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

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% | - |

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 |

Evaluated as indicated in "Course Outcomes" section. A score of 60 or more out of 100 points is required to pass this course.
To pass this course, students should understand basics applications to algebra in computer science.

ways of feedback | specific contents about "Other" |
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Feedback in the class |

- 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 |
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N/A | N/A |

Last modified : Fri Mar 01 04:33:17 JST 2024