Reading, Writing, and Proving: A Closer Look at Mathematics / Edition 2

Reading, Writing, and Proving: A Closer Look at Mathematics / Edition 2

by Ulrich Daepp, Pamela Gorkin
     
 

ISBN-10: 1441994785

ISBN-13: 9781441994783

Pub. Date: 06/29/2011

Publisher: Springer New York

This book, which is based on Pólya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematicsand ends with suggestedprojects for independent study.

Students will

Overview

This book, which is based on Pólya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematicsand ends with suggestedprojects for independent study.

Students will follow Pólya's four step approach:analyzing the problem, devising aplan to solve the problem, carrying out that plan, and thendetermining the implication of the result. In addition tothe Pólyaapproach to proofs, this book placesspecial emphasis on reading proofscarefully and writingthem well. The authors have included a wide variety of problems,examples, illustrations andexercises,some withhints and solutions, designed specificallyto improve the student's ability toread and write proofs.

Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.

Product Details

ISBN-13:
9781441994783
Publisher:
Springer New York
Publication date:
06/29/2011
Series:
Undergraduate Texts in Mathematics Series
Edition description:
2nd ed. 2011
Pages:
378
Product dimensions:
6.20(w) x 9.30(h) x 1.10(d)

Table of Contents

-Preface.-1. The How, When, and Why of Mathematics.- 2. Logically Speaking.- 3.Introducing the Contrapositive and Converse.- 4. Set Notation and Quantifiers.- 5. Proof Techniques.- 6. Sets.- 7. Operations on Sets.- 8. More on Operations on Sets.- 9. The Power Set and the Cartesian Product.- 10. Relations.- 11. Partitions.- 12. Order in the Reals.- 13. Consequences of the Completeness of (\Bbb R).- 14. Functions, Domain, and Range.-15. Functions, One-to-One, and Onto.- 16. Inverses.- 17. Images and Inverse Images.- 18. Mathematical Induction.- 19. Sequences.- 20. Convergence of Sequences of Real Numbers.- 21. Equivalent Sets.- 22. Finite Sets and an Infinite Set.- 23. Countable and Uncountable Sets.- 24. The Cantor-Schröder-Bernstein Theorem.- 25. Metric Spaces.- 26. Getting to Know Open and Closed Sets.- 27. Modular Arithmetic.- 28. Fermat’s Little Theorem.- 29. Projects.- Appendix.- References.- Index.

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >