Synopses & Reviews
Learn how to develop your reasoning skills and how to write well-reasoned proofs
Learning to Reason shows you how to use the basic elements of mathematical language to develop highly sophisticated, logical reasoning skills. Youll get clear, concise, easy-to-follow instructions on the process of writing proofs, including the necessary reasoning techniques and syntax for constructing well-written arguments. Through in-depth coverage of logic, sets, and relations, Learning to Reason offers a meaningful, integrated view of modern mathematics, cuts through confusing terms and ideas, and provides a much-needed bridge to advanced work in mathematics as well as computer science. Original, inspiring, and designed for maximum comprehension, this remarkable book:
- Clearly explains how to write compound sentences in equivalent forms and use them in valid arguments
- Presents simple techniques on how to structure your thinking and writing to form well-reasoned proofs
- Reinforces these techniques through a survey of setsthe building blocks of mathematics
- Examines the fundamental types of relations, which is "where the action is" in mathematics
- Provides relevant examples and class-tested exercises designed to maximize the learning experience
- Includes a mind-building game/exercise space at www.wiley.com/products/subject/mathematics/
Review
"A primary strength is its broad attention to ideas from logic, set theory and relations while focusing the key notions of symbolism and writing proofs." (Choice, Vol. 38, No. 7, March 2001)
"In this textbook for mathematics and computer science majors, Rodgers explains how to write compound sentences in equivalent forms and use them in valid arguments..." (SciTech Book News, March 2001)
Synopsis
NANCY RODGERS, PhD, is Professor of Mathematics at Hanover College, Hanover, Indiana.
Table of Contents
LOGICAL REASONING.
Symbolic Language.
Two Quantifiers.
Five Logical Operators.
Laws of Logic.
Logic Circuits.
Translations.
WRITING OUR REASONING.
Proofs and Arguments.
Proving Implications.
Writing a Proof.
Working with Quantifiers.
Using Cases.
Proof by Contradiction.
Mathematical Induction.
Axiomatic Systems.
SETS -
THE BUILDING BLOCKS.
Sets and Elements.
Operations on Sets.
Multiple Unions and Intersections.
Cross Product.
Finite Sets.
Infinite Sets.
RELATIONS -
THE ACTION.
Relations.
Equivalence Relations.
Functions.
Order Relations.
Summary.
Appendices.
Bibliography.