Description
Book SynopsisLearn 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 t
Trade Review"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)
Table of ContentsLOGICAL 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.
