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Analysis: With an Introduction to Proof

Analysis: With an Introduction to Proof Cover

 

Synopses & Reviews

Publisher Comments:

"Let me begin by saying that I really like this book, and I do not say that of very many books. What impresses me most is the level of motivation and explanation given for the basic logic, the construction of proofs, and the ways of thinking about proofs that this book provides in its first few sections. It felt that the author was talking to the reader the way I would like to talk to students. There was an air of familiarity there. All kinds of useful remarks were made, the type I would like to make in my lectures." — Aimo Hinkkanen, University of Illinois at Urbana

"The writing style is suitable for our students. It is clear, logical, and concise. The examples are very helpful and well-developed. The topics are thoroughly covered and at the appropriate level for our students. The material is technically accurate, and the pedagogical material is effectively presented." — John Konvalina, University of Nebraska at Omaha

Synopsis:

By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs. Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers. Offers a new boxed review of key terms after each section. Rewrites many exercises. Features more than 250 true/false questions. Includes more than 100 practice problems. Provides exceptionally high-quality drawings to illustrate key ideas. Provides numerous examples and more than 1,000 exercises. A thorough reference for readers who need to increase or brush up on their advanced mathematics skills.

Table of Contents

Chapter 1. Logic and Proof.

Section 1. Logical Connectives

Section 2. Quantifiers

Section 3. Techniques of Proof: I

Section 4. Techniques of Proof: II

    

     

2. Sets and Functions.

Section 5. Basic Set Operations

Section 6. Relations

Section 7. Functions

Section 8. Cardinality

Section 9. Axioms for Set Theory(Optional)

3. The Real Numbers.

Section 10. Natural Numbers and Induction

Section 11 Ordered Fields

Section 12 The Completeness Axiom

Section 13 Topology of the Reals

Section 14 Compact Sets

Section 15 Metric Spaces (Optional)

4. Sequences.

Section 16 Convergence

Section 17 Limit Theorems

Section 18 Monotone Sequences and Cauchy Sequences

Section 19 Subsequences

5. Limits and Continuity.

Section 20 Limits of Functions

Section 21 Continuous Functions

Section 22 Properties of Continuous Functions

Section 23 Uniform Continuity

Section 24 Continuity in Metric Space (Optional)

6. Differentiation.

Section 25 The Derivative

Section 26 The Mean Value Theorem

Section 27 L'Hospital's Rule

Section 28 Taylor's Theorem

7. Integration.

Section 29 The Riemann Integral

Section 30 Properties of the Riemann Integral

Section 31 The Fundamental Theorem of Calculus

8. Infinite Series.

Section 32 Convergence of Infinite Series

Section 33 Convergence Tests

Section 34 Power Series

9. Sequences and Series of Functions.

Section 35 Pointwise and uniform Convergence

Section 36 Application of Uniform Convergence

Section 37 Uniform Convergence of Power Series

Glossary of Key Terms

References.

Hints for Selected Exercises.

Index.

Product Details

ISBN:
9780131481015
Subtitle:
With an Introduction to Proof
Publisher:
Pearson
Author:
Lay, Steven R.
Subject:
Mathematical Analysis
Subject:
Functional Analysis
Subject:
Proof theory
Subject:
Advanced
Subject:
Mathematics : Functional Analysis
Copyright:
Edition Number:
4
Publication Date:
December 2004
Binding:
Hardback
Grade Level:
College/higher education:
Language:
English
Illustrations:
Y
Pages:
400
Dimensions:
9.3 x 8 x 1 in 916 gr

Related Subjects

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Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Mathematics » Real Analysis

Analysis: With an Introduction to Proof
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Product details 400 pages Prentice Hall - English 9780131481015 Reviews:
"Synopsis" by , By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs. Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers. Offers a new boxed review of key terms after each section. Rewrites many exercises. Features more than 250 true/false questions. Includes more than 100 practice problems. Provides exceptionally high-quality drawings to illustrate key ideas. Provides numerous examples and more than 1,000 exercises. A thorough reference for readers who need to increase or brush up on their advanced mathematics skills.
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