| Program / Major | mDP | Goals |
|---|---|---|
| Mathematical Sciences Course | DP-4・2 | キャリアを見据えた高度な専門知識 現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。 |
This course aims to provide fundamental knowledge in discrete mathematics. In particular, students will learn various algebraic
methods for solving combinatorial problems, understand the fundamentals and applications of graph theory, and study the basics
and applications of network optimization problems.
The course has the following three learning objectives:
1. To understand basic mathematical concepts such as partially ordered sets, sequences, and group actions, and to apply them to combinatorial problems.
2. To understand fundamental concepts and properties of graph theory and apply them to practical problems such as networks.
3. To understand various algorithms on graphs and apply them to concrete problems.
The course has the following three learning objectives:
1. To understand basic mathematical concepts such as partially ordered sets, sequences, and group actions, and to apply them to combinatorial problems.
2. To understand fundamental concepts and properties of graph theory and apply them to practical problems such as networks.
3. To understand various algorithms on graphs and apply them to concrete problems.
Discrete mathematics deals with “discrete” objects, which stand in contrast to “continuous” ones, and appears in a wide range
of fields including natural and social sciences. While mathematics dealing with continuous objects, such as calculus, has
a long history, discrete mathematics has rapidly developed in recent years alongside advances in information science and computational
power, leading to significant expansion in both theory and applications.
In this course, we cover a broad range of topics in discrete mathematics, including logic, counting methods, graph theory, networks, discrete optimization, and discrete dynamical systems. The aim is to develop a solid understanding of fundamental concepts and to explore their applications to real-world problems.
The course will be conducted in an omnibus format by three instructors and will consist of lectures supplemented with exercises.
In this course, we cover a broad range of topics in discrete mathematics, including logic, counting methods, graph theory, networks, discrete optimization, and discrete dynamical systems. The aim is to develop a solid understanding of fundamental concepts and to explore their applications to real-world problems.
The course will be conducted in an omnibus format by three instructors and will consist of lectures supplemented with exercises.
- Understand fundamental mathematical concepts such as partially ordered sets, sequences, and group actions, and apply them to combinatorial problems.
- Understand basic concepts and properties of graph theory and apply them to practical problems such as networks.
- Understand various graph algorithms and apply them to concrete problems.
| reports | exam | Total. | |
|---|---|---|---|
| 1. | 25% | 8% | 33% |
| 2. | 25% | 8% | 33% |
| 3. | 25% | 9% | 34% |
| Total. | 75% | 25% | - |
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Introduction | 190minutes | |
| 2. | Logic and Boolean Algebra | 190minutes | |
| 3. | Partially Ordered Sets and the Möbius Inversion Formula | 190minutes | |
| 4. | Generating Functions | 190minutes | |
| 5. | Permutations and Burnside’s Lemma | 190minutes | |
| 6. | Definitions of Graphs and Basic Terminology and Properties | 190minutes | |
| 7. | Classes of Graphs and Their Properties | 190minutes | |
| 8. | Connectivity, Eulerian Graphs, and Hamiltonian Graphs | 190minutes | |
| 9. | Network Measures and Examples of Complex Networks | 190minutes | |
| 10. | Graph Search Algorithms | 190minutes | |
| 11. | Shortest Path Problems | 190minutes | |
| 12. | Maximum Flow Problems | 190minutes | |
| 13. | Discrete Dynamical Systems | 190minutes | |
| 14. | Final Examination and Review | 190minutes | |
| Total. | - | 2660minutes |
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback outside of the class (ScombZ, mail, etc.) |
No specific textbook is assigned. Relevant materials will be introduced by each instructor during the lectures as needed.
- Ishiwata: Lunch time on Thursday (Please make an appointment in advance.)
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Wed Mar 25 04:05:36 JST 2026