner table, computes the CLERS symbols, and constructs an ordered list of vertex references. Vertices are encoded, in the order in which they appear on the list, as corrective displacements between their predicted and actual locations. Quantizing vertex coordinates to 12 bits and predicting each vertex as a linear combinations of its previously encoded neighbors leads to short displacements, for which entropy codes drop the total vertex location storage for heavily sampled typical meshes below 16V bits.

• Efficient Error Calculation for Multiresolution Texture-based Volume Visualization by Eric LaMar, Bernd Hamann, and Kenneth I. Joy
• Hierarchical Spline Approximations       by David F. Wiley, Martin Bertram, Benjamin W. Jordan, Bernd Hamann, Kenneth I. Joy, Nelson L. Max, and Gerik Scheuerraann
• Terrain Modeling Using Voronoi Hierarchies by Martin Bertram, Shirley E. Konkle, Hans Hagen, Bernd Hamann, and Kenneth I. Joy
• Multiresolution Representation of Datasets with Material Interfaces by Benjamin F. Gregorski, David E. Sigeti, John Ambrosiano, Gerald Graham, Murray Wolinsky, Mark A. Duchaineau, Bernd Hamann, and Kenneth I. Joy
• Approaches to Interactive Visualization of Large-scale Dynamic Astrophysical Environments by Andrew J. Hanson and Philip Chi-Wing Fu
• Data Structures for Multiresolution Representation of Unstructured Meshes by Kenneth I. Joy, Justin Legakis, and Ron MacCracken
• Scaling the Topology of Symmetric, Second-Order Planar Tensor Fields by Xavier Tricoche, Gerik Scheuermann, and Hans Hagen
• Simplification of Nonconvex Tetrahedral Meshes by Martin Kraus and Thomas Ertl
• A Framework for Visualizing Hierarchical Computations by Terry J. Ligocki, Brian Van Straalen, John M. Shalf, Gunther H. Weber, and Bernd Hamann
• Virtual-Reality Based Interactive Exploration of Multiresolution Data by Oliver Kreylos, E. Wes Bethel, Terry J. Ligocki, and Bernd Hamann
• Hierarchical Indexing for Out-of-Core Access to Multi-Resolution Data by Valerio Pascucci and Randall J. Frank
• Mesh Fairing Based on Harmonic Mean Curvature Surfaces by Robert, Schneider, Leif Kobbelt, and Hans-Peter Seidel
• Shape Feature Extraction by Georgios Stylianou and Gerald Farin

In this paper we present a method for automatic extraction of shape features, called crest lines. Shape features are important because they provide an alternative to describing an object, using its most important characteristics and reduce the amount of information stored. The algorithm is comprised of a curva­ture approximation technique, crest point classification and a crest lines tracing algorithm.

• Network-based Rendering Techniques for Large-scale Volume Data Sets         by Joerg Meyer, Ragnar Borg, Bernd Hamann, Kenneth I. Joy, and Arthur J. Olson
• A Data Model for Distributed Multiresolution Multisource Scientific Data           by Philip J. Rhodes, R. Daniel Bergeron, and Ted M. Sparr
• Adaptive Subdivision Schemes for Triangular Meshes by Ashish Amresh, Gerald Farin, and Anshuman Razdan
• Hierarchical Image-based and Polygon-based Rendering for Large-Scale Visualizations by Chu-Fei Chang, Zhiyun Li, Amitabh, Varshney, and Qiaode Jeffrey Ge
• Appendix: Color Plates  

Non-Self-Adjoin Boundary Eigenvalue Problems by Reinhard Mennicken, Manfred Moller (North-Holland Mathematics Studies, No 192: North-Holland) The purpose of this book is the study of non-self-adjoint boundary eigenvalue problems for first order systems of ordinary differential equations and n-th or-der scalar differential equations. The coefficients of the differential equations as well as the boundary conditions are allowed to depend polynomially, holomor­phically or asymptotically on the eigenvalue parameter. The boundary conditions may contain infinitely many interior points and an integral term. With the bound­ary eigenvalue problem a bounded operator function is associated which consists of two components, the differential operator function and the boundary operator function. These operator functions depend in general nonlinearly on the eigen­value parameter.

