1. Discrete Mathematics Transparency No. 0-1 Discrete Mathematics Cheng-Chia Chen September 2009

2. Discrete mathematics Transparency No. 0-2 Course information: Textbook: Discrete Mathematics and its applications, by Kenneth H. Rosen ( 歐亞書局 : TEL: 8912-1188) Time: 13:10~16:00 Tuesday Room: 大仁 3301 Grading: Two examinations (60%) assignments and quizzes (30%) Classroom participation (10%)

3. Discrete mathematics Transparency No. 0-3 Course outlines The foundations: Logic, sets and functions The fundamental: algorithms, the integers and matrices. Mathematical reasoning Methods of proofs, Mathematical induction, recursive definitions, recursive algorithms, program correctness. Counting: Basic counting method, pigeon hole principle, permutation and combinations. Advanced counting techniques: Recurrence relations, generating functions, inclusion- exclusion principle, applications.

4. Discrete mathematics Transparency No. 0-4 course outline(cont’d) Relations: definition, property of relations, closure of relations, kinds of relations(equivalence, partial order, lattices,..) Graphs: terminology, representation, connectivity, Euler and Hamilton paths, shortest path problems, planar graphs, graph coloring Trees: terminology, applications tree traversal, trees and sorting, spanning trees, minimum spanning trees

5. Discrete mathematics Transparency No. 0-5 courses outline (cont’d) Modeling of computations Languages and grammars, FSM with O/P (Mealey and Moore machines), FSM w/o O/P, CFL & CFG, Turing machine. [Boolean algebra:] [Abstract algebra: definition, monoid, group, ring, … ]

6. Discrete mathematics Transparency No. 0-6 Goal of this course Mathematical reasoning: In order to read, comprehend and construct mathematical arguments. Combinatorial Analysis Discrete structures: Familiar with math. structures used to represent discrete objects and relationships between these objects. include sets, multisets, permutations, relations, graphs, trees and finite state machines. groups, monoid(lists, or sequences), ring, field, lattices etc. Applications and modeling Algorithmic thinking: (constructive, procedural).