A Primer of Real Analysis by Dan Sloughter
A Primer of Real Analysis - Table of Contents
1. Fundamentals
2. Sequences and Series
3. Cardinality
4. Topology of the Real Line
5. Limits and Continuity
6. Derivatives
7. Integrals
8. More Functions
What You Will Learn in A Primer of Real Analysis
"A Primer of Real Analysis" by "Dan Sloughter" is a concise and approachable introduction to the fundamentals of "real analysis". Designed for students who have completed calculus and are beginning to explore rigorous mathematics, the book focuses on clear explanations and step-by-step development of essential concepts. It emphasizes understanding over memorization, helping students gain confidence in reading and constructing mathematical proofs. The writing is student-friendly, with examples that illustrate abstract ideas in a concrete, intuitive manner.
The text covers key topics in real analysis, including "sequences and series", limits and continuity, derivatives and integrals, and the topology of the real line. Each topic is presented with careful definitions, theorems, and proofs, enabling students to see the logical connections that underpin the subject. Exercises are included to reinforce concepts and encourage active engagement, helping learners build strong "proof-based reasoning" and develop mathematical maturity.
A major advantage of this book is that it is freely available as an "open textbook", making it accessible to a wide audience of students, instructors, and self-learners. Overall, "A Primer of Real Analysis" provides a solid foundation in real analysis, preparing students for more advanced courses while fostering deep "conceptual understanding" and appreciation of rigorous mathematics. Its clarity, structure, and accessibility make it an excellent resource for learning "undergraduate analysis".
Book Details & Specifications
Title:
A Primer of Real Analysis by Dan Sloughter
Publisher:
Dan Sloughter
Year:
2018
Pages:
157
Type:
PDF
Language:
English
ISBN-10 #:
B07GVQVMBB
ISBN-13 #:
License:
CC BY-NC-SA 3.0
Amazon:
Amazon
About the Author: Dan Sloughter
The author
Dan Sloughter
is a mathematician and professor at "Furman University", recognized for his dedication to "Mathematics Education" and clear, student-focused teaching. He has authored several instructional texts aimed at making complex concepts accessible to undergraduate learners. His book "A Primer of Real Analysis" serves as a concise introduction to "Real Analysis", guiding students through sequences, continuity, derivatives, and integrals. Designed as an "Introductory Text", it emphasizes understanding rigorous proofs and developing logical reasoning skills, making it ideal for those transitioning from calculus to advanced mathematical thinking.
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