Discrete Mathematics

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Discrete Mathematics

Cheng-Chia Chen

September 2009

Discrete mathematics

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Course information:

Textbook:

Discrete Mathematics and its applications, by Kenneth H. Rosen ( 歐亞書局 : TEL: 8912-1188)

Time: 13:10~16:00 TuesdayRoom: 大仁 3301Grading:

Two examinations (60%) assignments and quizzes (30%) Classroom participation (10%)

Discrete mathematics

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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.

Discrete mathematics

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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

Discrete mathematics

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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, … ]

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Goal of this course

Mathematical reasoning: In order to read, comprehend and construct mathematical

arguments.

Combinatorial AnalysisDiscrete 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 modelingAlgorithmic thinking: (constructive, procedural).