2020 Discrete, Algebraic and Geometric Structures II

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Suzuki Sakie  Umehara Masaaki  Miura Hideyuki  Murofushi Toshiaki  Nishibata Shinya 
Course component(s)
Lecture
Mode of instruction
ZOOM
Day/Period(Room No.)
Tue3-4(Zoom)  Fri3-4(Zoom)  
Group
-
Course number
MCS.T505
Credits
2
Academic year
2020
Offered quarter
3Q
Syllabus updated
2020/9/23
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

Discrete, algebraic and geometric structures appear in many stages of the study in mathematical and computing science. The objective of this course is to describe some advanced topics, and for students to know mathematical structures behind them.

Student learning outcomes

The audiences are expected to gain advanced mathematical methods to analyze discrete, algebraic and geometric structures.

Keywords

Poisson algebras and quantizations, quantum groups, quantum invariants of knots and 3-dimensional manifolds

Competencies that will be developed

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

Class flow

Lectures and exercises

Course schedule/Required learning

  Course schedule Required learning
Class 1 Lie algebras and symplectic manifolds Understand the contents covered by the lecture.
Class 2 Modules over rings of power series and completions Understand the contents covered by the lecture.
Class 3 Poisson algebras Understand the contents covered by the lecture.
Class 4 Quantizations of Poisson algebras Understand the contents covered by the lecture.
Class 5 Poisson manifolds Understand the contents covered by the lecture.
Class 6 Quantization of Poisson manifolds Understand the contents covered by the lecture.
Class 7 Physical meaning of quantization Understand the contents covered by the lecture.
Class 8 Knots and links Understand the contents covered by the lecture.
Class 9 Kauffman bracket and Jones polynomial Understand the contents covered by the lecture.
Class 10 Hopf algebras Understand the contents covered by the lecture.
Class 11 Quantum groups Understand the contents covered by the lecture.
Class 12 Colored Jones polynomial Understand the contents covered by the lecture.
Class 13 Universal quantum invariant Understand the contents covered by the lecture.
Class 14 Quantum invariants of 3-dimensional manifolds Understand the contents covered by the lecture.

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)

Not specified.

Reference books, course materials, etc.

References are provided in the lectures.

Assessment criteria and methods

Evaluate by homework.

Related courses

  • MCS.T331 : Discrete Mathematics
  • MCS.T231 : Algebra

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

Not specified.

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