Various eigenfunction expansions are proved by the contour integral method under regularity conditions which originally were introduced by Birkoff and Stone in case of A-independent boundary conditions. The calculation of the Fourier coefficients of these expansions is based on the theory of the inverses of holomorphic Fredholm operator valued functions which for the sake of complete­ness is included in this book. An important aspect of this theory is the representa­tion of the principal parts of the inverses of these functions at their poles by root functions (eigenvectors and associated vectors) of the given operator functions and their adjoints. The proofs of the eigenfunction expansions are based on sharp asymptotic estimates of the resolvents (Green's functions) for large values of the eigenvalue parameter.

Our approach is based on functional analytic methods. The reader should be familiar with basic concepts of Banach spaces and Lebesgue integration and should have some knowledge about distributions. Whenever we use these ba­sic results we give references so that the reader unfamiliar with these concepts can easily find them. Our main references to the basic topics are the monograph of T. Kato for Banach spaces, the monograph [HS] of E. Hewitt and K. Stromgberg for the theory of Lebesgue integration, and the monograph [H02] of L. Hormander for the theory of distributions.

Each chapter ends with a short section containing historical notes.

Chapters I and II are concerned with preparations from functional analysis and Sobolev space theory. In Chapters III–V first order systems are considered, followed by n-th order equations in Chapters VI—IX. Since n-th order equations are reduced to first order systems, some of the results of Chapters III—V are needed

in Chapters VI–IX. Chapter X contains applications to problems from physics and engineering.

The literature for n-th order linear differential equations and first order sys­tems is vast, and the bibliography is only a selection of publications in this field. The list of notations and the index should help the reader to navigate through the text.

Chapter I deals with spectral theory for holomorphic Fredholm valued oper­ator functions, in particular, the principal parts of their inverses at the poles are investigated. It is shown that these principal parts can be written in terms of eigen­vectors and associated vectors of the operator function and its adjoint. One-to-one connections between biorthogonal systems of eigenvectors and associated vectors and the principal parts of the inverse operator functions are established. Special attention is paid to the case of A-linear problems.

Chapter II contains the prerequisites for the study of differential operators. Sobolev spaces on intervals are introduced and their properties are investigated. These results are essentially well-known but, in general, are stated and proved for subsets of 1R" . The one dimensional case is easier and gives some additional prop­erties. Therefore, and to make the monograph more self-contained, this chapter is included. Also, some basic results for differential equations are stated.

Chapter III starts with the definition of boundary eigenvalue problems for first order systems. The adjoint and the inverse are calculated, and their relations to the "classical" adjoint and inverse for the differential operator considered in Lp spaces are discussed. Some examples show the difficulties which arise if one considers the classical adjoint. The inverse is an extension of the classical inverse, which is an integral operator whose kernel is the Green's matrix function.

Chapter IV is devoted to the estimate of the Green's matrix function. To this end, Birkhoff regularity is introduced for systems which are asymptotically linear in the eigenvalue parameter, and necessary and sufficient conditions for Birkhoff regularity are given. The characteristic determinant is estimated below away from its zeros, which are the eigenvalues of the given boundary eigenvalue problem. Then the Green's matrix function and finally the resolvent of the boundary eigenvalue operator functions are estimated on suitable circles in the complex plane tending to infinity.

In Chapter V the estimates of the previous chapter are used to prove expansion theorems for first order systems which are linear in the parameter; the boundary conditions are still allowed to depend polynomially on the parameter. Not only Birkhoff regularity is considered but also Stone regularity. Whereas all functions in Lp(a,b), 1 < p < 00, are expandable in eigenfunctions and associated functions if the problem is Birkhoff regular, the expandable functions must be sufficiently smooth and must satisfy certain auxiliary boundary conditions if the problem is Stone regular. Also uniform convergence is investigated, where even for Birkhoff regular problems the expandable functions have to satisfy certain regularity con­ditions and some boundary conditions.

Chapter VI is concerned with n-th order differential equations. Here the cor­responding results of Chapter III are obtained for an n-th order differential equa­tion, where also the equivalence of this problem to one for a first order system is established.

Chapter VII deals with boundary value problems for differential equations whose equivalent first order system can be linearized asymptotically. Using the estimates of Chapter IV, expansion theorems are proved.

