Course title
V01404003
Introduction to Applied Algebra

shimizu kenichi
Course description
This course introduces several applications of abstract algebra.
Purpose of class
The theory of finite groups and finite fields, and their applications to cryptography and coding theory.
Goals and objectives
  1. Understand and be able to explain basics on modular arithmetic
  2. Understand and be able to explain basics on finite groups and finite fields
  3. Understand and be able to explain some applications of finite fields to coding theory
  4. Understand and be able to explain some applications of finite fields to cryptography
Language
Japanese
Class schedule

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
Relationship between 'Goals and Objectives' and 'Course Outcomes'

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% -
Evaluation method and criteria
Evaluated by reports and discussion in the lecture.
Pass if a student is able to basics applications to algebra in computer science.
Textbooks and reference materials
None
Prerequisites
Linear Algebra I and II and Algebra I and II are assumed.
Office hours and How to contact professors for questions
  • 12:30-13:10 of Monday, or anytime I'm in the lab.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
    Last modified : Fri Mar 26 04:10:12 JST 2021