``My mind rebels at stagnation. Give me problems, give me work, give me the most abstruse cryptogram, or the most intricate analysis, and I am in my own proper atmosphere. I can dispense then with artificial stimulants. But I abhor the dull routine of existence. I crave for mental exaltation.''
Sir Arthur Conan Doyle, Sherlock Holmes, The Sign of Four, 1890
Martin J. Erickson
Contact: martin (dot) erickson (at) gmail (dot) com
My math blog: martinerickson.blogspot.com
Also see: sites.google.com/site/martinerickson/ and mathacadabra.com.
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.
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 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 focusing 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 illustrates gems in the field of discrete mathematics. 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 covers how to be a math student, how to study and do homework, how to write mathematics, and how to use computer tools such as LaTeX and computer algebra systems. Over 200 exercises.
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.
Mathematics for the Liberal Arts, with Donald Bindner and Joe Hemmeter (Wiley)
This book is for liberal arts college students. It introduces and explores mathematical concepts in the setting of history. It explains the mathematics in a down-to-earth style. It gives many examples and problems with solutions.