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| 1 |
群與子群、矩陣群
Groups and Subgroups, Matrix Groups |
問題集1 發出
Problem set 1 out |
| 2 |
循環群、置換
Cyclic Groups, Permutations |
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| 3 |
生成元、同構
Generators, Isomorphisms |
問題集2 發出
Problem set 2 out |
| 4 |
同態
Homomorphisms |
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| 5 |
陪集
Cosets |
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| 6 |
模算數
Modular Arithmetic |
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| 7 |
商群
Quotient Groups |
問題集3 發出
Problem set 3 out |
| 8 |
體與向量空間
Fields and Vector Spaces |
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| 9 |
基數與因次
Bases and Dimension |
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| 10 |
以基數來計算
Computation with Bases |
問題集4 發出
Problem set 4 out |
| 11 |
因次公式
The Dimension Formula |
問題集5 發出
Problem set 5 out |
| 12 |
第一次小考
First Quiz |
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| 13 |
線性運算子、特徵向量
Linear Operators, Eigenvectors |
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| 14 |
特徵多項式
The Characteristic Polynomial |
問題集6 發出
Problem set 6 out |
| 15 |
旋轉
Rotations |
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| 16 |
等矩映射
Isometries |
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| 17 |
等矩映射的面
Isometries of the Plane |
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| 18 |
有限群的移動
Finite Groups of Motions |
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| 19 |
離散群
Discrete Groups |
問題集7 發出
Problem set 7 out |
| 20 |
離散群 (續)
Discrete Groups (cont.) |
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| 21 |
群的運算
Group Operations |
問題集8 發出
Problem set 8 out |
| 22 |
有限旋轉群
Finite Rotation Groups |
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| 23 |
集方程式
The Class Equation |
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| 24 |
置換表示法
Permutation Representations |
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| 25 |
十二面體群
The Icosahedral Group |
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| 26 |
第二次小考
Second Quiz |
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| 27 |
雙線性結構
Bilinear Forms |
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| 28 |
對稱結構
Symmetric Forms |
問題集9 發出
Problem set 9 out |
| 29 |
厄密結構
Hermitian Forms |
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| 30 |
光譜定理（分譜定理？）
The Spectral Theorem |
問題集10 發出
Problem set 10 out |
| 31 |
二次函數
Quadrics |
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| 32 |
特殊單元群 SU2
The Special Unitary Group SU2 |
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| 33 |
旋轉群
The Rotation Group |
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| 34 |
單參數群
One-parameter Groups |
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| 35 |
單參數群 (續)
One-parameter Groups (cont.) |
問題集11 發出
Problem set 11 out |
| 36 |
李代數
The Lie Algebra |
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| 37 |
第三次小考
Third Quiz |
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| 38 |
簡單群
Simple Groups |
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| 39 |
交代群
The Alternating Groups |
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