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Analysis with an Introduction to Proof, 6th edition

  • Steven R. Lay, 
  • Richard G Ligo

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Overview

Hallmark features of this title

  • Over 250 true/false questions are unique to the text and tied to the narrative; perfect for stimulating class discussion and debate.
  • More than 100 practice problems throughout provide a simple problem for students to apply what they have just read. Answers are provided just prior to the exercises for reinforcement.
  • Exceptionally high-quality drawings illustrate key ideas.
  • Numerous examples and more than 1,000 exercises offer essential breadth and depth of practice.
  • Fill-in-the-blank proofs guide students in the art of writing proofs.
  • Review of Key Terms after each section emphasizes the importance of definitions and language in mathematics and helps students organize studying.

Published by Pearson (September 1st 2023) - Copyright © 2024

ISBN-13: 9780137871735

Subject: Advanced Math

Category: Intro to Proof / Transition to Advanced Math

Table of contents

  • 1. Logic and Proof
  • 1.1 Logical Connectives
  • 1.2 Quantifiers
  • 1.3 Techniques of Proof: I
  • 1.4 Techniques of Proof: II
  • 2. Sets and Functions
  • 2.1 Basic Set Operations
  • 2.2 Relations
  • 2.3 Functions
  • 2.4 Cardinality
  • 2.5 Axioms for Set Theory
  • 3. The Real Numbers
  • 3.1 Natural Numbers and Induction
  • 3.2 Ordered Fields
  • 3.3 The Completeness Axiom
  • 3.4 Topology of the Real Numbers
  • 3.5 Compact Sets
  • 3.6 Metric Spaces
  • 4. Sequences
  • 4.1 Convergence
  • 4.2 Limit Theorems
  • 4.3 Monotone Sequences and Cauchy Sequences
  • 4.4 Subsequences
  • 5. Limits and Continuity
  • 5.1 Limits of Functions
  • 5.2 Continuous Functions
  • 5.3 Properties of Continuous Functions
  • 5.4 Uniform Continuity
  • 5.5 Continuity in Metric Space
  • 6. Differentiation
  • 6.1 The Derivative
  • 6.2 The Mean Value Theorem
  • 6.3 L’Hôspital’s Rule
  • 6.4 Taylor’s Theorem
  • 7. Integration
  • 7.1 The Riemann Integral
  • 7.2 Properties of the Riemann Integral
  • 7.3 The Fundamental Theorem of Calculus
  • 8. Infinite Series
  • 8.1 Convergence of Infinite Series
  • 8.2 Convergence Tests
  • 8.3 Power Series
  • 9. Sequences and Series of Functions
  • 9.1 Pointwise and Uniform Convergence
  • 9.2 Application of Uniform Convergence
  • 9.3 Uniform Convergence of Power Series
Glossary of Key Terms
References
Hints for Selected Exercises
Index

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