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Challenge: Can you find all the integers $a$, $b$, $c$ satisfying $2a^ + 3b^ = 5c^$? Looks simple, and there are in fact a number of easy solutions. But most of them turn out to be anything but obvious! There are infinitely many possibilities, and as any computer will tell you, each of $a$, $b$, $c$ will usually be large. So the challenge remains ... Find all integers$a$, $b$, $c$satisfying$2a^ + 3b^ = 5c^$.

A major advance in number theory means this book can give an easy answer to this and countless similar questions. The idea behind the approach is transforming...

This is an informal and accessible introduction to plane algebraic curves that also serves as a natural entry point to algebraic geometry. There is a unifying theme to the book: give curves enough living space and beautiful theorems will follow. This book provides the reader with a solid intuition for the subject, while at the same time keeping the exposition simple and understandable, by introducing abstract concepts with concrete examples and pictures. It can be used as the text for an undergraduate course on plane algebraic curves, or as a companion to algebraic geometry at graduate level....

A collection of over 250 multiple-choice problems to challenge and delight everyone from school students to professional mathematicians.

Hassler Whitney was a giant of twentieth-century mathematics. This biography paints a picture of him and includes dozens of revealing anecdotes. Mathematically, he had a rare detector that went off whenever he spotted a piece of mathematical gold, and he would then draw countless pictures, gradually forging a path from hunch to proof. This geometric path is seldom reflected in the rigor of his formal papers, but thanks to a close friendship and many conversations over decades, author Kendig was able to see how he actually worked. This book shows this through accessible accounts of his major...