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2016　Discrete, Algebraic and Geometric Structures I

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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.)
Mon5-6(W832)  Thr5-6(W832)  
Group
-
Course number
MCS.T408
Credits
2
Academic year
2016
Offered quarter
1Q
Syllabus updated
2016/4/27
Lecture notes updated
-
Language used
English
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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, based on mathematical backgrounds equivalent to ones provided by college courses of the Department of Mathematical and Computing Science. The theme in 2016 is the geometric group theory.

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, geometric group theory

Competencies that will be developed

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

Class flow

The course starts with the very beginning of the geometric group theory and covers some of recent advanced topics eventually.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Review on Group Theory Understand the contents covered by the lecture.
Class 2 Fundamental Group and Covering Space Understand the contents covered by the lecture.
Class 3 Presentation of Group and Cayley Graph Understand the contents covered by the lecture.
Class 4 Quai-isometry Understand the contents covered by the lecture.
Class 5 Short Course of Constant Curvature Geometry Understand the contents covered by the lecture.
Class 6 Coxeter Group and Linear Representation Understand the contents covered by the lecture.
Class 7 Rright-angled Artin Group and Salvetti Complex Understand the contents covered by the lecture.
Class 8 Subgroup Separability Understand the contents covered by the lecture.
Class 9 Graph of Groups Understand the contents covered by the lecture.
Class 10 Non-positively Curved Cube Complex Understand the contents covered by the lecture.
Class 11 Special Group Understand the contents covered by the lecture.
Class 12 Delta-hyperbolic Space Understand the contents covered by the lecture.
Class 13 Canonical Completion by Wise Understand the contents covered by the lecture.
Class 14 Hyperbolic Group Understand the contents covered by the lecture.
Class 15 Rips Complex and Boundary 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.)

The fundamentals of group theory, point set topology and group action are assumed.

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