Course title
330012001
Introduction to Mathematics 1

 ENOMOTO Yuko

SHIMIZU Kenichi
Middle-level Diploma Policy (mDP)
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。
Purpose of class
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.
Course description
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.
Goals and objectives
  1. To be able to handle matrices and systems of linear equations at a basic level
  2. To be able to perform specific calculations of calculus with one variable
  3. Understand the basics of sets and mappings and be able to handle them concretely
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Exercises and assignments Exams Total.
1. 22% 20% 42%
2. 22% 20% 42%
3. 8% 8% 16%
Total. 52% 48% -
Evaluation method and criteria
Exercises, Assignments, and Exams
Language
Japanese
Class schedule

 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
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
Prerequisites
Office hours and How to contact professors for questions
    Regionally-oriented
    Non-regionally-oriented course
    Development of social and professional independence
      Active-learning course
      Most classes are interactive
      Course by professor with work experience
      Work experience Work experience and relevance to the course content if applicable
      Education related SDGs:the Sustainable Development Goals
      • 4.QUALITY EDUCATION
      Last modified : Mon Mar 23 04:06:47 JST 2026