| Program / Major | mDP | Goals |
|---|---|---|
| Mathematical Sciences Course | DP-4・1 | 研究者・技術者としての基礎的素養 代数、幾何、解析、応用数学、情報数学などの専門知識を修得し、課題を抽象化して数理的な問題設定をすると共に、適切な理論的考察・計算的手法を用いて問題解決策を構築できる。 |
This course builds on the content studied in the foundational courses Linear Algebra 1 and Calculus 1 and aims to provide
a systematic understanding of the proofs of theorems introduced there as well as related advanced topics. Rather than merely
acquiring computational techniques, students will develop mathematical reasoning skills by examining how theorems are established
within their underlying logical structures. Furthermore, through careful reading and analysis of proofs, and by gaining experience
in constructing proofs independently, students are expected to cultivate the ability to present logical arguments coherently
and to write precisely and rigorously.
The course provides explanations of the proofs of key theorems and related advanced topics. Sufficient time will be allocated
for exercises to ensure a solid understanding of the theorems and to acquire skills in structuring and presenting proofs.
In the exercises, students are encouraged to clarify the relationships between assumptions, claims, and reasoning, and to
develop the ability to construct proofs without logical gaps. Through this process, students are expected to deepen their
understanding of mathematical content and enhance their ability to express it clearly and logically.
- To be able to handle matrices and systems of linear equations at a basic level
- To be able to perform specific calculations of calculus with one variable
- Understand the basics of sets and mappings and be able to handle them concretely
| Exercises and assignments | Exams | Total. | |
|---|---|---|---|
| 1. | 22% | 20% | 42% |
| 2. | 22% | 20% | 42% |
| 3. | 8% | 8% | 16% |
| Total. | 52% | 48% | - |
Evaluation is based on in-class exercises and assignments (52%) and the final exam (48%); a total score of 60% or higher is
required to pass.
A passing grade is awarded if the student demonstrates an understanding of the fundamental concepts covered in the lectures and the ability to solve the problems.
A passing grade is awarded if the student demonstrates an understanding of the fundamental concepts covered in the lectures and the ability to solve the problems.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Review of complex numbers | Review of the high school mathematics | 200minutes |
| 2. | Review of vector | Review of the high school mathematics | 200minutes |
| 3. | Review of calculus | Review of a previous lecture | 200minutes |
| 4. | Matrix calculations | Review of a previous lecture | 200minutes |
| 5. | Continuous function | Review of a previous lecture | 200minutes |
| 6. | Gaussian elimination | Review of a previous lecture | 200minutes |
| 7. | Definition of the derivative and computation of derivatives | Review of a previous lecture | 200minutes |
| 8. | Fundamentals of Sets | Review of a previous lecture | 200minutes |
| 9. | Function (injective, surjective, bijective etc.) | Review of a previous lecture | 200minutes |
| 10. | Indefinite integral | Review of a previous lecture | 200minutes |
| 11. | Computation of determinants | Review of a previous lecture | 200minutes |
| 12. | Definite integral | Review of a previous lecture | 200minutes |
| 13. | Properties of determinants | Review of a previous lecture | 200minutes |
| 14. | Examination | Review of a previous lecture | 200minutes |
| Total. | - | - | 2800minutes |
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in the class |
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicable |
|---|
Last modified : Fri Jul 10 04:06:44 JST 2026