1. Overview Discrete Mathematics and Its Applications Baojian Hua bjhua@ustc.edu.cn

2. What ’ s this course about? Discrete mathematics: basic concepts and results theory-oriented Applications: heavily used in many fields focus on computer science project-oriented

3. Is this Course Important? Knowledge preparation (CS) Data structure, algorithms design & analysis, data base, computability & complexity, … Discrete mathematics itself is an amazing subject full of beautiful & elegant results Improve our thinking Not only in computer science Start point for current research We ’ ll cover some state-of-the-art research projects and open problems

4. Who are We? Instructor: Hua, Baojian 302 in Mingde buiding bjhua@ustc.edu.cn Office hour: at every class, or to appoint TAs: Wang, Xi: dolphin@mail.ustc.edu.cn Feel free to contact us for help :-)

5. Course Page Home page http://staff.ustc.edu.cn/~bjhua/spring091 http://staff.ustc.edu.cn/~bjhua/spring091 Course administrative Lecture notes Programming assignments Softwares Test and evaluation issues Check that page frequently Join the Google discussion group http://??? To be announced

6. Textbooks and References There are no required textbooks for this course None of them is as of the sufficient depth and width as we ’ d cover Instead, we ’ ll choose topics from various sources, see the course web page for some recommended references We ’ ll rely heavily on lecture notes Attend the class

7. Contents We ’ ll Cover (tentative) Inductive definition & structural induction Map, set, function, relation Counting Logic Syntax, semantics, soundness and completeness Constructive logic, Curry-Howard isomorphism Case studies & applications Graph and Trees Computability Formal language, automaton, lambda calculus

8. Homework Part theory, part practice theory on paper practice in code in whatever language you love Policy: Solve them independently Late homework should only be considered under extraordinary circumstances Submit to TAs

9. Programming Assignments Two purposes: Get more familiar with the theory in another way You understand it, if you can teach it to the computer See the applications of theory (in computer science) Approximately 1/every two weeks Solve them independently or a group of two Submitted to TAs

10. Test and Evaluation Policy for the final test: Close book Score evaluation: 20% homework 30% projects 50% test Be concerned this course is more profitable and illuminating (and exciting) than you may assume

11. Any question?