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 our 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 Fan, Dawei: fandawei@mail.ustc.edu.cn Yang, Simin: smin@mail.ustc.edu.cn Zhuang, Zhong: dyzz@mail.ustc.edu.cn Feel free to contact us for help :-)

5. Course Page Home page http://staff.ustc.edu.cn/~bjhua/fall081http://staff.ustc.edu.cn/~bjhua/fall081 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 want to 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 Set, function, relation Counting Logic Syntax, semantics, soundness and completeness Constructive logic, Curry-Howard isomorphism Case studies & applications Graph and Trees Computability 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 teach it to the computer See the applications of theory (in computer science) Approximately 1 per week Solver them independently (no collaboration) Submitted to TAs

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

11. Any questions about this course?