Studies in Modern Analysis, Vol. 1

Science & Math

Buck, R. C. (ed)

Mathematics

The Mathematical Association of America

Professor Aaboe gives here the reader a feeling for the universality of important mathematics, putting each chosen topic into its proper setting, thus bringing out the continuity and cumulative nature of mathematical knowledge. The material he selects is mathematically elementary, yet exhibits the depth that is characteristic of truly great thought patterns in all ages. The success of this exposition is due to the author's unique approach to his subject. He wisely refrains from attempting a general survey of mathematics in antiquity, but selects, instead, a few representative items that he can treat in detail. He describes Babylonian mathematics as revealed from cuneiform texts discovered only recently, as well as more familiar topics developed by the Greeks. Although each chapter can be read as a separate unit, there are many connecting threads. Aaboe stays as close to the original texts as is comfortable for a modern reader, and the bibliography enables the interested student to delve more deeply into any aspect of ancient mathematics that catches his or her fancy.

Episodes from the Early History of Mathematics

Asger Aaboe

Mathematics of Choice

Unknown, Author

The nineteen essays here illustrate many different aspects of mathematical thinking. The author is very well-known for his best-selling books of problems; in this volume he seeks to share his appreciation of the elegant and ingenious approaches used in thinking about even elementary mathematics. Standard high school courses in algebra and geometry furnish a sufficient basis for understanding each essay. Topics include number theory, geometry, combinatorics, logic and probability, and the methods used often involve an interaction between these disciplines. Some of the essays are easy to read, others more challenging; some of the exercises are routine, others lead the reader deeper into the subject.

Ingenuity in Mathematics (New Mathematical Library, No. 23)

Ross Honsberger

Arithmetic Theory of Quadratic Forms

Jones, Burton W.

The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities

Steele, J. Michael

Social Choice and the Mathematics of Manipulation (Outlooks)

Honesty in voting is not always the best policy. This is a book for mathematicians, political scientists, economists and philosophers who want to understand how it is impossible to devise a reasonable voting system in which voters can never gain by submitting a disingenuous ballot. The book requires no prerequisites except a willingness to follow rigorous mathematical arguments.

Taylor, Alan D.

Calculated Bets describes a gambling system that works. Steven Skiena, a jai-alai enthusiast and computer scientist, documents how he used computer simulations and modeling techniques to predict the outcome of jai-alai matches and increased his initial stake by 544% in one year. Skiena demonstrates how his jai-alai system functions like a stock trading system, and includes examples of how gambling and mathematics interact in program trading systems, how mathematical models are used in political polling, and what the future holds for Internet gambling. With humor and enthusiasm, Skiena explains computer predictions used in business, sports, and politics, and the difference between correlation and causation. An unusual presentation of how mathematical models are designed, built, and validated, Calculated Bets also includes a list of modeling projects with online data sources. Steven Skiena, Associate Professor of Computer Science at SUNY Stony Brook, is the author of The Algorithm Design Manual (Springer-Verlag, 1997) and the EDUCOM award-winning Computational Discrete Mathematics. He is the recipient of the ONR Young Investigator's Award and the Chancellor's Award for Excellence in Teaching at Stony Brook. His research interests include discrete mathematics and its applications, particularly the design of graph, string, and geometric algorithms.

Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win (Outlooks)

Computers & Technology

Skiena, Steven S.

Computer Science

The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions and Commentary (MAA Problem Book Series)

This third volume of problems from the William Lowell Putnam Competition is unlike the previous two in that it places the problems in the context of important mathematical themes. The authors highlight connections to other problems, to the curriculum and to more advanced topics. The best problems contain kernels of sophisticated ideas related to important current research, and yet the problems are accessible to undergraduates. The solutions have been compiled from the American Mathematical Monthly, Mathematics Magazine and past competitors. Multiple solutions enhance the understanding of the audience, explaining techniques that have relevance to more than the problem at hand. In addition, the book contains suggestions for further reading, a hint to each problem, separate from the full solution and background information about the competition. The book will appeal to students, teachers, professors and indeed anyone interested in problem solving as a gateway to a deep understanding of mathematics.

Vakil, Ravi

Kedlaya, Kiran S.

Poonen, Bjorn

The Changing Shape of Geometry: Celebrating a Century of Geometry and Geometry Teaching (Maa Spectrum Series)

Celebrating a century of geometry and geometry teaching, this volume includes popular articles on Pythagoras, the golden ratio and recreational geometry. Thirty "Desert Island Theorems" from distinguished mathematicians and educators disclose surprising results. (Contributors include a Nobel Laureate and a Pulitzer Prize winner.) Co-published with The Mathematical Association of America.

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