Learning to Reason

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/