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 many problems unorganized by topic. 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.
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 and error-correcting codes. It all also presents 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.
Tutorials
Getting Started With Mathematica