Chapter VIII is concerned with regular two-point boundary eigenvalue prob­lems for the differential equation , where K and H are differential operators such that K is of higher order than H. The structures of the fundamen­tal system, its adjoint, and the Green's function are investigated more thoroughly. However, the estimates of Chapter IV can still be used. Some applications to problems from mechanics are given, to which the results of Chapter VII are not directly applicable.

In Chapter IX problems depending polynomially on the eigenvalue parameter A are linearized with respect to A. The corresponding convergence theorems for first order systems lead to n-fold expansions for the original problem. Complete­ness and minimality for these problems are considered.

Chapter X contains further examples dealing with problems from mechanics like elastic bars and control of beams, fluid mechanics, magnetohydrodynamics, and meteorology.

Appendix A deals with estimates of exponential sums. They are needed for the estimate of the characteristic determinant in Chapter IV.  

Essential Mathematical Biology by Nicholas F. Britton (Springer Verlag) Essential Mathematical Biology is a self-contained introduction to the fast-growing field of mathematical biology. Written for students with a mathematical background, it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences.
A broad range of topics is covered including:

• Population dynamics
• Infectious diseases
• Population genetics and evolution
• Dispersal
• Molecular and cellular biology
• Pattern formation
• Cancer modelling

This book will appeal to 3rd and 4th year undergraduate students studying mathematical biology. A background in calculus and differential equations is assumed although the main results required are collected in the appendices. A dedicated website at www.springer.co.uk/britton/ accompanies the book and provides further exercises, more detailed solutions to the numerous exercises in the book, and links to other useful sites.  

Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics (3rd Edition) by Edward Saff, Arthur D. Snider (Prentice Hall) The raison d'existence for Fundamentals of Complex Analysis with Applications to Engineering and Science, 3/e is our conviction that engineering, science, and math­ematics undergraduates who have completed the calculus sequence are capable of understanding the basics of complex analysis and applying its methods to solve en­gineering problems. Accordingly, we address ourselves to this audience in our attempt to make the fundamentals of the subject more easily accessible to readers who have little inclination to wade through the rigors of the axiomatic approach. To accomplish this goal we have modeled the text after standard calculus books, both in level of expo­sition and layout, and have incorporated engineering applications throughout the text so that the mathematical methodology will appear less sterile to the reader.

To be more specific about our mode of exposition, we begin by addressing the question most instructors ask first: To what extent is the book self contained, i.e.., which results are proved and which are merely stated? Let us say that we have elected to include all the proofs that reflect the spirit of analytic function theory and to omit most of those that involve deeper results from real analysis (such as the convergence of Riemann sums for complex integrals, the Cauchy criterion for convergence, Goursat's generalization of Cauchy's theorem, or the Riemann mapping theorem). Moreover, in keeping with our philosophy of avoiding pedantics, we have shunned the ordered pairs interpretation of complex numbers and retained the more intuitive approach (grounded in algebraic field extensions).

Cauchy's theorem is given two alternative presentations in Chapter 4. The first is based on the deformation of contours, or what is known to topologists as homotopy. We have taken some pains to make this approach understandable and transparent to the novice because it is easy to visualize and to apply in specific situations. The second treatment interprets contour integrals in terms of line integrals and invokes Green's theorem to complete the argument. These parallel developments constitute the two parts of Section 4 in Chapter 4; either one may be read, and the other omitted, without disrupting the exposition (although it should not be difficult to discern our preference, from this paragraph).

Steady state temperature patterns in two dimensions are, in our opinion, the most familiar instances of harmonic functions, so we have principally chosen this interpre­tation for visualization of the theorems of analytic function theory. This application receives attention throughout the book, with special emphasis in Chapter 7 in the context of conformal mapping. There we draw the distinction between direct methods, wherein a mapping must be constructed to solve a specific problem, and indirect meth­ods that postulate a mapping and then investigate which problems it solves. In doing so we hope to dispel the impression, given in many older books, that all applications of the technique fall in the latter category.

In this third edition L. N. Trefethen and T. Driscoll have updated an appendix that reflects the progress made in recent years on the numerical construction of conformal mappings. A second appendix compiles a listing of some useful mappings having closed form expressions.

