1. Introduction

# 1. Introduction - MATH 224 Discrete Mathematics Why Study...

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1 08/27/09 MATH 224 – Discrete Mathematics Why Study Discrete Math Determination of the efficiency of algorithms, e.g., insertion sort versus selection sort. Can you provide an example? Boolean expressions for controlling loops and conditional statements are based on the propositional calculus and Boolean algebra. What is an example in C++? The building blocks of computers – logic gates implement Boolean expressions. Design of programs and algorithms is similar to developing mathematical proofs. Conversion of high level languages to machine code makes use of formal language theory. Name some high level languages. What is machine code? Induction and recursion are the basis for algorithms and programs that use repeated instructions, e.g., for statements, while statements and recursive functions.

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2 08/27/09 MATH 224 – Discrete Mathematics Why Study Discrete Math Continued Security including encryption and authentication make use of math concepts. Can you give an example of where encryption is used? What is authentication? Many data structures make use of trees, e.g., heaps, binary search trees, databases. The theory behind caching and paging uses mathematics. Do you know what these are? Graph theory is used in communication networks, artificial intelligence, computer games, computer animation among others. And much much more.
3 08/27/09 MATH 224 – Discrete Mathematics Propositions X <= Y Z > 10 && Z <= 20 !(Z <= 10 || Z > 20) Flag -- where Flag is a boolean variable !Flag || X % 2 == 0 -- When is X % 2 == 0 ?

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