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General Topology by Stephen Willard (Dover Publications, Inc.) Among the best available reference introductions to topology, General Topology is appropriate for advanced undergraduate and beginning graduate students. Written by Stephen Willard, University of Alberta, this is a Dover unabridged republication of the edition first published by Addison-Wesley Publishing Company, Reading, Massachusetts, 1970. More

Functioning in the Real World: A Precalculus Experience, Second Edition by Sheldon P. Gordon, Florence S. Gordon, Alan C. Tucker, and Martha J. Siegel (Pearson Addison Wesley) is a text designed to prepare students for calculus with a focus on ideas and reasoning, manipulation and decision-making. More

Sketches of an Elephant: A Topos Theory Compendium by Peter T. Johnstone ( Oxford Logic Guides, 43 & 44: Oxford University Press) Topos theory is an important branch of mathematical logic of interest to theoretical computer scientists, logicians and philosophers who study the foundations of mathematics, and to those working in differential geometry and continuum physics. This compendium contains material that was previously available only in specialist journals. This is likely to become the standard reference work for all those interested in the subject. More

Hierarchical and Geometrical Methods in Scientific Visualization edited by Bernd Hamann, Hans Hagen, Gerald E. Farin (Springer Verlag) This book 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. More

Mathematics and Art edited by Claude P. Brutter (Springer-Verlag) These are the proceedings of a colloquium on Mathematics and Art held in Maubeuge , France in September of 2000 at the Théâtre du Manége. They offer examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work. More

Geometry in Architecture: Texas Buildings Yesterday and Today by Clovis Heimsath ( University of Texas Press ) updates and expands the 1969 edition of Pioneer Texas Buildings: A Ge­ometry Lesson. Thirty‑four years ago it was ahead of its time, for it celebrated the simple geometry of early Texas buildings at a time when they were considered by many to be of no historic significance, and were rou­tinely torn down.

Fortunately the climate of opinion has changed over the last thirty­four years. Not only are the remaining buildings cherished for the heritage they preserve, but also Texas architects continue to design with simple geometry, straightforward structures, and local materi­als to address today's programs. More

Appraising Lakatos: Mathematics, Methodology, and the Man edited by George Kampis, Ladislav Kvasz, Michael Stoltzner (Vienna Circle Institute Library: Kluwer Academic Publishers) a critical re-evaluation of the ideas of Imre Lakatos, a leader in the shaping of what is called the new philosophy of science. The 17 contributions (the result of a joint venture between the Institute Vienna Circle and the Institute for History and Philosophy of Science of Eotvos U, Budapest ) address his main theme of locating rationality within the scientific process, as well as his philosophy of mathematics, which emphasizes heuristics and mathematical practice over logical justification. They also include discussion of his personal life and politics, and contain a part of his Debrecen Ph.D. thesis as well as a bibliography of his Hungarian writings. More

Elementary Statistics Using Excel (Second Edition) (with CD-ROM) by Mario F. Triola (Addison Wesley, Pearson) The use of Excel by statistics professors has recently experienced remarkable growth. A major reason for this growth is the extensive use of Excel in corporate America . Excel has become the pre­mier program for working with spreadsheets. Motivated by a desire to serve their students by preparing them for their professional careers, many profes­sors now include Excel as the medium of technology throughout the statistics course. However, the union of statistics and Excel is not without its pitfalls. Consequently, statistics professors and students using Excel require a guide that is effective in identifying Excel’s weaknesses, as well as providing al­ternatives that successfully overcome those weaknesses. Elementary Statistics Using Excel describes the many good statistics features in Excel, and it also identifies its weak­nesses, while providing suitable alternatives. More

CRC Concise Encyclopedia of Mathematics, Second Edition by Eric W. Weisstein (Chapman & Hall CRC) Allows readers to implement the formulas presented, perform calculations, construct geographical displays of results, and generate remarkable mathematical illustrations. More than 1000 new pages of terms defined, illustrated, and referenced. More

The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time by Keith J. Devlin (Basic) The definitive lay reader's account of the Everests of mathematics--the seven unsolved problems that definethe state of the art in contemporary math.
In 2000, the Clay Foundation of Cambridge , Massachusetts , announced a historic competition: whoever could solve any of seven extraordinarily difficult mathematical problems, and have the solution acknowledged as correct by the experts, would receive $1 million in prize money.  More

Finite Mathematics and Its Applications, Eighth Edition by Larry Joel Goldstein, David I. Schneider, Martha J. Siegel, T. E. Graedel (Prentice Hall) This work is the eighth edition of our text for the traditional finite mathematics course taught to first- and second-year college students, especially those majoring in business and the social and biological sciences. Finite mathematics courses exhibit tremendous diversity with respect to both content and approach. There­fore, in revising this book, we incorporated a wide range of topics from which an instructor may design a curriculum, as well as a high degree of flexibility in the order in which the topics may be presented. For the mathematics of finance, we even allow for flexibility in the approach of the presentation. More

