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Other titles in the Problem Books in Mathematics series:
A Problem Book in Real Analysis (Problem Books in Mathematics)by Asuman G. Aksoy
Synopses & Reviews
Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying. The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis. Prerequisites for the reader are a robust understanding of calculus and linear algebra.
This book systematically solves the problems related to the core concepts of most analysis courses. The wide variety of exercises presented in this book range from the computational to the more conceptual and vary in difficulty.
From the reviews:'Spread out over 11 chapters, this is a collection of 319 problems in what used to be called Advanced Calculus. ' The authors see their book primarily as an aid to undergraduates ' but I view it as being helpful to teachers in supplementing their courses or in preparing exams. ' However, kept on a course reserve shelf of an academic library, the book under review might entice and benefit the more dedicated student. It certainly merits the attention of instructors of elementary analysis.' (Henry Ricardo, The Mathematical Association of America, June, 2010)
Table of Contents
Preface.- Elementary Logic and Set Theory.- Real Numbers.- Sequences.- Limits of Functions.- Continuity.- Differentiability.- Integration.- Series.- Metric Spaces.- Fundamentals of Topology.- Sequences and Series of Functions.- Index.- References.
What Our Readers Are Saying
Science and Mathematics » Mathematics » Analysis General