主题目录

    • 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.

  • 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)

  • 其他教学资源(Other Resources)

    • Readings

      Readings are assigned weekly in the lecture notes.

      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.

    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