Group Theory and its Applications

Group Theory and its Applications, Autumn 2025 / 群论及其应用

考试时间：2026-01-03 10:30-12:30(星期六)，考试地点：教121

课程信息：

上课时间及地点 (4-18 周，9 月 17 日开始)：

• 线下教学：
  • 周三 第 5-6 节，费彝民楼 A-310 
  • 周五 第 5-6 节，费彝民楼 A-310

课程参考资料：

• 课程讲义主要参考 Greg Moore, Abstract Group Theory
• 其他建议阅读的参考书
  • Zee, Group Theory in a Nutshell for Physicists, Princeton Univ. Press, 2016（较简单，适合入门）
  • Dresselhaus, Dresselhaus, Jorio, Group Theory: Application to the Physics of Condensed Matter, Springer 2008（包含较多物理应用实例）
  • 陶瑞宝，《物理学中的群论》，高等教育出版社，2011（常用中文教材）
  • 马中骐，《物理学中的群论》，科学出版社，2006（常用中文教材）
  • 陈金全，《群表示论的新途径》，上海科学技术出版社，1984（南京大学）

课程讲义及资料：

1. 课程安排
2. Notes on 2025-09-17
3. Notes on 2025-09-19
4. Notes on 2025-09-24
5. Notes on 2025-09-26
6. Notes on 2025-10-10
7. Notes on 2025-10-11
8. Notes on 2025-10-15
9. Notes on 2025-10-17
10. Notes on 2025-10-22
11. Notes on 2025-10-24
12. Notes on 2025-10-29 | Mid-term review
13. Notes on 2025-10-31
14. Notes on 2025-11-05
15. Notes on 2025-11-12
16. Notes on 2025-11-14
17. Notes on 2025-11-19
18. Notes on 2025-11-21: up to page 15, including proof of Peter-Weyl theorem
19. Notes on 2025-11-26 after remainder of the note on 11.21
20. Notes on 2025-11-28
21. Notes on 2025-12-03, with correction on page 3.
22. Notes on 2025-12-05
23. Notes on 2025-12-10
24. Notes on 2025-12-12
25. Notes on 2025-12-17
26. Notes on 2025-12-19 | A companion Mathematica Notebook
27. Notes on 2025-12-24 | A companion Mathematica Notebook
28. Notes on 2025-12-26 | Review of group representations. See notes on 10-29 for review of basics of groups.

习题 (共十次)：

1. HW01 (Due on 2025-10-11) | Sol01
2. HW02 (Due on 2025-10-17) | Sol02
3. HW03 (Due on 2025-10-24) | Sol03
4. HW04 (Due on 2025-10-31) | Sol04
5. HW05 (Due on 2025-11-07) | Sol05
6. HW06 (Due on 2025-11-14) | Sol06
7. HW07 (Due on 2025-11-28) | Sol07
8. HW08 (Due on 2025-12-05) | Sol08
9. HW09 (Due on 2025-12-12) | Sol09
10. HW10 (Due on 2025-12-19) | Sol10