Linear systems analysis is another application that recurs in the text. The basic ideas of frequency analysis are introduced in Chapter 3 following the study of the transcendental functions; Smith charts, circuit synthesis, and stability criteria are ad­dressed at appropriate times; and the development culminates in Chapter 8 with the exposition of the analytic-function aspects of Fourier, Mellin, Laplace, Hilbert, and z transforms, including new applications in signal processing and communications. We hope thereby that our book will continue to serve the reader as a reference resource for subsequent coursework in these areas.

Features of the Third Edition

Novel features of the third edition are a discussion of the Riemann sphere, adding substance to the pragmatic concept of the "point at infinity" in complex analysis; an introduction to functional iteration and the picturesque Julia sets that thereby mani­fest themselves in the complex plane; an early exploration of the enrichment that the complex viewpoint provides in the analysis of polynomials and rational functions; and an introductory survey of harmonic function methods for calculating equilibrium tem­peratures for simple geometries. Optional sections are indicated with an asterisk so that readers can select topics of special interest. Summaries and suggested readings appear at the end of each chapter. As in previous editions, the text is distinguished by its wealth of worked-out examples that illustrate the theorems, techniques, and applications of complex analysis.

Teaching

Mathematical Reasoning for Elementary Teachers, Third Edition by Calvin T. Long, Duane W. Detemple (Addison Wesley) With enhanced skill at mathematical reasoning and a positive attitude toward mathemat­ics come confidence and an increased willingness to learn the mathematical content, skills, and effective teaching techniques necessary to become a competent teacher of mathe­matics. The principal goals of this text are to impart mathematical reasoning skills and a positive attitude to those who aspire to be elementary or middle school teachers.

Quite a few people have an aversion to mathematics and find it difficult and daunt­ing-something to be avoided if at all possible. Many who aspire to be elementary or mid­dle school teachers also share this view. It is not surprising that school teachers with this perception of mathematics soon impart similar attitudes to their students. In order to change this pervasive negative view of mathematics, we must begin by producing teachers who see mathematics in a different, more favorable light.

The attitudes of fear and dislike of mathematics are not unrelated. We endeavor to deal with both in this text. We make a concerted effort to involve students in learning sit­uations that promote mathematical reasoning in settings that are intrinsically interesting, surprising, and even aesthetically pleasing. Our main thrust is to stress problem solving (read "mathematical reasoning") throughout the text. This emphasis begins in Chapter 1 on problem solving and continues not only in the discussion of the various topics but, per­haps even more importantly, in the problem sets within the sections labeled Thinking Critically, Teaching Concepts, Thinking Cooperatively, Making Connections, Communicating, Using a Calculator Using a Computer, and From State Student Assessments. In fact, the text is replete with activities, investigations, and a host of problems with results and answers that are attractive, surprising, and unexpected; and yet are designed to engage the students in thoughtfully doing mathematics.

It is worth noting that in our own classes we have found it extremely profitable to spend considerable time (up to five weeks) on Chapter 1. This has gone a long way toward changing student attitudes and promoting their ability to reason mathematically. A course that begins and continues with extensive study of the number systems and algorithms of arithmetic is not attractive or interesting to students who feel they already know these things and have found them dull and boring. The material in Chapter 1, on the other hand, and the many problems in the problem sets are new, stimulating, and not what students expect. Aside from enhancing interest, we have found that the extensive time spent on Chapter 1 develops attitudes and skills that make it possible to deal much more quickly with the usual material on number systems, algorithms, and all the subsequent ideas important to the teaching of mathematics in elementary schools.

The content and processes of mathematics are presented in an appealing and logically sound manner with these three principal goals in mind:

1. to develop positive attitudes toward mathematics and mathematics teaching,
2. to develop mathematical knowledge and skills with particular emphasis on problem solving and mathematical reasoning, and
3. to develop excellent teachers of mathematics.

