Books like Mathletics by Wayne L. Winston

An encyclopedic reference edited by Fields Medalist Timothy Gowers, the Princeton Companion to Mathematics offers nearly 200 essays by leading mathematicians, covering key concepts, historical development, and interdisciplinary impact of modern mathematics.

Problem-Solving Strategies is a unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. The discussion of problem-solving strategies is extensive. It is written for trainers and participants of contests of all levels up to the highest level: IMO, Tournament of the Towns, and the noncalculus parts of the Putnam competition. It will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week," "problem of the month," and "research problem of the year" to their students, thus bringing a creative atmosphere into their classrooms with continuous discussions of mathematical problems. This volume is a must-have for instructors wishing to enrich their teaching with some interesting nonroutine problems and for individuals who are just interested in solving difficult and challenging problems.

What is a paradox? - Paradoxes for everyone - Paradoxes in arithmetic, geometry, probability, logic, higher mathematics - Algebraic fallacies - Geometrical fallacies - Paradoxes of the infinite; Pythagorean theorum - Numbers - Fibonnaci series - Circles - Curves