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This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-established mathematician will find the overall exposition engaging and enlightening. Each chapter, presented in a story-telling style, includes more than a simple collection of results on a particular topic. Each contribution conveys the history, evolution, and techniques used to solve the authors¿ favorite conjectures and open problems, enhancing the reader¿s overall comprehension and enthusiasm. The editors were inspired to create these volumes by the popular and well attended special sessions, entitled ¿My Favorite Graph Theory Conjectures," which were held at the winter AMS/MAA Joint Meeting in Boston (January, 2012), the SIAM Conference on Discrete Mathematics in Halifax (June,2012) and the winter AMS/MAA Joint meeting in Baltimore(January, 2014). In an effort to aid in the creation and dissemination of open problems, which is crucial to the growth and development of a field, the editors requested the speakers, as well as notable experts in graph theory, to contribute to these volumes.

With problems from National and International Mathematical Olympiads

Usually there is no closed-formula answer available, which is why there is no answer section, although helpful hints are often provided. This textbook offers a valuable asset for students and educators alike.

This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems. Anyone who works through the theory and problems in Part I will have acquired the background and techniques needed to do advanced studies in this area.

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

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

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.

With problems from National and International Mathematical Olympiads

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.

With problems from National and International Mathematical Olympiads

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.

Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on.

The theory of function spaces endowed with the topology of point wise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology.

A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have (or have forgotten) a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.

Many puzzles and problems presented here are either new within a problem solving context or are variations of classical problems which follow directly from elementary concepts. A small number of particularly instructive problems is taken from previous sources.

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.