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2019　Discrete, Algebraic and Geometric Structures I

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Suzuki Sakie  Nishibata Shinya  Umehara Masaaki  Miura Hideyuki  Murofushi Toshiaki 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(W831)  Fri3-4(W831)  
Group
-
Course number
MCS.T408
Credits
2
Academic year
2019
Offered quarter
4Q
Syllabus updated
2019/9/17
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 students are expected to learn advanced mathematical methods to analyze discrete, algebraic and geometric structures appeared in mathematical and computing science, and to be able to apply them to some practical problems.

Keywords

discrete structure, algebraic structure, geometric structure

Competencies that will be developed

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

Class flow

The course provides advanced topics of discrete, algebraic and geometric structures.

Course schedule/Required learning

  Course schedule Required learning
Class 1 PL manifolds Understand the contents covered by the lecture.
Class 2 Knots and links Understand the contents covered by the lecture.
Class 3 Knot groups Understand the contents covered by the lecture.
Class 4 Kauffman bracket and Jones polynomial Understand the contents covered by the lecture.
Class 5 Jones polynomial as a functor Understand the contents covered by the lecture.
Class 6 Hopf algebras Understand the contents covered by the lecture.
Class 7 Quantum groups Understand the contents covered by the lecture.
Class 8 Colored Jones polynomial Understand the contents covered by the lecture.
Class 9 Universal quantum invariant Understand the contents covered by the lecture.
Class 10 Commutativity of the Hopf algebra structure of quantum groups and that of bottom tangles Understand the contents covered by the lecture.
Class 11 Dehn surgery Understand the contents covered by the lecture.
Class 12 unified Witten-Reshetkhin-Turaev invariant Understand the contents covered by the lecture.
Class 13 triangulation Understand the contents covered by the lecture.
Class 14 Dijkgraaf-Witten invariant Understand the contents covered by the lecture.
Class 15 Hennings invariant Understand the contents covered by the lecture.

Textbook(s)

Not specified in particular.

Reference books, course materials, etc.

References and some handouts will be provided in the lectures.

Assessment criteria and methods

Students to write a report on some aspects of the course.

Related courses

  • MCS.T505 ： Discrete, Algebraic and Geometric Structures Ⅱ

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

None.

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