This course introduces several applications of abstract algebra. In the first-half part of this course, we will discuss group
actions and their applications to enumeration problems. We will also learn Sylow’s theorem for finite groups and its application
to classification of finite groups of small orders. In the second-half part, we will deal with finite fields. Basics on coding
theory will be presented as a real-world application.

The purpose of this course is to learn several applications of abstract algebra. Students will also obtain deeper understanding
on abstract algebra through its concrete applications.

- Understand basics of group theory and its application
- Understand theoretical and computational treatment of finite fields
- Understand basics of coding theory

Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
---|---|---|---|

1. | Course introduction | Review Algebra I, II and III | 180minutes |

2. | Finite groups: Introduction and Examples | Review of the last lecture | 180minutes |

3. | Finite groups: Group actions and orbits | Review of the last lecture | 180minutes |

4. | Finite groups: Burnside’s lemma | Review of the last lecture | 180minutes |

5. | Finite groups: Sylow’s theorem | Review of the last lecture | 180minutes |

6. | Finite groups: Classification of small groups | Review of the last lecture | 180minutes |

7. | Mid-term exam and review | Review of lectures 1-6 | 270minutes |

8. | Finite field arithmetic: Introduction and Examples | Review of the last lecture | 180minutes |

9. | Finite field arithmetic: Classification of finite fields | Review of the last lecture | 180minutes |

10. | Finite field arithmetic: Primitive element | Review of the last lecture | 180minutes |

11. | Coding theory: Introduction and Examples | Review of the last lecture | 180minutes |

12. | Coding theory: Linear code | Review of the last lecture | 180minutes |

13. | Coding theory: Cyclic code | Review of the last lecture | 180minutes |

14. | Final exam and review | Review of lectures 1-6 | 270minutes |

Total. | - | - | 2700minutes |

Midterm exam | Final exam | Active participation | Total. | |
---|---|---|---|---|

1. | 40% | 10% | 50% | |

2. | 20% | 5% | 25% | |

3. | 20% | 5% | 25% | |

Total. | 40% | 40% | 20% | - |

- 12:30-13:10 of Monday, or anytime I'm in the lab.

- Non-social and professional independence development course

Work experience | Work experience and relevance to the course content if applicatable |
---|---|

N/A | N/A |

Last modified : Thu May 30 04:23:34 JST 2019