The theory of finite groups and finite fields, and their applications to cryptography and coding theory.

- Understand and be able to explain basics on modular arithmetic
- Understand and be able to explain basics on finite groups and finite fields
- Understand and be able to explain some applications of finite fields to coding theory
- Understand and be able to explain some applications of finite fields to cryptography

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

1. | Algebra and information science | Survey some applications of algebra to information science | 200minutes |

2. | Modular Arithmetic (1) Euclidean Algorithm | Review basics on the theory of rings and fields | 200minutes |

3. | Modular Arithmetic (2) Chinese Remainder Theorem | Review the last class | 200minutes |

4. | Group Theory (1) Groups and subgroups | Review the last class | 200minutes |

5. | Group Theory (2) Lagrange's theorem | Review the last class | 200minutes |

6. | Group Theory (3) Group actions and orbits | Review the last class | 200minutes |

7. | Cryptographic Theory (1) RSA cryptosystem | Review the last class | 200minutes |

8. | Cryptographic Theory (2) Generating large prime numbers | Review the last class | 200minutes |

9. | Finite Field Arithmetic (1) Field Extensions | Review the last class | 200minutes |

10. | Finite Field Arithmetic (2) Primitive elements | Review the last class | 200minutes |

11. | Coding Theory (1) Basic idea of linear codes | Review the last class | 200minutes |

12. | Coding Theory (2) Basic idea of linear codes | Review the last class | 200minutes |

13. | Random number generation (1) | Review the last class | 200minutes |

14. | Random number generation (2) | Review the last class | 200minutes |

Total. | - | - | 2800minutes |

Report | Discussion | Active participation | Total. | |
---|---|---|---|---|

1. | 15% | 5% | 5% | 25% |

2. | 15% | 5% | 5% | 25% |

3. | 15% | 5% | 5% | 25% |

4. | 15% | 5% | 5% | 25% |

Total. | 60% | 20% | 20% | - |

Evaluated by reports and discussion in the lecture.

Pass if a student is able to basics applications to algebra in computer science.

Pass if a student is able to basics applications to algebra in computer science.

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

- Course that cultivates an ability for utilizing knowledge

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

N/A | N/A |

Last modified : Fri Mar 26 04:10:12 JST 2021