Elementary Real Analysis by Brian S. Thomson
Elementary Real Analysis - Table of Contents
1. Properties of the Real Numbers
2. Sequences
3. Infinite Sums
4. Sets of Real Numbers
5. Continuous Functions
6. More on Continous Functions and Sets
7. Differentiation
8. The Integral
9. Sequences and Series of Functions
10. Power Series
11. The Euclidean Spaces Rn
12. Differentiation on Rn
13. Metric Spaces
What You Will Learn in Elementary Real Analysis
"Elementary Real Analysis" by Brian S. Thomson, co-authored with Judith B. Bruckner and Andrew M. Bruckner, is an undergraduate "real analysis" textbook that bridges the gap between calculus and rigorous mathematics. The book revisits familiar calculus concepts such as limits, continuity, and "differentiation", but presents them with precise definitions and a focus on logical reasoning. It also introduces more advanced topics like sequences, "series", metric spaces, and uniform convergence to provide a comprehensive foundation in analysis.
The text is written in a clear and accessible style, emphasizing "proof-writing" and conceptual understanding. Each chapter includes carefully structured examples and exercises that allow students to apply definitions and theorems, helping them develop strong analytical skills. The book encourages students to think critically about mathematical structures, understand the reasoning behind results, and write precise, well-organized proofs, rather than relying on memorization.
Overall, "Elementary Real Analysis" is ideal for students transitioning to higher-level mathematics. It builds strong "understanding", reasoning, and problem-solving abilities, preparing learners for advanced courses in analysis, topology, and other theoretical areas. With its balanced approach to rigor and accessibility, the book serves as both a classroom resource and a guide for self-study, helping students achieve confidence and mastery in real analysis.
Book Details & Specifications
Title:
Elementary Real Analysis by Brian S. Thomson
Publisher:
Prentice Hall (Pearson)
Year:
2008
Pages:
1013
Type:
PDF
Language:
English
ISBN-10 #:
143484367X
ISBN-13 #:
978-1434843678
License:
External Educational Resource
Amazon:
Amazon
About the Author: Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner
The author Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner
is a respected "mathematician" and educator, best known as co-author of "Elementary Real Analysis" with Judith B. Bruckner and Andrew M. Bruckner. His work focuses on helping students transition from calculus to rigorous, proof-based "real analysis", emphasizing clarity and logical reasoning. Thomson’s teaching and writing foster strong "conceptual understanding" through precise definitions, structured examples, and well-designed exercises. By emphasizing "proof-writing" and analytical thinking, he equips students with essential "problem-solving" skills. His work remains influential in undergraduate "mathematics education", providing a solid foundation for advanced study in analysis and theoretical mathematics.
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