Discrete Mathematics Lecture 4 Proofs: Methods and Strategies 1 . Proof by induction: In this method, we proof one case, and then we attempt to proof that the next case must be true.It is usually used for natural numbers. If this is your first time encountering the subject, you will probably find discrete mathematics quite different from other math subjects. A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. •Methods of Proving •Common Mistakes in Proofs •Strategies : How to Find a Proof ? Mathematical induction, is a technique for proving results or establishing statements for natural numbers.This part illustrates the method through a variety of examples. This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. 2 . What is a Proof ? Welcome to Discrete Mathematics. •A proof is a valid argument that establishes the truth of a theorem (as the conclusion) •Statements in a proof can include the axioms Discrete Mathematics An Introduction to Proofs Proof Techniques Math 245 January 17, 2013 We proof a 'base case' and then prove that if a statement is true for one natural number, then it must be true for others too. Mathematical Induction is a mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number.. You might not even know what discrete math is! Outline •What is a Proof ? Definition. The text explains and The text covers the mathematical concepts that students will encounter in many disciplines such as computer science, engineering, Business, and the sciences.

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