Fundamental principle of counting. Introduction to discrete probability. Pigeonhole principle. The principle of inclusion and exclusion. Recurrence relations. Introduction to graph theory. Languages and finite state machines.
Vertical Tabs
Course Learning Outcomes
| Learning Outcomes | Program Learning Outcomes | Teaching Methods | Assessment Methods |
| 1) Understands and solves problems in counting using the basic principles of counting. | 1,2,4,7 | 1,2 | A |
| 2) Uses the principle of inclusion and exclusion to solve related problems indirectly. | 1,2,7 | 1,2 | A |
| 3) Solves first-order linear recurrence relations, second-order linear homogeneous recurrence relations with constant coefficients, and some particular nonhomogeneous recurrence relations. | 2,4,7 | 1,2 | A |
| 4) Models a given particular situation or a problem using graph theory. | 1,2,4,7 | 1,2 | A |
| 5) Decides whether or not given graphs are isomorphic. | 1,4,7 | 1,2 | A |
| 6) Understands the structure of languages and finite state machines | 1,2,4,7 | 1,2 | A |
Course Flow
|
Week |
Topics |
Study Materials |
|
1 |
The rules of sum and product. Permutations |
1.1, 1.2 |
|
2 |
Combinations. The binomial theorem. Combinations with repetition |
1.3, 1.4 |
|
3 |
The pigeonhole principle |
5.5 |
|
4 |
Well-ordering principle, Mathematical Induction |
4.1, 4.2 |
|
5 |
Division algorithm. The Euclidean algorithm. The fundamental theorem of arithmetic |
4.3, 4.4, 4.5 |
|
6 |
The principle of inclusion and exclusion. |
8.1, 8.2 |
|
7 |
Generating functions |
9.1, 9.2 |
|
8 |
Partition of integers |
9.3, 9.4 |
|
9 |
The first-order linear recurrence relation |
10.1 |
|
10 |
The Second-order linear homogeneous recurrence relation with constant coefficients |
10.2 |
|
11 |
The non-homogeneous recurrence relation |
10.3 |
|
12 |
Method of generating functions |
10.4 |
|
13 |
Graph theory: Graphs, subgraphs, complements, graph isomorphisms |
11.1, 11.2 |
|
14 |
Languages: Finite state machine |
6.1, 6.2, 6.3 |
Recommended Sources
| Textbook |
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| Additional Resources |
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Material Sharing
| Documents | |
| Assignments | |
| Exams |
Assessment
| IN-TERM STUDIES | NUMBER | PERCENTAGE |
| Mid-terms | 1 | 100 |
| Quizzes | ||
| Assignments | ||
| Total | 100 | |
| CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE | 60 | |
| CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE | 40 | |
| Total | 100 |
| COURSE CATEGORY | Core Courses |
Course’s Contribution to Program
| No | Program Learning Outcomes | Contribution | ||||
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) | x | ||||
| 2 | Acquiring fundamental knowledge on fundamental research fields in mathematics | x | ||||
| 3 | Ability form and interpret the relations between research topics in mathematics | x | ||||
| 4 | Ability to define, formulate and solve mathematical problems | x | ||||
| 5 | Consciousness of professional ethics and responsibilty | x | ||||
| 6 | Ability to communicate actively | x | ||||
| 7 | Ability of self-development in fields of interest | x | ||||
| 8 | Ability to learn, choose and use necessary information technologies | x | ||||
| 9 | Lifelong education | x | ||||
ECTS
| Activities | Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Course Duration (14x Total course hours) | 14 | 4 | 56 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 6 | 84 |
| Mid-terms (Including self study) | 1 | 15 | 15 |
| Quizzes | |||
| Assignments | |||
| Final examination (Including self study) | 1 | 20 | 20 |
| Total Work Load | 175 | ||
| Total Work Load / 25 (h) | 7 | ||
| ECTS Credit of the Course | 7 |