| Academic Year |
2026Year |
School/Graduate School |
Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program |
| Lecture Code |
WSA21000 |
Subject Classification |
Specialized Education |
| Subject Name |
代数数理基礎講義Ａ |
Subject Name
（Katakana） |
ダイスウスウリキソコウギエー |
Subject Name in
English |
Algebra A |
| Instructor |
MATSUI HIROKI |
Instructor
(Katakana) |
マツイ ヒロキ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, First Semester, 1Term |
| Days, Periods, and Classrooms |
(1T) Mon5-6,Weds5-6：SCI E104 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| Blackboard |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
B
:
Japanese／English |
| Course Level |
5
:
Graduate Basic
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
master course |
| Keywords |
rings, modules, homological algebra |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Class Objectives
/Class Outline |
This course provides an introduction to homological algebra, which can be regarded as linear algebra over rings, covering its fundamental concepts and applications.
|
| Class Schedule |
Lesson1: Review on rings and modules (1)
Lesson2: Review on rings and modules (2)
Lesson3: Hom modules
Lesson4: Chain complexes
Lesson5: Exact sequences
Lesson6: Homology groups of simplicial complexes (1)
Lesson7: Homology groups of simplicial complexes (2)
Lesson8: Tensor products
Lesson9: Projective modules and injective modules (1)
Lesson10: Projective modules and injective modules (2)
Lesson11: Tor modules and Ext modules (1)
Lesson12: Tor modules and Ext modules (2)
Lesson13: Universal coefficient theorem
Lesson14: Persistent homology (1)
Lesson15: Persistent homology (2)
|
Text/Reference
Books,etc. |
Handouts will be assigned during lectures. No specific textbook is fixed.
Any homological algebra textbook is suitable as a study-aid book. |
PC or AV used in
Class,etc. |
Handouts, moodle |
| (More Details) |
|
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
After each lecture, be sure to thoroughly review the course content. In addition, working through concrete examples is helpful for better understanding. |
| Requirements |
Although the lecture begins with a review, it is recommended that students have taken Algebra A.
|
| Grading Method |
Based on reports. Detailed explanations will be given in the class. |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |