Books in the Problem Books in Mathematics series

Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping.

Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research. The sets of problems are comprised in Part I.

Examining Sets and Relations.- Investigating Basic Properties of Functions.- Defining Distance in Sets.- Using Mathematical Induction.- Investigating Convergence of Sequences and Looking for Their Limits.- Dealing with Open, Closed and Compact Sets.- Finding Limits of Functions.- Examining Continuity and Uniform Continuity of Functions.- Finding Derivatives of Functions.- Using Derivatives to Study Certain Properties of Functions.- Dealing with Higher Derivatives and Taylor''s Formula.- Looking for Extremes and Examine Functions.- Investigating the Convergence of Series.- Finding Indefinite Integrals.- Investigating the Convergence of Sequences and Series of Functions.

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.

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.

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 second of two Exercises in Analysis volumes covers problems in five core topics of mathematical analysis: Function Spaces, Nonlinear and Multivalued Maps, Smooth and Nonsmooth Calculus, Degree Theory and Fixed Point Theory, and Variational and Topological Methods.

The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems and dimension theory.

This volume of Vladimir Tkachuk's series covers all the major topics in Cp-theory, providing 500 selected problems and exercises as well as their complete solutions and guiding the student from basic topological principles to the frontiers of modern research.

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.

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.

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.

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.

With problems from National and International Mathematical Olympiads

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 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.

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.

With problems from National and International Mathematical Olympiads