卒業研究I
理工学部 - 情報理工学科
SIC40301
コース情報
担当教員: TRIHAN Fabien
単位数: 1
年度: 2024
学期: 秋学期
曜限: 金3
形式: 対面授業
レベル: 400
アクティブラーニング: なし
他学部履修: 可
評価方法
出席状況
レポート
詳細情報
概要
This course is following the Policy 2 of Sophia University. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.
目標
Understand the basics about group theory and representation theory
授業外の学習
Each week, the student is supposed to prepare lectures on a given subject and also to write notes for his dissertations.
所要時間: 190 min
スケジュール
- Definition of groups
- Example of groups
- Group homomorphisms
- Subgroups
- Normal subgroups, quotients
- Cyclic subgroups
- Order of groups and elements
- Permutations
- Isomorphism theorems
- Finitely generated groups
- Free group on a set
- Presentation of finitely generated group
- Presentation by generators and relations
- Sylow Theorem
- Exercise
教科書
http://www2.math.umd.edu/~tjh/CommAlg.pdf
Abstract Algebra
著者: T. Hungerford
出版社: cengage learning/2012
参考書
http://www2.math.umd.edu/~tjh/CommAlg.pdf