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.
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.
discrete structure, algebraic structure, geometric structure
✔ Specialist skills | ✔ Intercultural skills | Communication skills | ✔ Critical thinking skills | ✔ Practical and/or problem-solving skills |
The course provides advanced topics of discrete, algebraic and geometric structures.
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. |
Not specified in particular.
References and some handouts will be provided in the lectures.
Students to write a report on some aspects of the course.
None.