Bøger i Problem Books in Mathematics serien

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. Cp-theory has an important role in the classification and unification of heterogeneous results from each of these areas of research. Through over 500 carefully selected problems and exercises, this volume provides a self-contained introduction to Cp-theory and general topology. By systematically introducing each of the major topics in Cp-theory, this volume is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research. Key features include:- A unique problem-based introduction to the theory of function spaces.- Detailed solutions to each of the presented problems and exercises.- A comprehensive bibliography reflecting the state-of-the-art in modern Cp-theory.- Numerous open problems and directions for further research.This volume can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists studying Cp-theory and related topics. This book also provides numerous topics for PhD specialization as well as a large variety of material suitable for graduate research.

This book convenes a selection of 200 mathematical puzzles with original solutions, all celebrating the inquisitive and inspiring spirit of Nobuyuki "Nob" Yoshigahara - a legend in the worldwide community of mathematical and mechanical puzzles.

This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics.

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.

While many problems can be solved at the undergraduate level, a number of challenging real-life applications have also been included as a way to motivate further research in this vast and fascinating field.

Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.

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

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.

Designed to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises. Most chapters open with a review followed by theoretical and programming exercises, with detailed solutions provided for all problems including programs.

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.

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.

With problems from National and International Mathematical Olympiads

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.

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

This text records the problems given for the first 15 annual undergraduate mathematics competitions, held in March each year since 2001 at the University of Toronto.

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.

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 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.

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.

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 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.

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

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.

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.

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.

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 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.