| 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 is based on the foundational subjects 「Linear Algebra 2」 and 「Calculus 2」, and aims to deepen students’ understanding
of the proofs of the principal theorems covered therein, as well as related advanced topics.
Rather than focusing solely on the acquisition of computational techniques, the course carefully examines the logical processes through which theorems are derived, thereby fostering mathematical reasoning skills. Furthermore, through analyzing the structure of proofs and gaining experience in constructing logical arguments independently, students will develop the ability to present explanations in a clear and coherent manner and to express themselves with logical precision.
Rather than focusing solely on the acquisition of computational techniques, the course carefully examines the logical processes through which theorems are derived, thereby fostering mathematical reasoning skills. Furthermore, through analyzing the structure of proofs and gaining experience in constructing logical arguments independently, students will develop the ability to present explanations in a clear and coherent manner and to express themselves with logical precision.
This course will be conducted in an omnibus format, with each instructor lecturing from the perspective of their area of expertise
on the proofs of the principal theorems in 「Linear Algebra 2」 and 「Calculus 2」, the theoretical frameworks underlying them,
and related advanced topics. Sufficient time will be devoted to exercises in order to solidify students’ understanding of
the theorems and to help them acquire skills in structuring proofs and presenting mathematical arguments. In the exercises,
students will aim to clarify the relationships among assumptions, claims, and reasoning, and to develop the ability to construct
proofs free of logical gaps. Through this process, the course seeks to enhance both a deep understanding of mathematical content
and the ability to express it accurately and logically.
- To be able to diagonalize specific matrices.
- Understand abstract linear algebraic concepts and apply them to concrete problems.
- To be able to perform concrete calculus calculations of multivariate functions.
| Exercises and assignments | Examination | Total. | |
|---|---|---|---|
| 1. | 15% | 12% | 27% |
| 2. | 12% | 12% | 24% |
| 3. | 25% | 24% | 49% |
| Total. | 52% | 48% | - |
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Review of matrices | Review of 「Linear Algebra 1」 | 200minutes |
| 2. | Continuous functions of multiple variables | Review of a previous lecture | 200minutes |
| 3. | Diagonalization of matrices (1) | Review of a previous lecture | 200minutes |
| 4. | Definition of partial derivative and partial derivative | Review of a previous lecture | 200minutes |
| 5. | Diagonalization of matrices (2) | Review of a previous lecture | 200minutes |
| 6. | Partial derivatives of composite functions | Review of a previous lecture | 200minutes |
| 7. | Unitary diagonalization | Review of a previous lecture | 200minutes |
| 8. | Differential equations | Review of 「Differential equations」 | 200minutes |
| 9. | Linear spaces and linear maps (1) | Review of a previous lecture | 200minutes |
| 10. | Conditional Extremum Problems | Review of a previous lecture | 200minutes |
| 11. | Linear spaces and linear maps (2) | Review of a previous lecture | 200minutes |
| 12. | Techniques for the computation of multiple integrals | Review of a previous lecture | 200minutes |
| 13. | Matrix representation | Review of a previous lecture | 200minutes |
| 14. | Final exam | Review of a previous lecture | 200minutes |
| Total. | - | - | 2800minutes |
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in the class |
| Work experience | Work experience and relevance to the course content if applicable |
|---|
Last modified : Mon Mar 23 04:06:49 JST 2026