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Analysis With An Introduction to Proof 5th Edition 5th INTENATIONAL Edition by Steven Lay

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

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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:

  1. Title Page
  2. Copyright Page
  3. Contents
  4. Preface
  5. Chapter 1 Logic and Proof
  6. Section 1.1 Logical Connectives
  7. Section 1.2 Quantifiers
  8. Section 1.3 Techniques of Proof: I
  9. Section 1.4 Techniques of Proof: II
  10. Chapter 2 Sets and Functions
  11. Section 2.1 Basic Set Operations
  12. Section 2.2 Relations
  13. Section 2.3 Functions
  14. Section 2.4 Cardinality
  15. Section 2.5 Axioms for Set Theory
  16. Chapter 3 The Real Numbers
  17. Section 3.1 Natural Numbers and Induction
  18. Section 3.2 Ordered Fields
  19. Section 3.3 The Completeness Axiom
  20. Section 3.4 Topology of the Real Numbers
  21. Section 3.5 Compact Sets
  22. Section 3.6 Metric Spaces
  23. Chapter 4 Sequences
  24. Section 4.1 Convergence
  25. Section 4.2 Limit Theorems
  26. Section 4.3 Monotone Sequences and Cauchy Sequences
  27. Section 4.4 Subsequences
  28. Chapter 5 Limits and Continuity
  29. Section 5.1 Limits of Functions
  30. Section 5.2 Continuous Functions
  31. Section 5.3 Properties of Continuous Functions
  32. Section 5.4 Uniform Continuity
  33. Section 5.5 Continuity in Metric Spaces
  34. Chapter 6 Differentiation
  35. Section 6.1 The Derivative
  36. Section 6.2 The Mean Value Theorem
  37. Section 6.3 L’Hospital’s Rule
  38. Section 6.4 Taylor’s Theorem
  39. Chapter 7 Integration
  40. Section 7.1 The Riemann Integral
  41. Section 7.2 Properties of the Riemann Integral
  42. Section 7.3 The Fundamental Theorem of Calculus
  43. Chapter 8 Infinite Series
  44. Section 8.1 Convergence of Infinite Series
  45. Section 8.2 Convergence Tests
  46. Section 8.3 Power Series
  47. Chapter 9 Sequences and Series of Functions
  48. Section 9.1 Pointwise and Uniform Convergence
  49. Section 9.2 Applications of Uniform Convergence
  50. Section 9.3 Uniform Convergence of Power Series
  51. Glossary of Key Terms
  52. References
  53. Hints for Selected Exercises
  54. 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 University of California 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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