**Analysis With An Introduction to Proof 5th Edition 5th INTENATIONAL Edition by Steven Lay, ISBN-13: 978-1292040240**

[PDF eBook eTextbook]

- Publisher: Pearson; 5th INTERNATIONAL edition

- Language: English
- 365 pages
- ISBN-10: 1292040246
- ISBN-13: 978-1292040240

For courses in undergraduate Analysis and Transition to Advanced **Mathematics**.

* Analysis with an Introduction to Proof, Fifth INTERNATIONAL Edition* helps fill in the groundwork students need to succeed in real analysis―often considered the most difficult course in the undergraduate curriculum. By introducing logic and emphasizing the structure and nature of the arguments used, this text helps students move carefully from computationally oriented courses to abstract mathematics with its emphasis on proofs. Clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers make this text readable, student-oriented, and teacher- friendly.

**Table of Contents:**

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

* Steven Lay* is a Professor of Mathematics at Lee University in Cleveland, TN. He received M.A. and Ph.D. degrees in mathematics from the

*at Los Angeles. He has authored three books for college students, from a senior level text on Convex Sets to an Elementary Algebra text for underprepared students. The latter book introduced a number of new approaches to preparing students for algebra and led to a series of books for middle school math. Professor Lay has a passion for teaching, and the desire to communicate mathematical ideas more clearly has been the driving force behind his writing. He comes from a family of mathematicians, with his father Clark Lay having been a member of the School Mathematics Study Group in the 1960s and his brother David Lay authoring a popular text on Linear Algebra. He is a member of the American Mathematical Society, the Mathematical Association of America, and the Association of Christians in the Mathematical Sciences.*

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