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Discrete Structures for Computer Science Course

Dive into logic, counting, graph theory, and number theory to understand algorithms, data structures, and cryptography. Learn through lectures, exams, and bonus questions in this comprehensive course.

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Discrete Structures for Computer Science Course

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  1. Discrete Structures for Computer Science Ruoming Jin MW 2:15 – 3:00pm Spring 2010 rm MSB115

  2. Course Material • Textbook: Discrete Mathematics and Its Applications • Kenneth H. Rosen, McGraw Hill

  3. Course Requirements • Homework, 20% • Quiz, 20% • Three Intermediate Exams: 10% • Final Exam, 30% • Bonus Questions 5-10%

  4. Why Discrete Math? Design efficient computer systems. • How did Google manage to build a fast search engine? • What is the foundation of internet security? algorithms, data structures, database, parallel computing, distributed systems, cryptography, computer networks… Logic, sets/functions, counting, graph theory…

  5. What is discrete mathematics? Logic: artificial intelligence (AI), database, circuit design Counting: probability, analysis of algorithm Graph theory: computer network, data structures Number theory: cryptography, coding theory logic, sets, functions, relations, etc

  6. Topic 1: Logic and Proofs How do computers think? Logic: propositional logic, first order logic Proof: induction, contradiction Artificial intelligence, database, circuit, algorithms

  7. Topic 2: Counting • Sets • Combinations, Permutations, Binomial theorem • Functions • Counting by mapping, pigeonhole principle • Recursions, generating functions Probability, algorithms, data structures

  8. Topic 2: Counting How many steps are needed to sort n numbers?

  9. Topic 3: Graph Theory • Relations, graphs • Degree sequence, isomorphism, Eulerian graphs • Trees Computer networks, circuit design, data structures

  10. Topic 4: Number Theory • Number sequence • Euclidean algorithm • Prime number • Modular arithmetic Cryptography, coding theory, data structures

  11. c b a Pythagorean theorem Familiar? Obvious?

  12. Good Proof c b a Rearrange into: (i) a cc square, and then (ii) an aa & a bb square

  13. Good Proof c b-a c c a b c 81 proofs in http://www.cut-the-knot.org/pythagoras/index.shtml

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