Every mathematician (beginner, amateur, and professional alike) thrills to find simple, elegant solutions to seemingly difficult problems. Such happy resolutions are called 'aha! solutions,' a phrase popularized by mathematics and science writer Martin Gardner. Aha! solutions are surprising, stunning, and scintillating: they reveal the beauty of mathematics. This collection includes one hundred problems in the areas of arithmetic, geometry, algebra, calculus, probability, number theory, and combinatorics. The problems start out easy and generally get more difficult as you progress through the book. A few solutions require the use of a computer. An important feature of the book is the discussion of related mathematics that follows the solution of each problem. This material is there to entertain and inform you or point you to new questions.
Martin Erickson is Professor of Mathematics at Truman State University. He received his PhD at University of Michigan in 1987. He has authored three mathematics textbooks: Introduction to Number Theory (with Anthony Vazzana; Chapman & Hall), Introduction to Combinatorics (Wiley), and Principles of Mathematical Problem Solving (with Joe Flowers; Prentice-Hall). He is a member of the American Mathematical Society and the Mathematical Association of America.