### University：Massachusetts Institute of Technology

### Instructors: Prof. Pavel Etingof

### Course Number: 18.712

### Level: Undergraduate

### Course Description

The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.

## 主题目录

### 教学大纲(Syllabus)

## Prerequisites

The prerequisites for the course are the standard algebra sequences Algebra I and II (18.701, 18.702) or Linear Algebra and Modern Algebra (18.700, 18.703). This means that to understand this course, it is necessary and sufficient to have a strong background in linear algebra and a decent understanding of basic algebraic structures, such as groups, rings, and fields. We will prove some general results, but a lot of the attention will be paid to examples, and there will be many hands-on exercises illustrating the course.

### 教学讲稿(Lecture Notes)

Students are assigned readings in these lecture notes each week. The present lecture notes arose from a representation theory course given by Prof. Etingof in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students. The students in that course — Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Elena Yudovina, and Dmitry Vaintrob — co-authored the lecture notes which are published here with their permission.

### 其他教学资源(Other Resources)

# Readings

Readings are assigned weekly in the lecture notes.

Course readings. WEEK # READINGS 1 Section 1.1-1.5 2 Section 1.6-1.13 3 Section 1.14-2.8 4 Section 2.9-3.5 5 Section 3.6-4.1 6 Section 4.2-4.9 7 Section 4.10-4.19 8 Section 4.20-4.24 9 Section 4.25-5.2 10 Section 5.3-5.5 11 Section 5.6-5.9 12 Chapter 6

### 作业

The homework problems are found in the lecture notes.

Assignment files. HOMEWORK # ASSIGNMENTS Homework 1 Problems 1.20-1.25 Homework 2 Problems 1.26, 1.27, 1.33, 1.38, and 1.49 Homework 3 Problems 1.51, 1.54, and 1.55 Homework 4 Problems 1.56 and 1.57 (problem 1.58 is optional) Homework 5 Problems 2.21 - 2.25 and 3.4 Homework 6 Problems 3.17 - 3.22 Homework 7 Problems 3.23 - 3.27 and 4.1 Homework 8 Problems 4.15, 4.31, 4.34, 4.39, 4.50, and 4.51 Homework 9 Problems 4.52, 4.68, and 4.69 Homework 10 Problems 5.1-5.5 Homework 11 Problems 5.39-5.41