2024 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)
- Jin Takahashi / Sakie Suzuki / Masaaki Umehara / Zin Arai / Shunsuke Tsuchioka / Toshiaki Murofushi / Shinya Nishibata
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 7-8 Mon / 7-8 Thu
- Class
- -
- Course Code
- MCS.T331
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 14, 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
Euclidean geometry to modern geometry, Numerical analysis, Symbolic dynamics, Chaos, Automaton, 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 | 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 2 | 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 3 | Hyperbolic geometry as non-Euclidean geometry (Negation of parallel postulate, hyperbolic geometry） | Understand the contents covered by the lecture. |
| Class 4 | Projective Geometry (Desarg's theorem, Pappus' theorem, Pascal's theorem) | Understand the contents covered by the lecture. |
| Class 5 | Geometry of Möbius strip (knot, writhe, malleable surface, singularity) | Understand the contents covered by the lecture. |
| Class 6 | Introduction to numerical analysis I (nonlinear equations) | Understand the contents covered by the lecture. |
| Class 7 | Introduction to numerical analysis II (system of nonlinear equations) | Understand the contents covered by the lecture. |
| Class 8 | Introduction to symbolic dynamics | Understand the contents covered by the lecture. |
| Class 9 | Symbolic dynamics, Chaos and Automaton | Understand the contents covered by the lecture. |
| Class 10 | Application of symbolic dynamics in data storage | Understand the contents covered by the lecture. |
| Class 11 | Integer partitions and Young diagrams | Understand the contents covered by the lecture. |
| Class 12 | Analytic combinatorics | Understand the contents covered by the lecture. |
| Class 13 | 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.
D. Lind & B. Marcus, An Introduction to Symbolic Dynamics and Coding, Cambridge University Press, 2009
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.
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
Masaaki Umehara (umehara[at]c.titech.ac.jp)
Office hours
To be announced in the first class of each instructor.