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Learning to Reason: An Introduction to Logic, Sets  and Relations

Learning to Reason: An Introduction to Logic, Sets and Relations


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About the Book

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. You'll 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 sets--the 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/

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.

About the Author :
NANCY RODGERS, PhD, is Professor of Mathematics at Hanover College, Hanover, Indiana.

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) "...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)



Product Details
  • ISBN-13: 9781118165690
  • Publisher: John Wiley & Sons Inc
  • Publisher Imprint: John Wiley & Sons Inc
  • Height: 250 mm
  • No of Pages: 454
  • Weight: 666 gr
  • ISBN-10: 1118165691
  • Publisher Date: 19 Sep 2011
  • Binding: Other digital
  • Language: English
  • Spine Width: 15 mm
  • Width: 150 mm


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