- Instructor: Prof.
Sung-Hyuk Cha
- Email: scha@pace.edu
- Tel: (212) 346-1253
- Office: 163 Williams, Rm. 228 at NYC
- Office Hours: Tuesday and Thursday 2:20 pm - 4:50 pm
- CRN: 71507
- Meeting:
- Time:
TR 12:15 P.M. - 02:15 P.M., Fall 2015
- Place: 163WM 1525
- Textbook:
Discrete Mathematics and Its Applicationss, 7th Edition by Kenneth Rosen, 2012
- Course Description:
This course covers the basic mathematical topics mainly for computer science major students.
The topics include boolean algebra, propositional logic, predicate logic,
relations, functions, set theory,
counting, probability, combinatorics,
proof methods, induction, recursion, number theory, and graph theory.
- Boolean algebra is essential in designing digital circuits.
- Logic is fundalmental in artificial intelligence such as theorem proving and in database queries.
- Relations and set theory play important roles mainly in the relational database systems.
- Recursive relation and induction are important in defining
problems, designing recursive algorithms, and proving the correctness of
algorithms.
- Number theory leads to cryptography and more.
- Probability and combinatorics are crucial in analysis of algorithms.
- Graph theory is directly related to computer networks and many applications.
- Prerequisites: None, This course will replace MAT 137 for Computer Science students ONLY
- Lecture Notes: can be accessed using the http://blackboard.pace.edu.
Blackboard Login Procedures for Registered Students are available
here
- Schedule: subject to change
| Week | Tuesday | Thursday | Topic |
|---|
| 1 |
9/1
|
9/3
Propositional Logic (1.1~1.3)
|
Logic & Set |
| 2
| 9/8
Propositional Logic (1.1~1.3)
|
9/10
Propositional Logic (1.1~1.3)
|
| 3
| 9/15
First order Logic (1.4~1.5)
|
9/17 Rules of Inference (1.6) |
| 4
|
9/22 Sets (2.1~2.2) |
9/24 Abstract Set Theory (2.5) |
| 5
|
9/29
Sequences (2.4)
|
10/1
Number systems (4.1~4.2)
|
Number Theory |
| 6
|
10/6
Primes (4.3) |
10/8
Congruences (4.4)
|
| 7
|
10/13
Proof by Contradiction
|
10/15
Review
|
| 8
|
10/20
Midterm Exam
|
10/22
Midterm review |
Exam |
| 9
|
10/27
Induction (5.1~5.3)
|
10/29
Recursion (5.3~5.5)
|
Combinatorics |
| 10
|
11/3
Counting (6.1~6.3)
|
11/5
Counting (6.4~6.6)
|
| 11
|
11/10
Recurrence relation (8.*)
|
11/12
Relations (9.*)
|
| 12
|
11/17
Graphs (10.1~10.4)
|
11/19
Graphs (10.1~10.4)
|
Graph Theory |
| 13
| 11/24
Graphs (10.5~10.8) |
11/26 Thanksgiving Break |
| 14
|
12/1
Trees (11.1~11.3)
|
11/3
Spanning Trees (11.4~11.5)
|
| 15
|
12/8
Study day |
12/10
Study day |
Exam |
| 16
|
12/15 Final Exam |
12/17
|
- Evaluation:
- Attendance (10%):
- Homeworks (30%):
- Midterm Exam (30%):
- Final Exam (30%):
- Course Policies
- All homeworks must be submitted at the beginning of the class.
- 10 percent progressive penalties for late homework submissions.
|