New York University Skopje
COURSE SYLLABUS
Discrete Mathematics 1
Spring 2008
Instructor: Magdalena Ivanovska
Class Hours: Wednesday 14:00-17:00
Classroom: Cl.6
Office Hours: Monday 13:00-
E-mail address: mivanovska@nyus.edu.mk
Phone Number: +389 (0)2 20 34 600, +389 (0)70 915 897
Prerequisite(s): Algebra
Textbook(s): Discrete Mathematics and its Applications 5-th editiod,
Kenneth H. Rosen, McGraw-Hill International Editions 2003,
ISBN 0-07-123374-1
Course Description and Related Requirements
v Course Description
The course is aimed to provide mathematical background for a computer science student, concentrating on the following important topics: Mathematical Reasoning, Combinatorial Analysis, Discrete Structures, Algorithmic Thinking, and Applications and Modeling.
The course shows the relevance and practicality of discrete mathematics concepts and techniques in computer applications.
v Course Objectives
Upon successful completion of the course the student will be able to:
- Understand and apply basic calculations in Mathematical Logic, Sets, and Functions;
- Operate with Algorithms, Integers and Matrices;
- Apply Mathematical Reasoning foundations;
- Implement basic Counting Techniques;
- Calculate Probabilities of events;
- Understand the concept of Relations and their applications.
v Course Structure
The course is structured as follows:
1. The foundations: Logic and Proof, Sets, and Functions
2. The Fundamentals: Algorithms, the Integers, and Matrices
3. Mathematical Reasoning, Induction and Recursion
4. Counting
5. Discrete Probability
6. Relations
v Grading
The grade depends on the following:
Attendance and Participation: 10%
Homework and Projects: 15%
Mid-Term Exam 35%
Final Exam 40%
Weekly Plan
|
Week (1x3 classes) |
Theme |
Chapter |
|
1 |
1.1 Logic 1.2 Propositional Equivalences
|
Chapter 1: The foundations: Logic and Proof, Sets, and Functions |
|
2 |
1.3 Predicates and Quantifiers 1.4 Nested Quantifiers
|
Chapter 1: The foundations: Logic and Proof, Sets, and Functions |
|
3 |
1.5 Methods of Proof
|
Chapter 1: The foundations: Logic and Proof, Sets, and Functions |
|
4 |
1.6 Sets 1.7 Set Operations 1.6 Functions
|
Chapter 1: The foundations: Logic and Proof, Sets, and Functions |
|
5 |
2.1 Algorithms 2.2 The Growth of Functions 2.3 Complexity of Algorithms
|
Chapter 2: The Fundamentals: Algorithms, Integers, and Matrices |
|
6 |
2.4 The Integers and Divisions 2.7 Matrices |
Chapter 2: The Fundamentals: Algorithms, Integers, and Matrices |
|
7 |
Mid Term Exam |
Mid Term Exam |
|
8 |
3.1 Proof Strategy 3.2 Sequences and Summations
|
Chapter 3: Mathematical Reasoning, Induction, and Recursion |
|
9 |
3.3 Mathematical Induction 3.4 Recursive Definitions and Structural Induction |
Chapter 3: Mathematical Reasoning, Induction, and Recursion |
|
10 |
4.1 The Basics of Counting 4.2 The Pigeonhole Principle
|
Chapter 4: Counting
|
|
11 |
4.3 Permutations and Combinations 4.4 Binomial Coefficients |
Chapter 4: Counting
|
|
12 |
5.1 An Introduction to Discrete Probability 5.2 Probability Theory 5.3 Expected Value and Variance |
Chapter 5: Discrete Probability |
|
13 |
7.1 Relations and Their Properties 7.2 n-ary Relations and Their Applications 7.3 Representing Relations |
Chapter 7: Relations
|
|
14 |
7.4 Closures of Relations 7.5 Equivalence Relations 7.6 Partial Orderings |
Chapter 7: Relations
|
|
15 |
Final Exam |
Final Exam |
v Grading Scale
Grade
|
Percentage |
Quality Points |
A
|
96-100 |
4.00 |
|
A- |
90-95 |
3.67 |
|
B+ |
87-89 |
3.33 |
|
B |
83-86 |
3.00 |
|
B- |
80-82 |
2.67 |
|
C+ |
77-79 |
2.33 |
|
C |
73-76 |
2.00 |
|
C- |
70-72 |
1.67 |
|
D+ |
67-69 |
1.33 |
|
D |
63-66 |
1.00 |
|
D- |
60-62 |
0.67 |
F
|
0 -59 |
0.00 |