Mathematics Books

Introduction to Combinatorics (Wiley)

This is an introductory book on combinatorics at the advanced undergraduate/beginning graduate student level.  The main themes of combinatorics are organized into three parts: existence, enumeration, and construction.   Many problems are discussed and solved.  Over 300 examples and exercises.

Principles of Mathematical Problem Solving, with Joe Flowers (Prentice Hall)

This book organizes the main methods of mathematical problem solving into nineteen chapters.  Each method is illustrated with examples, a selection of solved problems, and a further selection of problems given without solutions.  A final chapter presents a set of problems that can be solved using a variety of methods.  The text is suitable for undergraduate students in a problem solving class or preparing for a mathematical competition as well as others who enjoy challenging mathematical problems.  Approximately 500 examples and exercises.

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Introduction to Number Theory, with Anthony Vazzana (Chapman & Hall/CRC Press)

This is an introductory book on number theory at the advanced undergraduate/beginning graduate student level.  It covers the main topics of number theory as well as applied topics such as cryptography.  It all also discusses modern developments in number theory such as elliptic curves and the unsolvability of Hilbert's tenth problem.   Large-number computations are illustrated using Mathematics and Maple.  Over 100 examples and over 500 exercises.

Aha! Solutions (Mathematical Association of America) 

This is a problem-solving book that focuses on "lightning-bolt" solutions.  Contains 100  problems and solutions in arithmetic, geometry, algebra, calculus, probability, number theory, and combinatorics, as well as 100 discussions of related mathematics.  A few problems require the use of a computer. 

Pearls of Discrete Mathematics (CRC Press)

This book presents gems in the field of discrete mathematics.  Contains over 300 problems and solutions. 

 

 

A Student's Guide to the Study, Practice, and Tools of Modern Mathematics, with Donald Bindner (CRC Press)

 

This book is for undergraduate mathematics students.  It explains how to study mathematics, do homework and write proofs, and use tools such as LaTeX and computer algebra systems.  Over 200 exercises. 

 

 

 

 

 

 

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 Beautiful Mathematics (Mathematical Association of America)

This book is for advanced high school students, university students, and instructors.  It explores mathematical topics noted for their elegance and beauty.  It covers theorems, proofs, and problem-solving.  Includes an appendix of problems for the reader to solve, with solutions.

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For more artwork by the creator of the cover art of "Pearls of Discrete Mathematics," please visit Lorene Erickson's artist site: sites.google.com/site/loreneericksonartist/.