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 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/
|Product dimensions:||7.68(w) x 9.57(h) x 1.07(d)|
Table of Contents
Five Logical Operators.
Laws of Logic.
WRITING OUR REASONING.
Proofs and Arguments.
Writing a Proof.
Working with Quantifiers.
Proof by Contradiction.
THE BUILDING BLOCKS.
Sets and Elements.
Operations on Sets.
Multiple Unions and Intersections.