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analysis with an introduction to proof steven lay [pdf]

### Analysis With an Introduction to Proof (4E) by Steven R. Lay

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Analysis with an Introduction to Proof, Fifth 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. 1. Logic and Proof 2. Sets and Functions 3. The Real Numbers 4. Sequences 5. Limits and Continuity 6. Differentiation 7. Integration 8. Infinite Series Steven R. Lay Glossary of Key Terms Index
For courses in undergraduate Analysis and Transition to Advanced Mathematics. Analysis with an Introduction to Proof, Fifth 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.
To understand mathematics and mathematical arguments, it is necessary to have a solid understanding of logic and the way in which known facts can be combined to prove new facts. Although many people consider themselves to be logical thinkers, the thought patterns developed in everyday living are only suggestive of and not totally adequate for the precision required in mathematics. In this chapter we take a careful look at the rules of logic and the way in which mathematical arguments are constructed. Section 1 presents the logical connectives that enable us to build compound statements from simpler ones. Section 2 discusses the role of quantifiers. Sections 3 and 4 analyze the structure of mathematical proofs and illustrate the various proof techniques by means of examples.

Book Detail :-
Title: Analysis With an Introduction to Proof
Edition: 4th
Author(s): Steven R. Lay
Publisher: Pearson
Series:
Year: 2004
Pages: 394
Type: PDF
Language: English
ISBN: 0131481010, 978-0131481015
Country: US
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Author Steven R. 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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Book Contents :-
Analysis With an Introduction to Proof (4E) written by Steven R. Lay cover the following topics.
1. Logic and Proof
2. Sets and Functions
3. The Real Numbers
4. Sequences
5. Limits and Continuity
6. Differentiation
7. Integration
8. Infinite Series
Glossary of Key Terms

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