An Introduction to Proof through Real Analysis
by Daniel J. Madden, Jason A. Aubrey
1st Edition
Publisher: John Wiley & Sons, Inc.
Book Details
| Print ISBN | 9781119314721 |
| eText ISBN | 9781119314745 |
| Publisher | John Wiley & Sons, Inc. |
| Publishing Year | 2017 |
| Edition | 1st Edition |
| Language | English |
An Introduction to Proof through Real Analysis, 1st Edition, is a mathematics textbook that provides an accessible introduction to mathematical proof using concepts from real analysis. The volume presents foundational systems of numbers alongside formal deductive techniques.
Initial coverage focuses on the algebra of natural numbers, integers, rational numbers, ordered fields, and real numbers. The volume also introduces fundamental tools of mathematical practice, including formal logic, sets, relations, and functions.
In addition to establishing core theory, the text provides targeted advice for constructing proofs. Later discussions examine topological spaces, compact sets, and continuous functions.
Table of Contents
Chapter 1: Beginnings
Chapter 2: The Algebra of the Natural Numbers
Chapter 3: Integers
Chapter 4: Rational Numbers
Chapter 5: Ordered Fields
Chapter 6: The Real Numbers
Chapter 7: Logic
Chapter 8: Advice for Constructing Proofs
Chapter 9: Sets
Chapter 10: Relations
Chapter 11: Functions
Chapter 12: Images and Preimages
Chapter 13: Final Basic Notions
Chapter 14: ℕ, ℤ, and ℚ
Chapter 15: Ordered Fields and the Real Numbers
Chapter 16: Topology
Chapter 17: Theorems in Topology
Chapter 18: Compact Sets
Chapter 19: Continuous Functions
Chapter 20: Continuity and Topology
Chapter 21: A Few Final Observations
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