Course title
3301970A2
Introduction to Applied Algebra

 SHIMIZU Kenichi
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
Mathematical Sciences Course DP-4・2 キャリアを見据えた高度な専門知識
現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。
Purpose of class
The theory of finite groups and finite fields, and their applications to cryptography and coding theory.
Course description
This course introduces several applications of abstract algebra.
Goals and objectives
  1. Understand and be able to explain basics on modular arithmetic and finite group theory
  2. Understand and be able to explain some applications of group theory to cryptography
  3. Understand and be able to explain basics on finite field theory
  4. Understand and be able to explain some applications of finite fields to coding theory
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term exam Final exam Homework Total.
1. 20% 5% 25%
2. 20% 5% 25%
3. 20% 5% 25%
4. 20% 5% 25%
Total. 40% 40% 20% -
Evaluation method and criteria
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 be able to basics applications to algebra in computer science.
Language
English
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Modular Arithmetic (1) Euclidean Algorithm Survey some applications of algebra to information science 200minutes
2. Modular Arithmetic (2) Chinese Remainder Theorem Review basics on the theory of rings and fields 200minutes
3. Group Theory (1) Groups and subgroups Review the last class 200minutes
4. Group Theory (2) Lagrange’s theorem Review the last class 200minutes
5. Mathematical basis of RSA cryptosystem Review the last class 200minutes
6. Miller-Rabin probabilistic primality test Review 1-6 200minutes
7. Mid-term exam and review Review the last class 200minutes
8. Finite field arithmetic (1) Field extensions Review the last class 200minutes
9. Finite field arithmetic (2) Primitive elements Review the last class 200minutes
10. Finite field arithmetic (3) Classification of finite fields Review the last class 200minutes
11. Coding Theory (1) Basic idea of linear codes Review the last class 200minutes
12. Coding Theory (2) Minimum distance decoding Review the last class 200minutes
13. Coding Theory (3) Reed-Solomon codes Review the last class 200minutes
14. Final exam and review Review 8-13 200minutes
Total. - - 2800minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
None
Prerequisites
Office hours and How to contact professors for questions
  • 12:30-13:10 of Monday
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 : Mon Mar 23 04:06:56 JST 2026