Introduction to Advanced Mathematics

Course title

V0180001

	KAMEKO Masaki
	ENOMOTO Yuko
	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

Students will be able to read proofs critically.
Students will be able to write proofs rigorously.
Students will gain deeper understanding of linear algebra.
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
1.	LaTeX	Homework assignment #1-1
2.	Direct proof	Handout No.2	200minutes
2.	Direct proof	Homework assignment #1-2
3.	Proof by induction	Handout No.3	200minutes
3.	Proof by induction	Homework assignment #1-3
4.	Proof by contradiction	Handout No.4	200minutes
4.	Proof by contradiction	Homework assignment #1-4
5.	Review of linear algebra: vector spaces	Handout No.5	200minutes
5.	Review of linear algebra: vector spaces	Homework assignment #2-1
6.	Review of linear algebra: linear maps	Handout No.6	200minutes
6.	Review of linear algebra: linear maps	Homework assignment #2-2
7.	Review of linear algebra: bases	Handout No.7	200minutes
7.	Review of linear algebra: bases	Homework assignment #2-3
8.	Review of linear algebra: matrix representations	Handout No.8	200minutes
8.	Review of linear algebra: matrix representations	Homework assignment #2-4
9.	Exercise and Examination 1	Review	200minutes
9.	Exercise and Examination 1	Term-end assignment 1
10.	Review of calculus: derivatives	Handout No.9	200minutes
10.	Review of calculus: derivatives	Homework assignment #3-1
11.	Review of calculus: Mean value theorem	Handout No.10	200minutes
11.	Review of calculus: Mean value theorem	Homework assignment #3-2
12.	Review of calculus: indefinite integrals	Handout No.11	200minutes
12.	Review of calculus: indefinite integrals	Homework assignment #3-3
13.	Review of calculus: Riemann integrals	Handout No.12	200minutes
13.	Review of calculus: Riemann integrals	Homework assignment #3-4
14.	Exercise and Examination 2	Review	200minutes
14.	Exercise and Examination 2	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 https://scholarworks.gvsu.edu/books/24/

Prerequisites

Elementary set theory, Calculus and linear algebra.

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

Education related SDGs:the Sustainable Development Goals

4.QUALITY EDUCATION
9.INDUSTRY, INNOVATION AND INFRASTRUCTURE

Last modified : Sat Sep 09 06:33:25 JST 2023