Analyzing Multivariate Data by Jim Lattin, Doug Carroll, Paul E. Green (Brooks/Cole) Offering the latest teaching and practice of applied multivariate statistics, this text is perfect for students who need an applied introduction to the subject. Lattin, Green, and Carroll have created a text that speaks to the needs of applied students who have advanced beyond the beginning level, but are not yet advanced statistics majors. Their text accomplishes this through a three-part structure. First, the authors begin each major topic by developing students' statistical intuition through geometric presentation. Then, they are providing illustrative examples for support. Finally, for those courses where it will be valuable, they describe relevant mathematical underpinnings with matrix algebra. More

The A to Z of Mathematics: A Basic Guide by Thomas H. Sidebotham (Wiley Interscience) a guide that makes math simple without making it simplistic. Invaluable resource for parents and students, home schoolers, teachers, and anyone else who wants to improve his or her math skills and discover the amazing relevance of mathematics to the world around us. More

The Applicability of Mathematics As a Philosophical Problem by Mark Steiner (Harvard University Press) analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis - the success of mathematical physics appears to assign the human mind a special place in the cosmos.
This book has two separate objectives. The first is to examine in what ways mathematics can be said to be applicable in the natural sciences or to the empirical world. Mathematics is applicable in many senses, and this ambiguity has bred confusion and error--even among "analytic" philosophers: because there are many senses of "application" and "applicability," there are many questions about the application of mathematics that ought to be, but have not been, distinguished by philosophers. As a result, we do not always know what problem they are dealing with. More

Cryptanalysis of Number Theoretic Ciphers by Samuel S. Wagstaff, Jr., edited by Mikhail J. Atallah (Chapman & Hall/CRC) First book to take readers all the way from basic number theory through the inner workings of ciphers and protocols to their strengths and weaknesses. Presents cryptosystem as practical, workable algorithms, not just as oversimplified mathematical objects. More

Finite Mathematics by Bill Armstrong, Don Davis (Prentice Hall) modern in its writing style as well as in its applications, contains numerous exercises—both skill oriented and applications—, real data problems, and a problem solving method. The book features exercises based on data form the World Wide Web, technology options for those who wish to use a graphing calculator, review boxes, strategic checkpoints, interactive activities, section summaries and projects, and chapter openers and reviews. For anyone who wants to see and understand how mathematics are used in everyday life.  

Fuzzy Topology by N Palaniappan (CRC Press) imparts the latest developments for graduate students and research scholars covering various properties of fuzzy topology viz., fuzzy point and its neighbourhood structure, fuzzy nets and fuzzy convergence, fuzzy metric spaces, different fuzzy compactness, fuzzy connectedness, fuzzy separation axioms and properties, product spaces, convex fuzzy sets and fuzzy uniform spaces.

The key features are

• Large number of examples

• Counterexamples, characterizations, implications

• References to original sources

In recent years, many concepts in mathematics, engineering, computer science, and many other disciplines have been in a sense redefined to incorporate the notion of fuzziness. Designed for graduate students and research scholars, Fuzzy Topology imparts the concepts and recent developments related to the various properties of fuzzy topology. More

Elementary Differential Equations by W. E. Kohler, Lee W. Johnson (Addison Wesley) This book is designed for the sophomore differential equations course taken by students majoring in science and engineering. We assume the reader has had a course in elementary calculus.

The authors have integrated the underlying theory, the solution procedures, and the numerical and computational aspects of differential equations as seamlessly as possible. For example, when they introduce a new category of problems (such as first order equations, higher order equations, systems of differential equations, etc..), we begin with the basic existence-uniqueness theory since it forms the framework for understanding differential equations and attempting to solve them. However, because they want the text to be easy to read and understand, they discuss the theory as simply as possible and emphasize how to use it. More

Discrete Mathematics (5th Edition) by Kenneth A. Ross, Charles R. B. Wright (Prentice Hall) Presenting conceptual chains in an orderly and gradual fashion, this informal but thorough introduction to discrete mathematics offers a careful treatment of the basics essential for computer science such as relations, induction, counting techniques, logic, and graphs. It also covers the more advanced topics of Boolean algebra and permutation groups, and comes with a wealth of examples to reinforce material and to allow readers to view topics from several perspectives. The book includes new coverage of probability that examines such areas as random variables and distributions and new sections on the Euclidean algorithm and loop invariants, providing a powerful tool for designing algorithms and verifying their correctness. More

Invitation to Linear Operators: From Matrix to Bounded Linear Operators on a Hilbert Space by Takayuki Furuta (Gordon & Beach: Taylor & Francis) Essential guide explains in easy to follow steps, the newest essential and fundamental results on linear operators as based on matrix theory. Serves as a reference book for advanced readers in mathematics. Written for non-specialists with a good grasp of matrix theory, this introductory guide to linear operators situates its theory and recent results in the context of matrix theory. Furuta begins by describing the basic properties of a Hilbert space and then arranges the fundamental properties of bounded linear operators on a Hilbert space, and ends with a discussion of current research. Furuta teaches applied mathematics at the Science University of Tokyo. More

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