2024 Faculty Courses School of Computing Undergraduate major in Mathematical and Computing Science

Algebra

Academic unit or major: Undergraduate major in Mathematical and Computing Science
Instructor(s): Shunsuke Tsuchioka / Masaaki Umehara / Shinya Nishibata / Zin Arai / Toshiaki Murofushi / Sakie Suzuki / Jin Takahashi / Shunsuke Ichiki
Class Format: Lecture/Exercise (Face-to-face)
Media-enhanced courses: -
Day of week/Period (Classrooms): 5-8 Mon / 5-6 Thu
Class: -
Course Code: MCS.T231
Number of credits: 210
Course offered: 2024
Offered quarter: 4Q
Syllabus updated: Mar 17, 2025
Language: Japanese

Syllabus

Course overview and goals

The algebraic structure plays an important role in mathematical and computing sciences. The objectives of this course are to provide the fundamentals of algebra, particularly on congruence, group, subgroup, homomorphism, quotient group, homomorphism theorem, ring, ideal, finite fields and so on, and also for the students to built backgrounds to apply algebra in mathematical and computing sciences.

Course description and aims

The students are expected to understand the fundamentals of mathematical methods to handle algebraic structures appeared in mathematical and computing sciences and also to be able to apply them to practical problems.

Keywords

algebra, group, ring, field

Competencies

Specialist skills
Intercultural skills
Communication skills
Critical thinking skills
Practical and/or problem-solving skills

Class flow

The lectures provide the fundamentals of algebra with recitation sessions.

Course schedule/Objectives

	Course schedule	Objectives
Class 1	Integer and Congruence	Understand the contents covered by the lecture.
Class 2	Multiplicative Group	Understand the contents covered by the lecture.
Class 3	Exercises regarding the contents covered up to the 2nd lecture	Cultivate more practical understanding by doing exercises.
Class 4	Group	Understand the contents covered by the lecture.
Class 5	Examples	Understand the contents covered by the lecture.
Class 6	Exercises regarding the contents covered up to the 5th lecture	Cultivate more practical understanding by doing exercises.
Class 7	Subgroup	Understand the contents covered by the lecture.
Class 8	Homomorphism, Kernel and Image	Understand the contents covered by the lecture.
Class 9	Exercises regarding the contents covered up to the 8th lecture	Cultivate more practical understanding by doing exercises.
Class 10	Quotient Group	Understand the contents covered by the lecture.
Class 11	Homomorphism Theorem	Understand the contents covered by the lecture.
Class 12	Exercises regarding the contents covered up to the 11th lecture	Cultivate more practical understanding by doing exercises.
Class 13	Direct Product	Understand the contents covered by the lecture.
Class 14	Ring	Understand the contents covered by the lecture.
Class 15	Exercises regarding the contents covered up to the 14th lecture	Cultivate more practical understanding by doing exercises.
Class 16	Ideal and Quotient Ring	Understand the contents covered by the lecture.
Class 17	Field	Understand the contents covered by the lecture.
Class 18	Exercises regarding the contents covered up to the 17th lecture	Cultivate more practical understanding by doing exercises.
Class 19	Polynomial Ring	Understand the contents covered by the lecture.
Class 20	Finite Field	Understand the contents covered by the lecture.
Class 21	Exercises regarding the contents covered up to the 20th lecture	Cultivate more practical understanding by doing exercises.
Class 22	Algebraic Number Field	Understand the contents covered by the lecture.

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

The lecturer will open a webpage and upload materials.

Reference books, course materials, etc.

Further references are provided in the lectures.

Evaluation methods and criteria

By scores of examinations and recitation sessions.

Related courses

MCS.T203 ： Linear Algebra and Its Applications
MCS.T201 ： Set and Topology I

Prerequisites

None