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  • Textbook
  • © 2011

Reading, Writing, and Proving

A Closer Look at Mathematics

  • New to the second edition:

  • A useful appendix of formal definitions that can be used as a quick reference

  • Second edition includes new exercises, problems, and student projects

  • An electronic solutions manual for instructors and individual users

  • Includes supplementary material: sn.pub/extras

Part of the book series: Undergraduate Texts in Mathematics (UTM)

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4419-9479-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 74.95
Price excludes VAT (USA)
Hardcover Book USD 74.95
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Table of contents (29 chapters)

  1. Front Matter

    Pages i-xiii
  2. The How, When, and Why of Mathematics

    • Ulrich Daepp, Pamela Gorkin
    Pages 1-11
  3. Logically Speaking

    • Ulrich Daepp, Pamela Gorkin
    Pages 13-24
  4. Introducing the Contrapositive and Converse

    • Ulrich Daepp, Pamela Gorkin
    Pages 25-32
  5. Set Notation and Quantifiers

    • Ulrich Daepp, Pamela Gorkin
    Pages 33-46
  6. Proof Techniques

    • Ulrich Daepp, Pamela Gorkin
    Pages 47-58
  7. Sets

    • Ulrich Daepp, Pamela Gorkin
    Pages 59-71
  8. Operations on Sets

    • Ulrich Daepp, Pamela Gorkin
    Pages 73-80
  9. More on Operations on Sets

    • Ulrich Daepp, Pamela Gorkin
    Pages 81-88
  10. The Power Set and the Cartesian Product

    • Ulrich Daepp, Pamela Gorkin
    Pages 89-100
  11. Relations

    • Ulrich Daepp, Pamela Gorkin
    Pages 101-110
  12. Partitions

    • Ulrich Daepp, Pamela Gorkin
    Pages 111-119
  13. Order in the Reals

    • Ulrich Daepp, Pamela Gorkin
    Pages 121-131
  14. Consequences of the Completeness of ℝ

    • Ulrich Daepp, Pamela Gorkin
    Pages 133-141
  15. Functions, Domain, and Range

    • Ulrich Daepp, Pamela Gorkin
    Pages 143-156
  16. Functions, One-to-One, and Onto

    • Ulrich Daepp, Pamela Gorkin
    Pages 157-166
  17. Inverses

    • Ulrich Daepp, Pamela Gorkin
    Pages 167-179
  18. Images and Inverse Images

    • Ulrich Daepp, Pamela Gorkin
    Pages 181-191
  19. Mathematical Induction

    • Ulrich Daepp, Pamela Gorkin
    Pages 193-208
  20. Sequences

    • Ulrich Daepp, Pamela Gorkin
    Pages 209-221

About this book

Reading, Writing, and Proving is designed to guide mathematics students during their transition from algorithm-based courses such as calculus, to theorem and proof-based courses. This text not only introduces the various proof techniques and other foundational principles of higher mathematics in great detail, but also assists and inspires students to develop the necessary abilities to read, write, and prove using mathematical definitions, examples, and theorems that are required for success in navigating advanced mathematics courses.

In addition to an introduction to mathematical logic, set theory, and the various methods of proof, this textbook prepares students for future courses by providing a strong foundation in the fields of number theory, abstract algebra, and analysis. Also included are a wide variety of examples and exercises as well as a rich selection of unique projects that provide students with an opportunity to investigate a topic independently or as part of a collaborative effort.

New features of the Second Edition include the addition of formal statements of definitions at the end of each chapter; a new chapter featuring the Cantor–Schröder–Bernstein theorem with a spotlight on the continuum hypothesis; over 200 new problems; two new student projects; and more. An electronic solutions manual to selected problems is available online.

 From the reviews of the First Edition:

“The book…emphasizes Pòlya’s four-part framework for problem solving (from his book How to Solve It)…[it] contains more than enough material for a one-semester course, and is designed to give the instructor wide leeway in choosing topics to emphasize…This book has a rich selection of problems for the student to ponder, in addition to "exercises" that come with hints or complete solutions…I was charmed by this book and found it quite enticing.”

– Marcia G. Fung for MAA Reviews

“… A book worthy of serious consideration for courses whose goal is to prepare students for upper-division mathematics courses. Summing Up: Highly recommended.”

– J. R. Burke, Gonzaga University for CHOICE Reviews

Keywords

  • Higher Mathematics
  • Introduction to Proof
  • Mathematical Induction
  • Mathematical Logic
  • Mathematics Major
  • Polya's Method
  • Problem Solving
  • Set Theory
  • Undergraduate Mathematics
  • Writing Proofs

Reviews

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

Authors and Affiliations

  • College Arts and Science, Dept. Mathematics, Bucknell University, Lewisburg, USA

    Ulrich Daepp, Pamela Gorkin

About the authors

Ueli Daepp is an associate professor of mathematics at Bucknell University in Lewisburg, PA. He was born and educated in Bern, Switzerland and completed his PhD at Michigan State University. His primary field of research is algebraic geometry and commutative algebra.

Pamela Gorkin is a professor of mathematics at Bucknell University in Lewisburg, PA. She also received her PhD from Michigan State where she worked under the director of Sheldon Axler. Prof. Gorkin’s research focuses on functional analysis and operator theory.

Ulrich Daepp and Pamela Gorkin co-authored of the first edition of “Reading, Writing, and Proving” whose first edition published in 2003. To date the first edition (978-0-387-00834-9 ) has sold over 3000 copies.

Bibliographic Information

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • ISBN: 978-1-4419-9479-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 74.95
Price excludes VAT (USA)
Hardcover Book USD 74.95
Price excludes VAT (USA)