|
課程名稱 |
線性代數一
Linear Algebra (Ⅰ) |
|
開課學期 |
108-1 |
|
授課對象 |
理學院 數學系 |
|
授課教師 |
余正道 |
|
課號 |
MATH1103 |
|
課程識別碼 |
201 49590 |
|
班次 |
|
|
學分 |
4.0 |
|
全/半年 |
半年 |
|
必/選修 |
必帶 |
|
上課時間 |
星期三3,4(10:20~12:10)星期五3,4(10:20~12:10) |
|
上課地點 |
新103新103 |
|
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 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1081math1103 |
|
課程簡介影片 |
|
|
核心能力關聯 |
本課程尚未建立核心能力關連 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
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. |
|
課程目標 |
Basic and standard concepts of linear algebra needed for students in mathematics department |
|
課程要求 |
|
|
預期每週課後學習時數 |
|
|
Office Hours |
每週二 15:30~16:30
每週五 08:10~10:00
每週四 12:30~13:30
每週三 12:30~13:30
每週二 12:30~13:30 備註： Tuesday noon (林自立) and afternoon (林浚沂): Astro-Math 103, Wednesday (余正道): Astro-
Math 461, Thursday (王羿璁):
Astro-Math 548, Friday (呂治鴻): Astro-Math 555 |
|
指定閱讀 |
Hoffman and Kunze, Linear Algebra. 2nd edition. 1971.
The PDF-version is available on the website https://archive.org |
|
參考書目 |
|
|
評量方式
(僅供參考) |
|
|
週次 |
日期 |
單元主題 |
|
Week 1 |
9/11 |
Vector spaces, subspaces (§2.1, 2.2) |
|
Week 2 |
9/18, 20 |
Linear combinations, linear dependence, bases, dimension (§2.3) |
|
Week 3 |
9/25, 27 |
Linear maps (§3.1, part of 3.2, 3.3), Quiz 1 |
|
Week 4 |
10/02, 04 |
Coordinates and matrix representations (§2.4, 3.2, 3.4); TA session is replaced by a lecture |
|
Week 5 |
10/09 |
Dual space, transpose (part of §3.5, §3.7) |
|
Week 6 |
10/16, 18 |
Annihilator, double dual (§3.5, 3.6) |
|
Week 7 |
10/23, 25 |
Linear equations, Gauss elimination (Chap.1), Quiz 2 |
|
Week 8 |
10/30, 11/01 |
Determinant - uniqueness (parts of §5.2, 5.3) |
|
Week 9 |
11/06, 08 |
Determinant - existence (§5.2, 5.3), Midterm |
|
Week 10 |
11/13 |
Determinant - properties (§5.4); eigenvalues (§6.2) |
|
Week 11 |
11/20, 22 |
Characteristic polynomial, arithmetic multiplicity and geometric multiplicity (§6.2, part of §6.6) |
|
Week 12 |
11/27, 29 |
T-invariant subspaces, decomposition (§§6.4, 7.1, part of §6.7), Quiz 3 |
|
Week 13 |
12/04, 06 |
minimal polynomial, T-conductor, primary decomposition (§6.3, §6.8) |
|
Week 14 |
12/11, 13 |
Jordan form: statement and structure (part of §7.3), interlude: inner product, projection |
|
Week 15 |
12/18, 20 |
Jordan form: construction, rational form I (§7.3, part of §7.1), Quiz 4 |
|
Week 16 |
12/25, 27 |
Rational form II (§§ 7.1, 7.2) |
|
Week 17 |
1/03 |
Final exam |
|