Learning to Reason

Learn how to develop your reasoning skills and how to writewell-reasoned proofs

Learning to Reason shows you how to use the basic elements ofmathematical language to develop highly sophisticated, logicalreasoning skills. You'll get clear, concise, easy-to-followinstructions on the process of writing proofs, including thenecessary reasoning techniques and syntax for constructingwell-written arguments. Through in-depth coverage of logic, sets,and relations, Learning to Reason offers a meaningful, integratedview of modern mathematics, cuts through confusing terms and ideas,and provides a much-needed bridge to advanced work in mathematicsas well as computer science. Original, inspiring, and designed formaximum comprehension, this remarkable book:
* Clearly explains how to write compound sentences in equivalentforms and use them in valid arguments
* Presents simple techniques on how to structure your thinking andwriting to form well-reasoned proofs
* Reinforces these techniques through a survey of sets--thebuilding blocks of mathematics
* Examines the fundamental types of relations, which is "where theaction is" in mathematics
* Provides relevant examples and class-tested exercises designed tomaximize the learning experience
* Includes a mind-building game/exercise space atwww.wiley.com/products/subject/mathematics/ 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. "A primary strength is its broad attention to ideas from logic, settheory and relations while focusing the key notions of symbolismand 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 equivalentforms and use them in valid arguments..." (SciTech Book News, March2001) NANCY RODGERS, PhD, is Professor of Mathematics at Hanover College, Hanover, Indiana. 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/