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Korea Advanced Institute of Science and Technology, Dept. of EECS, Div. of CS, Information Systems Lab. 1/10 CS204 Course Overview 2011. 02. 08. Prof. Chin-Wan Chung
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Information Systems Lab. http://islab.kaist.ac.kr/ 2/10 What is Mathematics, really? It’s not just about numbers! Mathematics is much more than that: But, the concepts can relate to numbers, symbols, visual patterns, or anything! Mathematics is, most generally, the study of any and all absolutely certain truths about any and all perfectly well-defined concepts.
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Information Systems Lab. http://islab.kaist.ac.kr/ 3/10 So, what ’ s this class about? What are “discrete structures” anyway? “Discrete” ( “discreet”!) - Composed of distinct, seperable parts. (Opposite of continuous.) discrete:continuous :: digital:analog “Structures” - objects built up from simpler objects according to a definite pattern. “Discrete Mathematics” - The study of discrete, mathematical objects and structures.
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Information Systems Lab. http://islab.kaist.ac.kr/ 4/10 Discrete Structures We ’ ll Study Propositions Predicates Sets (Discrete) Functions Algorithms Integers Proofs Summations Permutations Combinations Relations
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Information Systems Lab. http://islab.kaist.ac.kr/ 5/10 Relationships Between Structures “ → ” :≡ “ Can be defined in terms of ” Sets Sequences n-tuples Matrices Natural numbers Integers Relations Functions Graphs Real numbers Complex numbers Strings Propositions Proofs Trees Operators Programs Infinite ordinals Vectors Groups Bits
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Information Systems Lab. http://islab.kaist.ac.kr/ 6/10 Some Notations We ’ ll Learn
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Information Systems Lab. http://islab.kaist.ac.kr/ 7/10 Why Study Discrete Math? The basis of all of digital information processing: Discrete manipulations of discrete structures represented in memory. It’s the basic language and conceptual foundation of all of computer science. Discrete concepts are also widely used throughout math, science, engineering, economics, biology, etc., … A generally useful tool for rational thought!
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Information Systems Lab. http://islab.kaist.ac.kr/ 8/10 Uses for Discrete Math in Computer Science Advanced algorithms & data structures Programming language compilers & interpreters. Computer networks Operating systems Computer architecture Database management systems Cryptography Error correction codes Graphics & animation algorithms, game engines Just about everything!
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Information Systems Lab. http://islab.kaist.ac.kr/ 9/10 Course Outline 1.Logic 2.Proof methods 3.Set theory 4.Functions 5.Algorithms 6.Number Theory 7.Matrices 8.Sequences 9.Summations 10.Inductive proofs 11.Recursion 12.Combinatorics 13.Probability 14.Relations
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Information Systems Lab. http://islab.kaist.ac.kr/ 10/10 Course Objectives Upon completion of this course, the student should be able to: Check the validity of simple logical arguments. Check the correctness of simple algorithms. Creatively construct simple valid logical arguments. Creatively construct simple correct algorithms. Describe the definitions and properties of a variety of specific types discrete structures. Correctly read, write and analyze various types of structures using standard notations.
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