; 沒有投影片標題
Documents
User Generated
Resources
Learning Center
Your Federal Quarterly Tax Payments are due April 15th

# 沒有投影片標題

VIEWS: 2 PAGES: 6

• pg 1
```									                        Discrete Mathematics

Discrete Mathematics

Cheng-Chia Chen

September 2009

Transparency No. 0-1
Discrete mathematics
Course information:

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

Time: 13:10~16:00 Tuesday
l Room:大仁 3301
￿Two examinations (60%)
￿assignments and quizzes (30%)
￿Classroom participation (10%)

Transparency No. 0-2
Discrete mathematics
Course outlines
l The foundations:
￿Logic, sets and functions
l The fundamental:
￿algorithms, the integers and matrices.
l Mathematical reasoning
￿Methods of proofs, Mathematical induction, recursive
definitions, recursive algorithms, program correctness.
l Counting:
￿Basic counting method, pigeon hole principle,
permutation and combinations.
￿Recurrence relations, generating functions, inclusion-
exclusion principle, applications.

Transparency No. 0-3
Discrete mathematics
course outline(cont’d)
l Relations:
￿definition, property of relations, closure of relations,
￿kinds of relations(equivalence, partial order, lattices,..)
l Graphs:
￿ terminology, representation, connectivity,
￿ Euler and Hamilton paths, shortest path problems,
￿ planar graphs, graph coloring
l Trees:
￿terminology, applications
￿tree traversal, trees and sorting,
￿spanning trees, minimum spanning trees

Transparency No. 0-4
Discrete mathematics
courses outline (cont’d)

l Modeling of computations
￿ Languages and grammars,
￿ FSM with O/P (Mealey and Moore machines),
￿ FSM w/o O/P,
￿CFL & CFG,
￿Turing machine.
l [Boolean algebra:]
l [Abstract algebra:
￿definition, monoid, group, ring, … ]

Transparency No. 0-5
Discrete mathematics
Goal of this course
l Mathematical reasoning:
￿In order to read, comprehend and construct mathematical
arguments.
l Combinatorial Analysis
l 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.
l Applications and modeling
l Algorithmic thinking: (constructive, procedural).
Transparency No. 0-6

```
To top
;