# proof techniques in discrete mathematics

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. 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. Welcome to Discrete Mathematics. Outline •What is a Proof ? What is a Proof ? The text covers the mathematical concepts that students will encounter in many disciplines such as computer science, engineering, Business, and the sciences. Mathematical induction, is a technique for proving results or establishing statements for natural numbers.This part illustrates the method through a variety of examples. If this is your ﬁrst time encountering the subject, you will probably ﬁnd discrete mathematics quite diﬀerent from other math subjects. This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. •A proof is a valid argument that establishes the truth of a theorem (as the conclusion) •Statements in a proof can include the axioms 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. 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! Definition. 2 . •Methods of Proving •Common Mistakes in Proofs •Strategies : How to Find a Proof ? Discrete Mathematics Lecture 4 Proofs: Methods and Strategies 1 . The text explains and

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