In short, the goals of this text are to implement the recommendations of the National Council of Teachers in Mathematics (NCTM) Principles and Standards for School

Mathematics (the Principles and Standards) published in the year 2000. In light of recent research in teaching mathematics and ten years' experience since the first of the NCTM Standards were published in 1989, the various Standards were combined, refined, and updated. Principles and Standards now effectively unifies, explains, and builds upon the original Standards. The Principles and Standards are to "ensure quality, indicate goals, and promote positive changes in mathematics education in grades preK-12." Our approach to achieving the goals of this text reflects the recommendations of the NCTM Principles and Standards 2000, which we cite throughout the text.

Aside from mastering content and skills, teachers often pattern their own teaching after the ways they have been taught. This text models effective teaching by emphasizing activities, manipulatives, investigations, written projects, discussion questions, appropriate use of technology, and above all else, problem solving and mathematical reasoning.

It is our hope that this book will provide future elementary school teachers with the posi­tive attitudes and mathematical skills they need to convey the beauty, usefulness, and power of mathematics to their own students.

Mathematical Background

This text is for use in mathematics content courses for prospective elementary and middle school teachers. We assume the students enrolled in these courses have completed two years of high school algebra and one year of high school geometry. We do not assume that the students will be highly proficient in algebra and geometry but that they have a basic knowledge of these subjects and reasonable arithmetic skills. Typically, students bring widely varying backgrounds to these courses and this text is written to accommodate this diversity.

Problem Solving We begin the text with an extensive introduction to problem solving in Chapter 1. This theme is continued throughout the text in special problem-solving examples and featured in the exercises in the problems grouped under the headings Thinking Critically, Teaching Concepts, Thinking Cooperatively, Making Connections, Communicating, Using a Calculator, Using a Computer, and From State Student Assessments.

Number Systems Chapters 2, 3, 5, 6, and 7 focus on the various number systems and make use of discussion, pictorial and graphical representations, and manipulatives to promote understanding of the systems, their properties, and the various modes of computation. Students are given plenty of opportunity for drill and practice as well as for individual and cooperative problem solving, reasoning, and communication.

Number Theory Chapter 4 contains much material that is new and interesting to students. Notions of divisibility, divisors, multiples, greatest common divisors, and least common multiples are first developed via informative diagrams and then through the use of manipulatives, sets, prime factor representations, and the Euclidean algorithm. A final section contains interesting applications to zip codes, numbering of credit cards, and the ISBN book number codes in common use.

Algebraic Reasoning and Representation Though algebraic notions are used earlier in the text, Chapter 8 gives a careful but readable discussion of algebraic ideas needed in elementary and middle school-variables, algebraic expressions and equations, functions, and graphing. All of these notions increasingly appear in texts for elementary school students and, even more so, in middle school texts. School teachers must be conversant with algebraic ideas to be comfortable teaching from these new texts. Statistics Chapter 9 on statistics is designed not only to give the students an appreciation of the basic measures and graphical representations of data but also of the uses and misuses of statistics. This last issue is particularly important since we are confronted daily with a stream of "facts and figures" seductively intended to influence our thinking. The informed citizen needs not only to be aware of the legitimate predictive and descriptive power of statistics but also to be wary of the way statistics can mislead.

Probability In Chapter 10, we first study empirical probability-probability based on experience and repeated trials. This prepares the way for the subsequent study of the elements of theoretical probability of an event based on counting and other a priori considerations. The great surprise for the students is how closely the results agree, particularly when the number of trials is large. Of course, it is necessary to consider various methods of counting in order to compute theoretical probabilities. At the same time counting is an important topic in its own right, and we have made it accessible through the use of tree diagrams, Venn diagrams, and careful explanation of the use of the words "or" and "And".

The creative and inductive nature of geometric discovery is emphasized in Chapters 11, 12, 13, and 14, and students who have acquired a distaste for the subject from a previous heavily axiomatic and deductive course will often see geometry in a positive new way. The text's approach to geometry is constructive and visual. Students are often asked to draw, cut, fold, paste, count, and so on, making geometry an experimental science. While the traditional construction and measurement tools continue to have a place, the visual and dynamic scope of geometry is enhanced with computer geometry software, such as The Geometer's Sketchpad, which can be purchased for use with this text. Problem solving and applications permeate the geometry chapters, and sections on tilings and symmetry provide an opportunity to highlight the aesthetic and artistic aspects of geometry. Examples are often taken from culturally diverse sources.