Elementary Real Analysis
A Practical Introduction
- 1st Edition - February 1, 2026
- Author: Thomas Bieske
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 3 6 7 4 7 - 2
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 3 6 7 4 8 - 9
Elementary Real Analysis: A Practical Introduction provides a robust foundation for success in real analysis, presenting traditional material in an accessible, engaging manner… Read more
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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 three well-designed sections, the book begins with a comprehensive review of prerequisite knowledge. Section I includes chapters such as "Sets," "Mathematical Statements," and "Proof Methods", which establish the essential language and techniques of advanced mathematics. Section II explores the properties of real numbers, integers, and functions, each accompanied by a wealth of exercises that encourage exploration and practice. The final section delves into advanced topics such as sequences, continuity, and differentiation, culminating in a synthesis of concepts that prepares students for rigorous mathematical analysis.
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.
Organized into three well-designed sections, the book begins with a comprehensive review of prerequisite knowledge. Section I includes chapters such as "Sets," "Mathematical Statements," and "Proof Methods", which establish the essential language and techniques of advanced mathematics. Section II explores the properties of real numbers, integers, and functions, each accompanied by a wealth of exercises that encourage exploration and practice. The final section delves into advanced topics such as sequences, continuity, and differentiation, culminating in a synthesis of concepts that prepares students for rigorous mathematical analysis.
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.
- Lays a strong foundation for success in first real analysis courses, presenting traditional material in a contemporary and engaging manner
- Introduces essential concepts and relevant background knowledge with an accessible approach
- Caters to junior and senior undergraduate mathematics students who have completed calculus and linear algebra, as well as early graduate-level students seeking deeper insights
- Fills the gap between basic principles and advanced mathematical concepts, ensuring clarity and precision for transitioning to rigorous analysis
- Includes a variety of exercises in each chapter, promoting exploration and practice of key topics to reinforce understanding and foster independent learning
Junior and Senior level undergraduate or early graduate level mathematics students
Section I - Background Material
1. 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
1. 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
- Edition: 1
- Published: February 1, 2026
- Language: English
TB
Thomas Bieske
Professor Thomas Bieske earned his Ph.D. from the University of Pittsburgh in 1999. His research concerns partial differential equations and analysis in metric spaces, with a focus on sub-Riemannian spaces. After a brief hiatus, Professor Bieske is currently serving a second stint 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 Central Florida, Tampa.
Affiliations and expertise
Chair of the Undergraduate Committee-Upper Level, Department of Mathematics and Statistics, University of Central Florida, Tampa., USA