Course title
V01404003
Introduction to Applied Algebra

 shimizu kenichi
Course description
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.
Purpose of class
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.
Goals and objectives
  1. Understand basics of group theory and its application
  2. Understand theoretical and computational treatment of finite fields
  3. Understand basics of coding theory
Language
English
Class schedule

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

 Midterm exam Final exam Active participation Total.
1. 40% 10% 50%
2. 20% 5% 25%
3. 20% 5% 25%
Total. 40% 40% 20% -
Evaluation method and criteria
Mid-term exam (40%). Final exam (40%). Active participation (20%).
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.
Relation to the environment
Non-environment-related course
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
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 applicatable
N/A N/A
Last modified : Thu May 30 04:23:34 JST 2019