Course title
Introduction to Advanced Mathematics

KAMEKO Masaki Click to show questionnaire result at 2018


TAMORI Hiroyoshi
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.
Class schedule

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

Take-home examination Homework assignment Term-end assignment Examination Total.
1. 15% 15%
2. 15% 15%
3. 20% 15% 35%
4. 35% 35%
Total. 30% 20% 15% 35% -
Evaluation method and criteria
Take-home exam 30%
Homework assignment 20%
Term-end assignment 15%
Examination 35%
If applicable, based on quizzes and classroom activities, points may be added to final scores.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
Ted Sundstrom, Mathematical Reasoning: Writing and Proof Version 3, available at
Elementary set theory, Calculus and linear algebra.
Office hours and How to contact professors for questions
  • Send e-mail for appointment if necessary.
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
Education related SDGs:the Sustainable Development Goals
Last modified : Sat Sep 09 06:33:25 JST 2023