卒業研究I

理工学部 - 情報理工学科

SIC40137

コース情報

担当教員: TRIHAN Fabien

単位数: 1

年度: 2024

学期: 春学期

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:

評価方法

出席状況

0%

レポート

100%

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

  1. Definition of groups
  2. Example of groups
  3. Group homomorphisms
  4. Subgroups
  5. Normal subgroups, quotients
  6. Cyclic subgroups
  7. Order of groups and elements
  8. Permutations
  9. Isomorphism theorems
  10. Finitely generated groups
  11. Free group on a set
  12. Presentation of finitely generated group
  13. Presentation by generators and relations
  14. Sylow Theorem
  15. 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

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