SYLLABUS

Linear Algebra (Math 544, Section 3)
Spring 2001, USC

Lecture
Tu Th 4:30-5:45 pm LC 115
Instructor
Professor Mohammad Ghomi
Check the course web site periodically for revised versions of this syllabus, and to obtain homework assignments and copies of old tests and quizzes.

Course Description
This is an introduction to linear algebra and its applications. Main topics include matrix algebra, solution of linear systems, determinants, notions of vector space, basis, dimension, linear transformations, eigenvalues, and diagonaliztions. We will develop at each step the applications of these concepts to a range of problems in Mathematics, Engineering, and Economics.

Prerequisites
Math 241--familiarity with vectors.

Textbook
Linear Algebra and it Applications, by David C. Lay, Second Edition.

Homework and Quizzes
There will be weekly homework assignments due every Tuesday. Late homeworks will not be accepted.

Also, there will be weekly quizzes every Thursday. No calculators, textbooks, or notes will be allowed during quizzes. You should save copies of these quizzes as they are a very good source for preparing for the final and midterms. There may be a number of practice quizzes during the lectures as well.

Doing the homework problems is the most important part of any math class. You may work with a group of your classmates if you are all at about the same level; however, you should definitely try to do many problems on your own. Further, try to practice doing at least some of the problems in settings which resemble that of the test and quizzes, i.e., without using your calculator or constantly referring to the textbook.

Lecture and Reading Schedule
You should make a sincere effort to keep up with your reading assignments.
Dates Lectures
Jan 16
18		 T
TH		 1.1
1.2		 Systems of Linear Equations
Row Reduction and Echelon Forms
23
25		 T
TH		 1.3
1.4		 Vector Equations
The Matrix Equation Ax=b
30 T 1.5 Solutions of Linear Systems
Feb 1 TH 1.6 Linear Independence
6
8		 T
TH		 1.7
1.8		 Intro to linear transformations
Matrix of a linear transformation
13
15		 T
TH		 1.9
.		 Linear Models in Science
Midterm 1
20
22		 T
TH		 2.1
2.2		 Matrix Operations
The Inverse of a Matrix
27 T 2.3 Characterizations of Invertible Matrices
Mar 1 Th 2.8 Applications to Computer Graphics
6
8		 T
TH		 2.9
2.9		 Subspaces of R^n
Subspaces of R^n
13
15		 T
TH		 .
.		 Spring Break
Spring Break
20
22		 T
TH		 3.1
3.2, 3.3		 Intro to Determinants
Properties, Volume
27
29		 T
TH		 .
.		 Review
Midterm 2
Apr 3
5		 T
TH		 4.1
4.2, 4.3		 Vector Spaces and Subspaces
Null Spaces, Column Spaces, and Bases
10
12		 T
TH		 4.4
4.5		 Coordinate Systems
The Dimension of a vector Space
17
19		 T
TH		 4.7
5.1, 5.2		 Change of basis
Eigenvalues, Characteristic Equation
24
26		 T
TH		 5.3
.		 Diagonalization
Fibonacci Sequence
May 1 T . Review
9 W . Final Exam

Assignments
You should plan to work on these problems over a period of several days. Getting a head start on each assignment is perhaps the most critical factor determining your success in this class.
Homework # Due Date Problems
1 Jan 23 1.1) 2, 6, 8, 12, 14, 24, 28, 34, 35;
1.2) 2, 6, 10, 14, 31, 32, 33, 35.
2 Jan 30 1.3) 6, 8, 10, 12, 14, 23, 29;
1.4) 4, 8, 10, 12, 14, 18.
3 Feb 6 1.5) 2, 6, 14, 16, 26, 36, 38;
1.6) 4, 6, 10, 20, 22, 26, 28, 30, 32, 34, 36.
4 Feb 13 1.7)2, 4, 10, 12, 14, 16, 18, 20, 24, 30, 34;
1.8) 2, 6, 10, 12, 18, 24, 26, 28, 33.
5 Feb 20 1.9)2, 4, 10, 12;
Chap 1 Supplementary Exercises) 1, 3, 6, 11.
6 Feb 27 2.1)2, 4, 8, 12, 16, 20, 24, 26, 30;
2.2) 4, 6, 10, 12, 13, 25, 26.
7 Mar 6 2.2)23, 24, 30, 32, 34;
2.3)4, 6, 8, 14, 16, 26, 28, 34;
2.8)2, 4, 6, 8, 10, 11.
8 Mar 20 2.8)7,14;
2.9)2, 4, 6, 8, 10, 16, 18, 22, 24, 26, 28, 34.
9 Mar 27 3.1)4, 10, 16, 20, 22, 28, 34, 42;
3.2)16, 18, 22, 26, 28, 31, 32, 33, 34, 35;
3.3) 20, 24, 29, 30, 31.
10 Apr 3 Chap 3 Supplementary Exercises) 4, 6, 7, 9, 12.
11 Apr 10 4.1) 2, 4, 6, 8, 10, 12, 14, 24, 26, 28, 30;
4.2) 2, 6, 8, 10, 26, 28, 34;
4.3) 2, 4, 6, 11, 12, 23, 24.
12 Apr 17 4.4) 4, 6, 12, 14, 28;
4.5) 2, 4, 9, 22, 24, 27, 28.
13 Apr 24 4.7) 8, 10, 14;
5.1) 2, 6, 10, 24, 32;
5.2) 4, 8, 10, 16, 25.
14 May 1 5.3) 2, 8, 10, 24;
Handout) 2, 3, 4, 5, 7, 8.

Tests and Exams
There will be two midterms, on Thursday Feb 15 and on Thursday Mar 29. The final exam will be on Wednesday May 9 at 5:30 pm. No calculators, or notes will be allowed during the exams. Note: bring a bluebook to the exams.

Grading
The final grade is based on homeworks 10%, quizzes, 10%, midterms, 20% each, and the final exam, 40%.

A Few More Study Hints and Guidelines
Learning Mathematics is a demanding affair. It requires a good deal of self discipline and hard work to appreciate the power and beauty of the subject. Further, solving math problems, much like playing a musical instrument, is a skill, which can be developed only through persistent practice. You should plan to work on your exercises everyday, and for a total of at least 8 hours each week. Also, it is very important that you faithfully attend all lectures.

A good deal of class time shall be devoted to working through problems. Do not get into the habit of sitting passively and expecting the professor to make you understand. Rather, you should take out your paper and pencil and try to do the problems at the same time with your instructor. If something is unclear to you, feel free to ask questions, and if you need more help, go see your instructor during the office hours. If you cannot come during the office hours, you are welcome to knock on the professor's door at another time, or send an email for an appointment.