Faculty of Engineering and Natural Sciences · Computer Engineering · Undergraduate
Course Objective
To provide students with the fundamental knowledge of Discrete Mathematics alongside Basic Mathematics, which they will need throughout their undergraduate and graduate studies. The aim is to develop students' mathematical thinking, equip them with the ability to formulate algorithms and construct proofs, and enable the use of mathematical structures in other scientific disciplines. It also seeks to enhance mathematical thinking and problem-solving techniques, ensure the comprehension of their real-life applications, and foster students' understanding of Discrete Mathematics topics and applications while developing their analytical thinking and evaluation skills.
Course Content
Logic, Logical Statements and Arguments, Mathematical Proof Techniques, The Principle of Mathematical Induction, Application of Proof Techniques to Basic Number Theory, Sets, Relations and Functions,
Basic Combinatorics and Counting Principles, Graph Theory, Trees
Required Resources
I. Lecture Notes
II Susanna S. Epp, Discrete Mathematics with Applications, 4th Edition, International Edition.
Recommended Resources
Kenneth Rosen. Discrete Mathematics and Its Applications, 6 th Edition, McGraw Hill Publishing Co., 2007
Rules
- Calculators are NOT allowed in all exams and quizzes.
- Attendance: It is the university policy that if a student is absent 30% of the class sessions (which, in our case, amount to 9 hours), he/she will be withdrawn from the course with a grade of DZ.
3. Late attendance: Not only are you expected to be in class, but you are also expected to be there on time. Three (3) late attendances will count as one absence. Lateness is defined as: showing up to class after the instructor has finished calling the class roster, and within the first 10 minutes of the lecture. Showing up more than 10 minutes late to the lecture counts as an absence.
4. Missing quizzes or exams: Quizzes cannot be made up.
5. Academic integrity: You are expected to submit your own work. Copying, cheating or plagiarism, if detected, will be reported to the university administration and further action might be taking from the university.
6. Getting Help: Students are encouraged to consult their instructor during his office hours or by appointment.
Course Learning Outcomes
- To be able to comprehend logical statements and evaluate the validity of logical arguments.
- Apply mathematical proof techniques to basic number theoretical problems.
- Be able to construct mathematical proofs involving different techniques such as mathematical induction and contradiction
- Prove and solve problems related to relations and functions depending on their corresponding definitions.
- Apply operations and algebraic proofs on Set theoretical examples.
- Apply basic counting and probability techniques such as pigeonhole principle.
- Analyze, model, and solve real life problems using Graph Theoretical structures and trees.
- Deduce information about structural properties of graphs from their adjacency matrices
- Explore isomorphic relations between graphs
- Apply shortest path algorithms and identify minimum spannig tree of a graph
Core Area Distribution
Teaching Methods
Assessment & Evaluation
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 16 | 3 | 48 |
| Out of Class Study Period | 16 | 2 | 32 |
| Midterm | 1 | 15 | 15 |
| Quiz | 4 | 1 | 4 |
| Assignment | 4 | 1 | 4 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 20 | 20 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | Propositions and Truth Tables | Ch 2.1 and 2.2 |
| 2 | Logical Arguments, Validity of Arguments, Quantifiers | Ch 2.3, 2.4 and 3.1 |
| 3 | Basic Number Theory and the Method of Direct Proof | Ch. 4.1, 4.2, 4.3 |
| 4 | Indirect Proofs: Contradiction and Contraposition | Ch. 4.4, 4.6 |
| 5 | The Principle of Mathematical Induction and its Applications | Ch. 5.1, 5.2, 5.4, 5.6 |
| 6 | Algebra of Sets and Proofs in Set Theory | Ch. 6.1, 6.2, 6.3 |
| 7 | Review for Midterm | Ch. 2,4,5,6 |
| 8 | Ara Sınav | Ara Sınav |
| 9 | Relations on Sets Properties of Relations and Their Proofs Equiavalence Relations and Partitions | Relations |
| 10 | Well Definition Property Injectivitiy, Surjectivity and Inverse Functions | Functions |
| 11 | Rules of Counting: Multiplication and Addition Rules Possibility Trees Permutations, Combinations, Pigeonhole Principle r-Combinations with Repetitions | Permutations, Combinations, Probability |
| 12 | Graphs: Definitions and Properties Trails, Paths and Circuits Matrix Representaion of Graphs Isomorphism of Graphs | Chapter 10 |
| 13 | Isomorphism of Graphs, Trees | Chapter 10 |
| 14 | Weighted Graphs Spanning Trees and Algorithms of Shortest Paths | Chapter 10 |
| 15 | Review for Final Exam | Review |
| 16 | Final Sınavı | Final Sınavı |