| Academic Year |
2025Year |
School/Graduate School |
Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program |
| Lecture Code |
WSA23000 |
Subject Classification |
Specialized Education |
| Subject Name |
代数数理特論Ａ |
Subject Name
（Katakana） |
ダイスウスウリトクロンエー |
Subject Name in
English |
Topics in Algebra A |
| 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,Fri5-6：SCI E211 |
| Lesson Style |
Lecture |
Lesson Style
(More Details) |
Face-to-face, Online (simultaneous interactive), Online (on-demand) |
| |
| Credits |
2.0 |
Class Hours/Week |
4 |
Language of Instruction |
J
:
Japanese |
| Course Level |
4
:
Undergraduate Advanced
|
| Course Area（Area） |
25
:
Science and Technology |
| Course Area（Discipline） |
01
:
Mathematics/Statistics |
| Eligible Students |
|
| Keywords |
Combinatorial Games, Infinite, Infinitesimals, Surreal Number, NIM |
| 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 |
Conway's book "On Numbers and Games" and Knuth's book "Surreal Numbers" treats very interesting mathematical Object, namely Surreal numbers, but are mathematically not rigorous enough. In this lecture, we try to fix their problems and give a logical introduction to the theory of Surreal Numbers. If time permits, we also discuss NIM values. |
| Class Schedule |
lesson1 Introduction: notion of numbers, notion of infinity
lesson2 Finite Hackenbush
lesson3 Definition of Combinatorial Games, Sum of games, Inverse games, and Outcomes
lesson4 Outcome of sums of games
lesson5 Definition of Numbers in short games, totally ordered Abelian group structure
lesson6 Game values of finite Hackenbush, and their products
lesson7 Simplicity Theorem
lesson8 Transfinite Ordinal Numbers
lesson9 Transfinite Hackenbush and Surreal Numbers
lesson10 Products of Surreal Numbers
lesson11 Quotients of Surreal Nubers
lesson12 Cantor Normal Form
lesson13 Sturm's Theorem
lesson14 Algebraic Equations and real closedness
lesson15 Characteristic 2 case, Transfinite NIM values |
Text/Reference
Books,etc. |
Lecture is based on Conway's "On Numbers and Games", but will try to fix the problems there,
so students do not have to prepare the book. Recommended Text Books are Abuku et at "組合せゲーム理論の世界", and in English, Siegel "Combinatorial Game Theory". |
PC or AV used in
Class,etc. |
|
| (More Details) |
|
| Learning techniques to be incorporated |
|
Suggestions on
Preparation and
Review |
The tools are games, which may sound like an easy topic, but this lecture is supposed to be very logical and mathematical. No prior knowledge is required except for rudimentary abstract mathematical knowledge like Cantor's Set Theory, but advanced mathematical thinking will be required to follow the lectures. |
| 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. |