2023 Faculty Courses School of Computing Undergraduate major in Mathematical and Computing Science
Discrete Mathematics
- Academic unit or major
- Undergraduate major in Mathematical and Computing Science
- Instructor(s)
- Masaaki Umehara / Toshiaki Murofushi / Shinya Nishibata / Hideyuki Miura / Sakie Suzuki / Shunsuke Tsuchioka
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 7-8 Mon (W8E-308(W834)) / 7-8 Thu (W8E-308(W834))
- Class
- -
- Course Code
- MCS.T331
- Number of credits
- 200
- Course offered
- 2023
- Offered quarter
- 2Q
- Syllabus updated
- Jul 8, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Discrete mathematics plays an important role in mathematical and computing sciences. The objective of this course is to provide the fundamentals of discrete mathematics.
Course description and aims
The students are expected to understand the fundamentals of discrete mathematics appeared in mathematical and computing sciences and also to be able to apply them to practical problems.
Keywords
Euler characteristic, Four color problem, Euclidean Geometry to Modern Geometry, Partially ordered sets, Lattices, Formal Concept Analysis, Generating function, Integer partitions, Representation theory, Hyperbolic summation, Groebner basis, Experimental mathematics
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The lectures provide the fundamentals of discrete mathematics.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Curvature and Euler characteristic | Understand the contents covered by the lecture. |
| Class 2 | Four color problem I | Understand the contents covered by the lecture. |
| Class 3 | Four color problem II | Understand the contents covered by the lecture. |
| Class 4 | Knots and invariants | Understand the contents covered by the lecture. |
| Class 5 | Jones polynomial | Understand the contents covered by the lecture. |
| Class 6 | The first half of volume 1 of Elements (The axiom of parallel lines, sum of interior angles of a triangle) | Understand the contents covered by the lecture. |
| Class 7 | The last half of volume 1 of Elements (Parallelogram, area, the Pythagorean theorem) | Understand the contents covered by the lecture. |
| Class 8 | Hyperbolic geometry as non-Euclidean geometry (Negation of parallel postulate, hyperbolic geometry） | Understand the contents covered by the lecture. |
| Class 9 | Partially ordered sets | Understand the contents covered by the lecture. |
| Class 10 | Lattices | Understand the contents covered by the lecture. |
| Class 11 | Formal Concept Analysis | Understand the contents covered by the lecture. |
| Class 12 | Integer partitions and Young diagrams | Understand the contents covered by the lecture. |
| Class 13 | Analytic combinatorics | Understand the contents covered by the lecture. |
| Class 14 | Modular forms | Understand the contents covered by the lecture. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Not specified.
Reference books, course materials, etc.
B. A. Davey & H. A. Priestley, “Introduction to Lattices and Order”, 2nd ed., Cambridge Univ. Press, 2002,
B. Ganter & R. Wille, “Formal Concept Analysis — Mathematical Foundations”, Springer, 1999
O. Suzuki, T. Murofushi, Formal Concept Analysis: Introduction, Support Software, and Applications,
Journal of Japan Society for Fuzzy Theory and Intelligent Informatics, vol. 19, no. 2 (2007) pp. 103-142.
Evaluation methods and criteria
By scores of reports.
Related courses
- MCS.T231 ： Algebra
- MCS.T201 ： Set and Topology I
- MCS.T202 ： Exercises in Set and Topology I
Prerequisites
None.