2020 Faculty Courses School of Computing Department of Mathematical and Computing Science Graduate major in Mathematical and Computing Science
Topics in Algebra
- Academic unit or major
- Graduate major in Mathematical and Computing Science
- Instructor(s)
- Shunsuke Tsuchioka
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 7-8 Mon (Zoom) / 7-8 Thu (Zoom)
- Class
- -
- Course Code
- MCS.T417
- Number of credits
- 200
- Course offered
- 2020
- Offered quarter
- 4Q
- Syllabus updated
- Jul 10, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Give an introductory course on integer partitions
Course description and aims
Get understand integer partitions and related topics
Keywords
integer partitions, generating functions, Young diagrams, q-series, representation theory
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Give lectures on the textbook
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | introduction |
Understand the content of the class |
| Class 2 | Euler partition theorem |
Understand the content of the class |
| Class 3 | Young diagrams |
Understand the content of the class |
| Class 4 | Rogers-Ramanujan identities |
Understand the content of the class |
| Class 5 | generating functions |
Understand the content of the class |
| Class 6 | partition numbers |
Understand the content of the class |
| Class 7 | Gaussian polynomials |
Understand the content of the class |
| Class 8 | Durfee square |
Understand the content of the class |
| Class 9 | random partitions |
Understand the content of the class |
| Class 10 | plane partitions |
Understand the content of the class |
| Class 11 | Hook length formula |
Understand the content of the class |
| Class 12 | symmetric groups and integer partitions |
Understand the content of the class |
| Class 13 | affine Lie algebras and Rogers-Ramanujan identities |
Understand the content of the class |
| Class 14 | Open problems |
Understand the content of the class |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Integer partitions, George E. Andrews and Kimmo Eriksson, Cambridge University Press (2004)
Reference books, course materials, etc.
I will open a lecture webpage and upload supplementing materials
Evaluation methods and criteria
based on report assignments
Related courses
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
- MTH.A331 ： Algebra III
Prerequisites
Nothing in particular