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2017　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.)
Mon3-4(W832)  Thr3-4(W832)  
Group
-
Course number
MCS.T408
Credits
2
Academic year
2017
Offered quarter
4Q
Syllabus updated
2017/3/17
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. Topics include word, combinatorics of tableau, Weyl group, Coxeter system, matching of graph.

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 Word Understand the contents covered by the lecture.
Class 2 Length of word Understand the contents covered by the lecture.
Class 3 Coxeter system Understand the contents covered by the lecture.
Class 4 Weyl group Understand the contents covered by the lecture.
Class 5 Lattice path Understand the contents covered by the lecture.
Class 6 R-polynomial Understand the contents covered by the lecture.
Class 7 Hecke algebra Understand the contents covered by the lecture.
Class 8 Matching of graph Understand the contents covered by the lecture.
Class 9 Crystal Understand the contents covered by the lecture.
Class 10 Combinatorics of tableau Understand the contents covered by the lecture.
Class 11 Order of words Understand the contents covered by the lecture.
Class 12 Quantum group Understand the contents covered by the lecture.
Class 13 Quantum invariant Understand the contents covered by the lecture.
Class 14 Quantum computation Understand the contents covered by the lecture.
Class 15 Topological code 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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