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.
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.
algebra, group, ring, field
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
The lectures provide the fundamentals of algebra with recitation sessions.
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. |
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.
Kazuo Matsuzaka, Algebraic Systems, Iwanami Shoten
References are provided in the lectures.
By scores of examinations and recitation sessions.
None