Introduction to Real Analysis (Dover Books on Mathematics)

Book Details

• Author: Schramm, Michael J.

• Brand: Dover

• Edition: 3005th Edition

• Binding: Paperback

• Number of Pages: 384

• Release Date: 24-11-2008

• EAN: 9780486469133

• Dimensions: 8.5 x 5.6 x 1.7 inches

About The Book

This book by Michael J. Schramm serves as a bridge between calculus and real analysis, offering a detailed and structured approach to the concepts of mathematical proof. It is particularly suited for upper-level undergraduates and graduate students in real analysis, and also acts as a reference for advanced mathematics courses.

The text is divided into four parts:

1. Introduction to Basic Logical Structures and Proof Techniques: Covers essential proof methods and the concept of cardinality, including algebraic and order structures of the real and rational number systems.

2. Completeness of the Real Number System: In-depth exploration of the completeness of the real number system and its topological properties.

3. Extended Review of the Real Number System: Revisits and further develops concepts explored in the second part, with a focus on deeper understanding.

4. Real Function Theory: Final section featuring various topics related to real functions.

The book includes numerous exercises ranging from basic exercises of articulating omitted steps to more complex tasks like completing partial proofs. This makes it an excellent resource for reinforcing the concepts covered.

Table of Contents

• Chapter 1: Introduction to Mathematical Proofs

• Chapter 2: Cardinality and Algebraic Structures

• Chapter 3: Topology of the Real Numbers

• Chapter 4: Completeness of the Real Numbers

• Chapter 5: Advanced Topics in Real Function Theory

• Chapter 6: Exercises and Solutions

• Index