Course title
V01800012
Introduction to Advanced Mathematics
 kameko masaki enomoto yuko oya hironori
Course description
We focus on the tools necessary for writing and thinking like a mathematician. Students will learn to read proofs critically and to write proofs rigorously. In addition, not only methods of proof, in this course, we review linear algebra and calculus.
Purpose of class
Successful students will be able to read proofs critically.
Successful students will be able to write proofs rigorously.
Successful students will gain deeper understanding of linear algebra.
Successful students will gain deeper understanding of calculus.
Goals and objectives
1. Students will be able to read proofs critically.
2. Students will be able to write proofs rigorously.
3. Students will gain deeper understanding of linear algebra.
4. Students will gain deeper understanding of calculus.
Language
English
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. LaTeX Handout No.1 200minutes
2. Direct proof Handout No.2 200minutes
3. Proof by induction Handout No.3 200minutes
4. Proof by contradiction Handout No.4 200minutes
5. Review of linear algebra: vector spaces Handout No.5 200minutes
6. Review of linear algebra: linear maps Handout No.6 200minutes
7. Review of linear algebra: bases Handout No.7 200minutes
8. Review of linear algebra: matrix representations Handout No.8 200minutes
9. Examination 1 Review 200minutes
10. Review of calculus: derivatives Handout No.9 200minutes
11. Review of calculus: Mean value theorem Handout No.10 200minutes
12. Review of calculus: indefinite integrals Handout No.11 200minutes
13. Review of calculus: Riemann integrals Handout No.12 200minutes
14. Examination 2 Review 200minutes
Total. - - 2800minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Take-home examination Examination 1 Examination 2 Total.
1. 15% 15%
2. 15% 15%
3. 35% 35%
4. 35% 35%
Total. 30% 35% 35% -
Evaluation method and criteria
Take-home exam 30%
Examination 1 35%
Examination 2 35%
If applicable, based on quizzes, homework assignments and/or classroom activities, points may be added to exam scores.
Textbooks and reference materials
Agata Stefanowicz, Proofs and Mathematical Reasoning. University of Birmingham, Mathematics support centre,
Prerequisites
Elementary set theory, Calculus and linear algebra.

TOEIC 550 以上相当の英語力があることが望ましい.
Office hours and How to contact professors for questions
• Send e-mail for appointment if necessary.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
• Course that cultivates an ability for utilizing knowledge
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A 該当しない
Education related SDGs:the Sustainable Development Goals
• 4.QUALITY EDUCATION
• 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Wed May 12 04:44:43 JST 2021