Reading, Writing, and Proving: A Closer Look at Mathematics [Undergraduate Texts

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ISBN
9781441994783
Kategorie

Über dieses Produkt

Product Identifiers

Publisher
Springer New York
ISBN-10
1441994785
ISBN-13
9781441994783
eBay Product ID (ePID)
108172475

Product Key Features

Number of Pages
Xiv, 378 Pages
Language
English
Publication Name
Reading, Writing, and Proving : a Closer Look at Mathematics
Subject
Study & Teaching, Number Theory, Logic, Technical Writing, Mathematical Analysis
Publication Year
2011
Type
Textbook
Author
Pamela Gorkin, Ulrich Daepp
Subject Area
Mathematics, Technology & Engineering
Series
Undergraduate Texts in Mathematics Ser.
Format
Hardcover

Dimensions

Item Weight
26.3 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Edition Number
2
Intended Audience
Scholarly & Professional
LCCN
2011-931085
Reviews
From the reviews of the second edition:This is at heart a fairly conventional transition text, but it has a number of features that encourage students to practice and improve their mathematical reading, writing, and proving skills. … The book is primarily concerned with an exposition of those parts of mathematics in which students need a more thorough grounding before they can work successfully in upper-division undergraduate courses. … a mathematically-conventional but pedagogically-innovative take on transition courses. (Allen Stenger, The Mathematical Association of America, September, 2011), From the reviews of the second edition: "This is at heart a fairly conventional transition text, but it has a number of features that encourage students to practice and improve their mathematical reading, writing, and proving skills. ... The book is primarily concerned with an exposition of those parts of mathematics in which students need a more thorough grounding before they can work successfully in upper-division undergraduate courses. ... a mathematically-conventional but pedagogically-innovative take on transition courses." (Allen Stenger, The Mathematical Association of America, September, 2011), From the reviews of the second edition: "The book is written in an informal way, which could please the beginners and not offend the more experienced reader. A reader can find a lot of problems for independent study as well as a lot of illustrations encouraging him/her to draw pictures as an important part of the process of mathematical thinking." -- European Mathematical Society , September 2011 "Several areas like sets, functions, sequences and convergence are dealt with and several exercises and projects are provided for deepening the understanding. ...It is the impression of the author of this review that the book can be particularly strongly recommended for teacher students to enable them to catch and transfer the "essence" of mathematical thinking to their pupils. But also everybody else interested in mathematics will enjoy this very well written book. --Burkhard Alpers (Aalen), zbMATH "The book is primarily concerned with an exposition of those parts of mathematics in which students need a more thorough grounding before they can work successfully in upper-division undergraduate courses. ... a mathematically-conventional but pedagogically-innovative take on transition courses." --Allen Stenger, The Mathematical Association of America , September, 2011, From the reviews of the second edition: This is at heart a fairly conventional transition text, but it has a number of features that encourage students to practice and improve their mathematical reading, writing, and proving skills. … The book is primarily concerned with an exposition of those parts of mathematics in which students need a more thorough grounding before they can work successfully in upper-division undergraduate courses. … a mathematically-conventional but pedagogically-innovative take on transition courses. (Allen Stenger, The Mathematical Association of America, September, 2011)
Dewey Edition
22
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
510
Table Of Content
-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.
Synopsis
This book, which is based on P lya'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 mathematics and ends with suggested projects for independent study. Students will follow P lya's four step approach: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. In addition to the P lya approach to proofs, this book places special emphasis on reading proofs carefully and writing them well. The authors have included a wide variety of problems, examples, illustrations and exercises, some with hints and solutions, designed specifically to improve the student's ability to read 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., This book not only introduces proof techniques and other foundational principles of higher mathematics, but also helps students develop the necessary abilities to read, write and prove using mathematical definitions, examples and theorems., 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 mathematics and ends with suggested projects for independent study. Students will follow Pólya's four step approach: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. In addition to the Pólya approach to proofs, this book places special emphasis on reading proofs carefully and writing them well. The authors have included a wide variety of problems, examples, illustrations and exercises, some with hints and solutions, designed specifically to improve the student's ability to read and write proofs. Historical connections are made throughout the text, and students are encouraged to use the rather extensivebibliography 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.
LC Classification Number
QA8.9-10.3

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