Bücher der Reihe Problem Books in Mathematics

With problems from National and International Mathematical Olympiads

This book is aimed to undergraduate STEM majors and to researchers using ordinary differential equations. It covers a wide range of STEM-oriented differential equation problems that can be solved using computational power series methods. Many examples are illustrated with figures and each chapter ends with discovery/research questions most of which are accessible to undergraduate students, and almost all of which may be extended to graduate level research. Methodologies implemented may also be useful for researchers to solve their differential equations analytically or numerically. The textbook can be used as supplementary for undergraduate coursework, graduate research, and for independent study.

The large number of popular books on logic has given rise to the hope that by applying mathematical logic, students will finally learn how to distinguish between necessary and sufficient conditions and other points of logic in the college course in mathematics.

This concise book covers the classical tools of Partial Differential Equations Theory in today's science and engineering. The rigorous theoretical presentation includes many hints, and the book contains many illustrative applications from physics.

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.

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.

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

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

What is particularly pleasant is the fact that the authors are quite successful in giving to the reader the feeling behind the demonstrations which are sketched. This really enhances the value of this book and puts it at the level of a particularly interesting reference tool.

This second volume in a two-volume series provides an extensive collection of conjectures and open problems in graph theory.

With problems from National and International Mathematical Olympiads

This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks.

Versatile and comprehensive in content, this book of problems will appeal to students in nearly all areas of mathematics.

Written in the Socratic/Moore method, this book presents a sequence of problems which develop aspects in the field of semigroups of operators. The reader can discover important developments of the subject and quickly arrive at the point of independent research.

This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years.

Exercises in Analysis will be published in two volumes. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic. This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership.

This unique collection of new and classical problems provides full coverage of algebraic inequalities. Algebraic Inequalities can be considered a continuation of the book Geometric Inequalities: Methods of Proving by the authors. This book can serve teachers, high-school students, and mathematical competitors.

The main idea of this approach is to start from relatively easy problems and "step-by-step" increase the level of difficulty toward effectively maximizing students' learning potential. In addition to providing solutions, a separate table of answers is also given at the end of the book.

This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability.

This second volume in a two-volume series provides an extensive collection of conjectures and open problems in graph theory.

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.

This book offers tools for solving problems specializing in three topics of mathematical analysis: limits, series and fractional part integrals. Includes a section of Quickies: problems which have had uexpectedly succinct solutions, as well as Open Problems.

This is the latest edition of the ultimate collection of challenging probems from The International Mathematical Olympiad (IMO) of high-school-level mathematics problems. This volume collects 143 new problems, picking up where the 1959-2004 edition left off.

Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems.

With problems from National and International Mathematical Olympiads

This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis.

This unique collection of new and classical problems provides full coverage of geometric inequalities. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities.

With problems from National and International Mathematical Olympiads

With problems from National and International Mathematical Olympiads