Elementary Real Analysis: A Practical Introduction provides a robust foundation for success in real analysis, presenting traditional material in an accessible, engaging manner with the support of clearly outlined learning objectives and exercises.
Organized into two well-designed sections, the book begins with a comprehensive review of prerequisite knowledge. Section I includes chapters such as “Sets,” “Properties of Real Numbers,” “Properties of Integers,” and “Functions and Relations,” each accompanied by a wealth of exercises that encourage exploration and practice. These chapters lay the foundation for the second section which delves into advanced topics such as sequences, continuity, and differentiation, culminating in a synthesis of concepts that prepares students for further study of mathematical analysis. For easy reference, two appendices entitled “Mathematical Statements” and “Proof Methods” provide the reader with an accessible reference to the essential language and techniques of proof writing.
Whether used in a classroom or for self-directed learning, Elementary Real Analysis: A Practical Introduction is a vital companion for students seeking an introduction to real analysis, bridging the gap between basic principles and advanced mathematical concepts with clarity and precision.
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Table of Contents
Section I Background Material1. Sets
2. Properties of Real Numbers
3. Properties of Integers
Section II Elementary Topics
4. Functions and Relations
5. Sequences Part 1
6. Continuity and Differentiation
Section III Advanced Topics
7. Sequences Part 2
8. Putting It All Together
9. Riemann Integration Part 1
10. Riemann Integration Part 2
Authors
Thomas Bieske Chair of the Undergraduate Committee-Upper Level, Department of Mathematics and Statistics, University of South Florida, Tampa., USA.Professor Thomas Bieske earned his PhD from the University of Pittsburgh, United States, in 1999. His research concerns partial differential equations and analysis in metric spaces, with a focus on sub-Riemannian spaces. Professor Bieske is currently serving as the Department of Mathematics and Statistics Chair of the Undergraduate Committee-Upper Level, focusing on the performance of mathematics and statistics majors in upper-level courses, at the University of South Florida, Tampa, United States.
