| Academic Year |
2026Year |
School/Graduate School |
Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program |
| Lecture Code |
WSA25000 |
Subject Classification |
Specialized Education |
| Subject Name |
代数数理特論Ｃ |
Subject Name
（Katakana） |
ダイスウスウリトクロンシー |
Subject Name in
English |
Topics in Algebra C |
| Instructor |
KIMURA SHIYUNICHI |
Instructor
(Katakana) |
キムラ シュンイチ |
| Campus |
Higashi-Hiroshima |
Semester/Term |
1st-Year, First Semester, 2Term |
| Days, Periods, and Classrooms |
(2T) Tues7-8,Fri3-4：SCI E102 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face |
| |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
B
:
Japanese／English |
| Course Level |
7
:
Graduate Special Studies
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
Combinatorial Games, Theory born at Hiroshima University |
| Special Subject for Teacher Education |
|
Special Subject |
|
Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) | |
|---|
Class Objectives
/Class Outline |
In 2024 and 2025, Hiroshima University Combinatorial Game Research Group made a major advance in the theory of option-impartial games. In this lecture, assuming only rudimentary set theory, we present our new results for non-experts. Professor Urban Larsson (Indian Institute of Technology) plans to visit Hiroshima University during the lecture, and if the plan materializes, we give this lecture mainly in English. |
| Class Schedule |
lesson1 Introduction: What is a combinatorial game?
lesson2 Definition of Combinatorial Games: Short, Noether, and Loopy games
lesson3 Remark on Finiteness conditions: Ordinal numbers and their natural sums and natural products
lesson4 Existence theorem of winning strategies (The Fundamental Theorem of Combinatorial Game Theory)
lesson5 Sum of games and Grundy Numbers: Wada's symmetry theorem
lesson6 Equivalence of Games, and Nim as a universal impartial game
lesson7 Kawakami's Crush Car Nim
lesson8 Enforce Operator and Odawara's Theorem
lesson9 Moriwaki's Mory sequence, Conti-Nim, and Conway's Folklore Theorem
lesson10 Yamashita's Yama Nim, Triangular Nim and their Wythoff variations
lesson11 Inoue-Watanabe's S-Wtyhoff and Assymetric Wythoff games, Yamashita-Inazu's Triangle Game
lesson12 Misere Games: Omiya's Greedy Nim
lesson13 Inoue-Kadowaki's Ending Partizan Games
lesson14 Inazu's Quotients
lesson15 Suetsugu-Inazu's Conway-style presentation of Ending Partizan Games |
Text/Reference
Books,etc. |
You can find presentation files from
https://sites.google.com/view/hiroshima-cgt/activities
(sorry, the web-page is only in Japanese, but some presentation files are in English) |
PC or AV used in
Class,etc. |
Text, Handouts |
| (More Details) |
|
| Learning techniques to be incorporated |
Discussions |
Suggestions on
Preparation and
Review |
This lecture is a progress report on on-going research. By actively joining the discussions, you can contribute to the progress to the research. Please ask questionsa and give comments on possible generalizations or simplifications of proofs. |
| Requirements |
|
| Grading Method |
Reports |
| Practical Experience |
|
| Summary of Practical Experience and Class Contents based on it |
|
| Message |
|
| Other |
|
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. |