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2016　Discrete, Algebraic and Geometric Structures II

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Academic unit or major
Graduate major in Mathematical and Computing Science
Instructor(s)
Kojima Sadayoshi  Terashima Yuji 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(W832)  Fri3-4(W832)  
Group
-
Course number
MCS.T505
Credits
2
Academic year
2016
Offered quarter
3Q
Syllabus updated
2016/4/27
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

Discrete, algebraic and geometric structures appear in many stages of the study of mathematical and computing science. The objective of this lecture is to describe some advanced such topics. The topics in 2016 are discrete structures in graph theory, braid group, knot theory.

Student learning outcomes

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

Keywords

discrete structure, algebraic structure, geometric structure, graph, braid group, knot

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 Generating function with graph Understand the contents covered by the lecture.
Class 2 Algebraic structure of graphs Understand the contents covered by the lecture.
Class 3 Braid group Understand the contents covered by the lecture.
Class 4 Knot Understand the contents covered by the lecture.
Class 5 Knot invariant Understand the contents covered by the lecture.
Class 6 Knots and graphs Understand the contents covered by the lecture.
Class 7 Discrete structure of surfaces Understand the contents covered by the lecture.
Class 8 Discrete structure of manifolds Understand the contents covered by the lecture.
Class 9 Representaion of braid groups Understand the contents covered by the lecture.
Class 10 Mapping class group Understand the contents covered by the lecture.
Class 11 Representation of mapping class gorups Understand the contents covered by the lecture.
Class 12 Quantum invariant Understand the contents covered by the lecture.
Class 13 Discrete system Understand the contents covered by the lecture.
Class 14 Algebraic structure of discrete systems Understand the contents covered by the lecture.
Class 15 Discrete structure in mathematical physics Understand the contents covered by the lecture.

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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