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Introduction to Real Analysisby Michael J. Schramm
Synopses & ReviewsPublisher Comments:This text forms a bridge between courses in calculus and real analysis. It focuses on the construction of mathematical proofs as well as their final content. Suitable for upperlevel undergraduates and graduate students of real analysis, it also provides a vital reference book for advanced courses in mathematics.The fourpart treatment begins with an introduction to basic logical structures and techniques of proof, including discussions of the cardinality concept and the algebraic and order structures of the real and rational number systems. Part Two presents indepth examinations of the completeness of the real number system and its topological structure. Part Three reviews and extends the previous explorations of the real number system, and the final part features a selection of topics in real function theory. Numerous and varied exercises range from articulating the steps omitted from examples and observing mechanical results at work to the completion of partial proofs within the text. Synopsis:This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition. Synopsis:This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition. About the AuthorMichael J. Schramm has a Ph.D. from Syracuse University.
Table of ContentsPreface Part One: Preliminaries Chapter 1. Building Proofs Chapter 2. Finite, Infinite, and Even Bigger Chapter 3. Algebra of the Real Numbers Chapter 4. Ordering, Intervals, and Neighborhoods Part Two: The Structure of the Real Number System Chapter 5. Upper Bounds and Suprema Chapter 6. Nested Intervals Chapter 7. Cluster Points Chapter 8. Topology of the Real Numbers Chapter 9. Sequences Chapter 10. Sequences and the Big Theorem Chapter 11. Compact Sets Chapter 12. Connected Sets Part Three: Topics from Calculus Chapter 13. Series Chapter 14. Uniform Continuity Chapter 15. Sequences and Series of Functions Chapter 16. Differentiation Chapter 17. Integration Chapter 18. Interchanging Limit Processes Part Four: Selected Shorts Chapter 19. Increasing Functions Chapter 20. Continuous Functions and Differentiability Chapter 21. Continuous Functions and Integrability Chapter 22. We Build the Real Numbers References and further reading Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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