Course title
6M0185001
Linear Representations of Finite Groups
Course content
We cover Part I of Serre's textbook "Representations and Characters", pp.3–45.
Purpose of class
This is a course on the representation theory of finite groups over the complex numbers. Representation theory is a dominant theme in mathematics. It has a significant influence on physic, chemistry, and other disciplines. The representation theory of finite groups over the complex numbers is a beautiful and relatively elementary subject. However, it also exhibits the most fundamental features of other representation theories. It also offers the computation of tractable examples.
Goals and objectives
1. Successful students will understand complex representations of finite groups.
2. Successful students will be able to be able to compute characters of finite groups.
3. Successful students will be able to explain elementary properties of characters of finite groups.
Language
English
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Generalities on linear representations Read 1.1–1.6 of the text book. 200minutes
2． The character of a representation Read 2.1 of the textbook. 200minutes
3． Schur’s lemma, orthogonality relations Read 2.2, 2.3 of the textbook. 200minutes
4． The regular representation Read 2.4, 2.5 of the textbook. 200minutes
5． Decomposition of a representation Read 2.6, 2.7 of the textbook. 200minutes
6． Subgroups, products induced representations Read 3.1–3.3 of the textbook. 200minutes
7． Examples Read 5.1, 5.3 of the textbook. 200minutes
Take Home Exam 240minutes
Total. - - 1640minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Quiz Take Home Exam Total.
1. 20% 20% 40%
2. 20% 20% 40%
3. 20% 20%
Total. 40% 60% -
Evaluation method and criteria
Quizzes and Take Home Examination.
Textbooks and reference materials
Serre's textbook "Representations and Characters",
Prerequisites
Linear Algebra, Algebra, , Group Theory (undergraduate level)
Office hours and How to contact professors for questions
• By appointment. Send me an e-mail kameko@shibaura-it.ac.jp
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
• Course that cultivates an ability for utilizing knowledge
• Course that cultivates a basic self-management skills
• Course that cultivates a basic problem-solving skills
Active-learning course
N/A
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
• 1.NO POVERTY
• 3.GOOD HEALTH AND WELL-BEING
• 4.QUALITY EDUCATION
• 5.GENDER EQUALITY
• 8.DECENT WORK AND ECONOMIC GROWTH
• 16.PEACE, JUSTICE AND STRONG INSTITUTIONS