| Course Type | Compulsory Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | 2 |
|---|
| Semester | Third Term (Fall) |
|---|
| ECTS | 6 |
|---|
| Name of Lecturer(s) |
|
| Learning Outcomes |
At the end of this course, the students;
- Represent the propositions using logical connectives and interpret symbolic expressions.
- Determine is a mathematical argument correct or not.
- Develop the knowledge on recursively-defined structures
- Gain the ability to think algorithmically.
- Have theoretical knowledge on Equivalence relations and Partial orders; solve related application problems.
- Learn the basic principles of counting and advanced counting techniques.
- Obtain information about basic concepts, methods and applications of graph theory.
- Apply discrete structures and related methods to solve problems in Computer Engineering.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | None |
|---|
| Course Description | Logic. Logical operations and laws of logic, quantifiers and proofs of theorems. Sets. Subsets and operations on sets. Principles of counting. Inclusion-exclusion and pigeon-hole principles. Integers, mathematical induction. Relations and functions. Operations on relations. Partially ordered sets. Lattices. Boolean algebras. Graphs. Euler and Hamiltonian paths and circuits. Trees. Binary trees, spanning trees. Tree searching. Elements of coding theory. |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
Logic, Propositions, Logical Operations |
|
2nd Week |
Rules of Logical Equivalence |
|
3rd Week |
Logical Inference and Rules, Methods of Proving Theorems |
|
4th Week |
Propositional Functions, Quantifiers, Mathematical Induction |
|
5th Week |
Sets, Subsets, Operations on Sets, Recursively Defined Sets |
|
6th Week |
Sequences, Recurrence Relations |
|
7th Week |
Recursively Defined Structures and Algorithms |
|
8th Week |
Midterm |
|
9th Week |
Relations, Functions, and Their Properties |
|
10th Week |
Operations on Relations, Equivalence Relations |
|
11th Week |
Partial Orders, Hasse Diagrams, Lattice Theory |
|
12th Week |
Counting Principles, Permutations, Combinations |
|
13th Week |
Advanced Counting Techniques, Pigeonhole Principle |
|
14th Week |
Introduction to Graph Theory, Directed and Undirected Graphs, Definitions |
|
15th Week |
Euler Circuits and Paths, Hamiltonian Circuits and Paths |
|
| Recommended or Required Reading | 1. Rosen K.H., Discrete Mathematics and Its Applications, 6/E, McGraw-Hill, 2007
2. Kolman B., Busby R.C., Ross S., Discrete Mathematical Structures, 5/E, Prentice Hall, 2004
3. Grimaldi R.P., Discrete and Combinatorial Mathematics, 5/E, Addison Wesley, 2003 |
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
- Presentation
- Report Preparation
- Project
- Experiment
- Practice
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
30 |
| Assignment |
8 |
15 |
| Quiz |
4 |
15 |
| Total(%) |
|
60 |
| Contribution of In-term Studies to Overall Grade(%) |
|
60 |
| Contribution of Final Examination to Overall Grade(%) |
|
40 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
1.5 |
1.5 |
| Preparation for Quiz |
4 |
4 |
16 |
| Individual or group work |
|
|
|
| Preparation for Final exam |
1 |
40 |
40 |
| Course hours |
14 |
4 |
56 |
| Preparation for Midterm exam |
1 |
30 |
30 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
1 |
2 |
2 |
| Homework |
8 |
3.5 |
28 |
| Quiz |
4 |
0.5 |
2 |
| Total Work Load | 175.5 |
| Total Work Load / 30 (h) | 5.85 |
| ECTS Credit of the Course | 6 |
|
| Language of Instruction | - |
|---|
| Work Placement(s) | No |
|---|
