Suggested Syllabus for Math 3A – INTRO TO LINEAR ALGEBRA (rev. 6/04)
Textbook – “Linear Algebra” by Steven J. Leon (6th edition)
Lecture #
Chapter/Section
Topics
1
3.1
VECTOR SPACES: Definition and Examples
2
3.1
(continued)
3
3.2
Subspaces
4
3.2
(continued)
5
3.3
Linear Independence
6
3.3
(continued)
7
3.4
Basis and Dimension
8
3.4
(continued)
9
3.5
Change of Basis
10
3.6
Row Space and Column Space
11
3.6
(continued)
12
Midterm Exam
13
4.1
LINEAR TRANSFORMATIONS: Definition and Examples
14
4.1
(continued)
15
4.2
Matrix Representation of Linear Transformations
16
4.2
(continued)
17
4.3
Similarity
18
5.1
ORTHOGONALITY: The Scalar Product in R_n
19
5.1
(continued)
20
5.2
Orthogonal Subspaces
21
5.2
(continued)
22
5.2
(continued)
23
5.3
Least Square Problems
24
5.4
Inner Product Spaces
25
5.4
(continued)
26
5.5
Orthonormal Sets
27
5.5
(continued)
28
5.6
The Gram-Schmidt Orthogonalization Process
29
5.6
(continued)
*The lecture numbers correspond to a 3-lectures per week schedule.
COMMENTS: The first two chapters and sections 1-3 of chapter 6 of Leon have been covered in Math
2J, which is a prerequisite for 3A. This course is intended for Math majors and should provide an
introduction to abstraction, axiomatics and proof. This is more important than covering all the topics in
the syllabus, since the material will be seen again (in even greater generality) in Math 121A-B.