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2021　Algebra

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Instructor(s)
Tsuchioka Shunsuke  Umehara Masaaki  Nishibata Shinya  Miura Hideyuki  Murofushi Toshiaki  Suzuki Sakie  Takahashi Jin  Ichiki Shunsuke 
Class Format
Lecture / Exercise     
Media-enhanced courses
Day/Period(Room No.)
Mon5-8(W641)  Thr5-6(W641)  
Group
-
Course number
MCS.T231
Credits
3
Academic year
2021
Offered quarter
4Q
Syllabus updated
2021/9/29
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

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.

Student learning outcomes

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 that will be developed

✔ 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/Required learning

  Course schedule Required learning
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.

Out-of-Class Study Time (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)

Kazuo Matsuzaka, Algebraic Systems, Iwanami Shoten

Reference books, course materials, etc.

Further references are provided in the lectures.

Assessment criteria and methods

By scores of examinations and recitation sessions.

Related courses

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

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None

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