2020 Topics in Algebra

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Tsuchioka Shunsuke 
Course component(s)
Lecture     
Day/Period(Room No.)
Mon7-8(Zoom)  Thr7-8(Zoom)  
Group
-
Course number
MCS.T417
Credits
2
Academic year
2020
Offered quarter
4Q
Syllabus updated
2020/10/1
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

Give an introductory course on integer partitions

Student learning outcomes

Get understand integer partitions and related topics

Keywords

integer partitions, generating functions, Young diagrams, q-series, representation theory

Competencies that will be developed

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

Class flow

Give lectures on the textbook

Course schedule/Required learning

  Course schedule Required learning
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

Out-of-Class Study Time (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

Assessment criteria and methods

based on report assignments

Related courses

  • MTH.A301 : Algebra I
  • MTH.A302 : Algebra II
  • MTH.A331 : Algebra III

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

Nothing in particular

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