應用數學(四)(群論)
Applied Mathematics IV (Group Theory)
| 節 | 週二 |
|---|---|
7 15:30–16:20 | 應用數學(四)(群論) SC160（光復） 3 節連堂 |
8 16:30–17:20 | |
9 17:30–18:20 |
* 根據陽明交大上課時間表所列
understand finite group theory and group representations, several continuous group
Calculus and Linear algebra
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作業70%，期末報告30%
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| 週次 | 主題 |
|---|---|
| 第 1 週 | Definition and examples of groups |
| 第 2 週 | Subgroups, cosets, and Lagrange's theorem |
| 第 3 週 | Normal subgroups and quotient groups |
| 第 4 週 | Group homomorphisms and isomorphisms |
| 第 5 週 | common group and small group classification |
| 第 6 週 | Sylow theorems and applications |
| 第 7 週 | Introduction to group representations |
| 第 8 週 | mid term (no class) |
| 第 9 週 | Matrix representations and characters, Irreducible representations |
| 第 10 週 | Orthogonality relation |
| 第 11 週 | Applications in physics and chemistry |
| 第 12 週 | Definition and basic properties of Lie algebras/lie group，Structure constants and the Jacobi identity |
| 第 13 週 | SO(3), SU(2), U(1), Lorentz group and its applications |
| 第 14 週 | SO(3), SU(2), U(1), Lorentz group and its applications |
| 第 15 週 | Introduction to classification of Lie algebra |
| 第 16 週 | Final Presentation (no class) |
Serge Lang, Algebra, Graduate Texts in Mathematics. J.-P. Serre, Linear Representations of Finite Groups. Howard Georgi, Lie Algebras in Particle Physics
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