Overview Discrete Mathematics and Its Applications Baojian Hua

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

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

Who are We? Instructor: Hua, Baojian 302 in Mingde buiding Office hour: at every class, or to appoint TAs: Wang, Xi: Feel free to contact us for help :-)

Course Page Home page Course administrative Lecture notes Programming assignments Softwares Test and evaluation issues Check that page frequently Join the Google discussion group To be announced

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

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

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

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

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

Any question?