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課程名稱 |
線性代數一
Linear Algebra (Ⅰ) |
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開課學期 |
109-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
楊一帆 |
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課號 |
MATH1103 |
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課程識別碼 |
201 49590 |
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班次 |
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學分 |
4.0 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期三3,4(10:20~12:10)星期五3,4(10:20~12:10) |
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上課地點 |
新103新103 |
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備註 |
201 14410線性代數一得用201 49590線性代數一(4學分)替代
總人數上限：90人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1091MATH1103_ |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
This course provides the first step toward understanding and manipulating abstract algebraic systems. Explicit goals include familiarize with the main characters -- linear spaces (possibly equipped with additional structures), and the relations between them or upon themselves -- linear transformations, kernels, quotients, eigenvalues, etc. |
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課程目標 |
Basic and standard concepts of linear algebra needed for students in mathematics department |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Friedberg, Insel, and Spence, Linear Algebra. 4th Edition |
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參考書目 |
Hoffman and Kunz, Linear Algebra. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Midterm Exam I |
25% |
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2. |
Midterm Exam II |
25% |
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3. |
Final Exam |
25% |
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4. |
Homework |
20% |
原則上每週都有作業，期末取最高的十次成績做計算。 |
5. |
Quizzes |
10% |
共三次小考，取兩次高分的成績做計算。 |
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週次 |
日期 |
單元主題 |
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第1週 |
9/16,9/18 |
1. Definition of Fields and Vector Spaces. (1.1-1.2)
2. Subspaces. (1.3) |
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第2週 |
9/23,9/25 |
1. Linear Combination. (1.4)
2. Linear Dependence and Linear Independence. (1.5)
3. Basis. (1.6) |
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第3週 |
9/30 |
Dimension, Replacement Theorem. (1.6) |
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第4週 |
10/07 |
Linear Transformations and Rank-Nullity Theorem. (2.1) |
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第5週 |
10/14,10/16 |
1. Matrix Representation of Linear Transformations. (2.2)
2. Composition of Linear Transformation and Matrix Multiplication. (2.3) |
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第6週 |
10/21,10/23 |
1. Invertibility and Isomorphism. (2.4)
2. The Change of Coordinate Matrix. (2.5)
* Quiz 1 on Friday, October 23. |
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第7週 |
10/28,10/30 |
The Gauss Elimination and Elementary Matrices. (3.1)
* Midterm Exam I on Friday, October 30.(1.1-1.6, 2.1-2.5) |
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第8週 |
11/04,11/06 |
Matrix Rank and Matrix Inverse. (3.2) |
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第9週 |
11/11,11/13 |
1. System of Linear Equations. (3.3-3.4)
2. Determinants. (4.1) |
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第10週 |
11/18,11/20 |
自主學習週停課 |
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第11週 |
11/25,11/27 |
1. Computation of Determinant.(4.2)
2. (TA session) Characterization. (4.5) |
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第12週 |
12/02,12/04 |
1. Properties of Determinant (4.3-4.4)
2. Classical Adjoint(Adjugate) of a Matrix.
3. Eigenvalues and Eigenvectors. (5.1)
* Quiz 2 on Friday, December 4. |
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第13週 |
12/09,12/11 |
Characteristic Polynomial. (5.1)
* Midterm Exam II on Friday, December 11.(3.1-3.4, 4.1-4.4, Classical adjoint) |
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第14週 |
12/16,12/18 |
1. Cayley-Hamilton Theorem and Minimal Polynomial.
2. Diagonalization. (5.1-5.2) |
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第15週 |
12/23,12/25 |
Diagonalizability and Direct Sums. (5.2) |
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第16週 |
12/30 |
Invariant Subspaces and Cyclic Subspaces. (5.4) |
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第17週 |
1/06,1/08 |
More on Properties of Polynomials. (Preparation of Chapter 7)
* Quiz 3 on Friday, January 8. |
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第18週 |
1/13,1/15 |
No class on 1/13.
* Final Exam on Friday, January 15. |
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