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Discrete Mathematics . Why Are You Studying this Course. This course will develop your mathematical maturity Discrete mathematics provides the mathematical foundations for many computer science courses Data Structures Algorithm Analysis and Design
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Why Are You Studying this Course • This course will develop your mathematical maturity • Discrete mathematics provides the mathematical foundations for many computer science courses • Data Structures • Algorithm Analysis and Design • Database Management Systems and Database Theory • Compiler Construction • Computer Security • Digital Logic Design • Artificial Intelligence
Course Information • Syllabus: • Logic • Sets • Relations • Functions. • Combinatory: counting, permutations, combinations. • Recursion • Probibility • Mathematical Induction • Graph theory: Graphs and Trees
Course Information • Textbook: • Discrete Mathematics and its Applications by Kenneth. H. Rosen, 7th Edition • Discrete Mathematics with Application” by Susana. 4th edition, 2010
How will you master Discrete Structures • “I hear and I forget. I see and I remember. I do and understand” - Chinese proverb
Terminology Discrete - Composed of distinct OR separable/unconnected parts. (Opposite of continuous.) Structures- Objects built up from simpler objects according to some definite pattern.
Introduction • What is discrete mathematics? • Part of mathematics devoted to the study of discrete objects. • Discrete means consisting of distinct or unconnected elements. • As computers are discrete object operating one jumpy, discontinuous step at a time, Discrete Math is the right framework for describing precisely Computer Science concepts.
Introduction • What is discrete mathematics? • In computer science we usually deal with finite, discrete objects. • For example, we cannot store a real number (infinite precision) in a computer but can only store bits (finite precisions). • Definition • Discrete Mathematics is a collection of mathematical topics that examine and use finite or countably infinite mathematical objects.
Statements & Truth Values – 9b T T F F
Advanced versions of many Internet search engines allow you to use some form of and, or and not to refine the search process. • Imagine that you want to find web pages about careers in mathematics or computer science but not finance or marketing. • With a search engine that uses quotation marks to enclose exact phrases and expresses and as AND, or as OR, and not as NOT, you would write • Careers AND (mathematics OR "computer science") • AND NOT (finance OR marketing).