Bücher der Reihe Problem Books in Mathematics

This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics.

However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses.

The contents are intended to provide graduate and ad vanced undergraduate students as well as the general mathematical public with a modern treatment of some theorems and examples that constitute a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology.

This new edition offers solved exercises on differentiable manifolds, Lie groups, fibre bundles and Riemannian manifolds. Includes exercises ranging from elementary computations to sophisticated tools, and studies solved problems of differentiable manifolds.

Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition.

Written as a supplement to Marcel Berger's popular two-volume set, Geometry I and II (Universitext), this book offers a comprehensive range of exercises, problems, and full solutions.

A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students.

This book provides the mathematical tools and problem-solving experience needed to successfully compete in high-level problem solving competitions.