Syllabus for Linear Algebra
00071004
Current Lecturer
Dr. Xiaofei Xu, Email: xfxu@suda.edu.cn
Course Time
1st Semester
Lectures: 3 sessions/week, 50 min/session. 18 weeks.
Office Hours
Thursday 2:00—4:00 PM, Building of Physical Technology 232
Course Description
Linear algebra is the branch of mathematics concerning vector spaces and linear mapping between such spaces. It is central to both pure and applied mathematics. Techniques from linear algebra are useful in both social sciences and natural sciences. The course aims to (1) provide students with a good understanding of the concepts and methods of linear algebra; (2) help the students develop the ability to solve problems using linear algebra; (3) connect linear algebra to other fields both within and without mathematics; (4) develop abstract and critical reasoning by studying logical proofs and the axiomatic method as applied to linear algebra.
Prerequisites
Mathematics in high school.
Textbooks
Linear Algebra with Applications, 8th edition, Steven J. Leon, China Machine Press, 2011, ISBN: 978-7-111-34199-4
Main Contents
Week | Teaching Contents | Sessions | Objectives |
1 | Chapter 1: Matrices and systems of equations | 3 | Systems of linear equations; Row Echelon Form; Matrix Arithmetic; |
2 | Chapter 1: Matrices and systems of equations | 3 | Matrix Algebra; Elementary Matrices; Partitioned Matrices |
3 | Chapter 2: Determinants | 3 | The determinant of a matrix; Properties of determinants; Cramer’s Rule; |
4 | Quiz 1 | 3 | Review and quiz |
5 | Chapter 3: Vector spaces | 3 | Vector spaces; Subspaces; Linear Independence; |
6 | Chapter 3: Vector spaces | 3 | Basis and dimension; Change of Basis |
7 | Chapter 3: Vector spaces | 3 | Row space and column space; Linear transformations; |
8 | Chapter 4: Linear transformations | 3 | Matrix representation of linear transformation; Similarity; |
9 | Mid-term exam | 3 | Review and exam |
10 | Chapter 5: Orthogonality | 3 | The scalar product; Orthogonal subspaces |
11 | Chapter 5: Orthogonality | 3 | Least squares problems; Inner product spaces |
12 | Chapter 5: Orthogonality | 3 | Orthonormal sets; The Gram-Schmidt orthogonalization process |
13 | Chapter 5: Orthogonality Chapter 6: Eigenvalues | 3 | Orthogonal polynomials; Eigenvalues and Eigenvectors |
14 | Quiz 2 | 3 | Review and quiz |
15 | Chapter 6: Eigenvalues | 3 | Diagonalization; Hermitian matrices; The singular value decomposition; |
16 | Chapter 6: Eigenvalues | 3 | |
17 | Review | 3 | Review for final exam |
18 | Final exam | 3 | Final exam |
Grading Scheme:
Homework | Attendance | Quiz | Midterm | Final exam |
15% | 10% | 2*10% | 15% | 40% |
1
