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

by Ulrich Daepp, Pamela Gorkin

Overview

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.

Product Details

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

About the Author

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.

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.

Editorial 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

From the Publisher