Logic Logical Methods

Logical Methods

Many believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science, its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more. In the book you will, among other things, find answers to: What is a proof? What is a counterexample? What does it mean to say that something follows logically from a set of premises? What does it mean to abstract over something? How can knowledge and information be represented and used in calculations? What is the connection between Morse code and Fibonacci numbers? Why could it take billions of years to solve Hanoi's Tower? Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.

Logic: Logical methods

A Logical Approach to Discrete Math

This text attempts to change the way we teach logic to beginning students. Instead of teaching logic as a subject in isolation, we regard it as a basic tool and show how to use it. We strive to give students a skill in the propo sitional and predicate calculi and then to exercise that skill thoroughly in applications that arise in computer science and discrete mathematics. We are not logicians, but programming methodologists, and this text reflects that perspective. We are among the first generation of scientists who are more interested in using logic than in studying it. With this text, we hope to empower further generations of computer scientists and math ematicians to become serious users of logic. Logic is the glue Logic is the glue that binds together methods of reasoning, in all domains. The traditional proof methods -for example, proof by assumption, con tradiction, mutual implication, and induction- have their basis in formal logic. Thus, whether proofs are to be presented formally or informally, a study of logic can provide understanding.