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 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.

Table of Contents

Chapter 0 The Art of Thinking Abstractly and Mathematically

Chapter 1 Basic Set Theory

Chapter 2 Propositional Logic

Chapter 3 Semantics for Propositional Logic

Chapter 4 Concepts in Propositional Logic

Chapter 5 Proofs, Conjectures, and Counterexamples

Chapter 6 Relations

Chapter 7 Functions

Chapter 8 A Little More Set Theory

Chapter 9 Closures and Inductively Defined Sets

Chapter 10 Recursively Defined Functions

Chapter 11 Mathematical Induction

Chapter 12 Structural Induction

Chapter 13 First-Order Languages

Chapter 14 Representation of Quantified Statements

Chapter 15 Interpretation in Models

About the Author

Roger Antonsen is a Computer scientist, mathematician, logician, author, artist, public speaker, PhD & Associate Professor @ University of Oslo, Norway