COURSE: MATH 300-001 -- Linear Algebra (3 credit hours)
COURSE OBJECTIVES: This course will examine the solution of systems of linear equations and how matrices are used to investigate these systems. The course will also study the elementary theory of vector spaces and linear transformations, determinants, eigenvalues, and eigenvectors. The computer algebra system Mathematica will be used. This course addresses General Education Goals 2 and 3 (see the Winthrop University Undergraduate Catalog 2009-2010, pp. 14-15)
STUDENT LEARNING OUTCOMES: Students will develop a deep understanding of systems of linear equations, and how matrices are used to solve these systems, to show that no solution exists, and to show that a solution is unique. Students will develop an understanding of matrices as mathematical objects independent of their role in the solution of systems of linear equations, including a basic understanding of the matrix of a linear transformation, determinants, eigenvalues, and eigenvectors. Students will master the reading and writing of short definition-based proofs. Students will develop an appreciation for applications of linear algebra to biology, economics, statistics, and other fields.
TIME/LOCATION: Mondays, Wednesdays, and Fridays, 11:00 - 11:50 a.m., Kinard 305
INSTRUCTOR: Tom Polaski
OFFICE: Bancroft 158 OFFICE PHONE: 323-4604
E-MAIL ADDRESS: polaskit@winthrop.edu HOME PHONE: 704-523-8279
HOME PAGE: http://faculty.winthrop.edu/polaskit/
OFFICE HOURS: Thursdays 10:00 a.m. - 10:50 a.m.; Tuesdays and Thursdays 1:00 p.m. - 2:30 p.m.
Other times may be arranged by appointment.
TEXT: Linear Algebra and its Applications by David C. Lay. Updated Third Edition. Boston: Addison-Wesley, 2006. A Study Guide which comes bundled with this text is suggested.
HOMEWORK ASSIGNMENTS: At the end of each class session, a homework assignment will be made. You are expected to complete the assignment by computing and recording your answers in the Mathematica notebook for the appropriate section of the text; these notebooks are available at the course website, and contain the data for each exercise. You will then e-mail the completed Mathematica notebook to your instructor before the next class session. Each homework assignment will be given a grade out of a possible 10 points. At the close of these semester, these homework grades will be averaged and converted to a 100-point scale.
TESTS AND GRADING: There will be three 100-point tests given along with a 200-point cumulative final examination. No make-up tests will be given unless prior arrangements have been made with the instructor. A point system will determine your final grade. There are 600 points possible; 300 from the tests, 100 from the homework assignments, and 200 from the final. An approximate grading scale for each test and the homework assignments will be determined after they are graded. The semester grading scale will be based upon these grading scales and on the scale for the final examination.
ATTENDANCE POLICY: Attendance at all scheduled class meetings is strongly encouraged. Your number of absences will not be counted, nor will they be used to determine your grade. Attendance is mandatory for those meetings which include a test. If no prior arrangements are made with the instructor, a zero will be recorded for a test not taken due to absence.
LAST DAY TO WITHDRAW FROM THE CLASS: Wednesday, March 10. Students withdrawing prior to this date will receive an "N" in the course. Students may not withdraw from a course after this date without documented extenuating circumstances.
FINAL EXAMINATION DATE AND TIME: Monday, May 3 at 8:00 a.m.
ACADEMIC INTEGRITY: Each student is responsible for conforming to University policies on academic misconduct. Academic misconduct can result in failing grades for individual assignments and for a failing grade in this course. The complete Student Code of Conduct is available at http://www2.winthrop.edu/studentaffairs/handbook/StudentHandbook.pdf.
PROGRAM ASSESSMENT: Your work in this course will be used for assessment of the Department of Mathematics. Samples of your work will be taken and assessed after the conclusion of the course; your grade will not be affected.
FOR
STUDENTS WITH DISABILITIES: Winthrop
University is dedicated to providing access to education. If you have a disability
and require specific accommodations to complete this course, contact Services for Students with
Disabilities at 323-3290 as early as possible. Once you have your official notice of accommodations
from this office, please inform your instructor.
HELP: You should discuss your homework with your classmates and instructor as a part of your study. The instructor's office hours are a good time to clear up any difficulties you have with the material.
TECHNOLOGY:
This class will use the software package Mathematica.
This software is available in all campus labs. You are encouraged to use Mathematica on your homework, and required to use Mathematica on homework sets and on each test. It
will be assumed that you have a basic working knowledge of this software
package.
ALTERATIONS TO THIS
SYLLABUS: The
instructor reserves the right to make modifications to this syllabus. Students
will be notified in class and by email of any modifications.
COURSE SCHEDULE
|
LESSON |
DATE |
SECTION(S) |
CONTENTS |
|
1 |
M 1/11 | 1.1 |
Systems of Linear Equations |
|
|
W 1/13 |
|
|
|
3 |
F 1/15 |
|
|
|
4 |
M 1/18 |
|
|
|
5 |
W 1/20 |
1.2 |
Row Reduction and Echelon Forms |
|
6 |
F 1/22 |
1.3 |
Vector Equations |
|
7 |
M 1/25 |
1.4 |
The Matrix Equation Ax=b |
|
8 |
W 1/27 |
1.5 |
Solution Sets of Linear Systems |
|
9 |
F 1/29 |
1.6 |
Applications of Linear Systems |
|
10 |
M 2/1 |
1.7 |
Linear Independence |
|
11 |
W 2/3 |
1.8 |
Introduction to Linear Transformations |
|
12 |
F 2/5 |
1.9 |
The Matrix of a Linear
Transformation |
|
13 |
M 2/8 |
1.10 |
Linear Models in Business,
Science, and Engineering |
|
14 |
W 2/10 |
2.1 |
Matrix Operations |
|
15 |
F 2/12 |
2.2 |
The Inverse of a Matrix |
|
16 |
M 2/15 |
2.3 |
Characterizations of Invertible
Matrices |
|
17 |
W 2/17 |
2.5 |
Matrix Factorizations |
|
18 |
F 2/19 |
TEST 1 |
|
|
19 |
M 2/22 |
2.6 |
The Leontief Input-Output Model |
|
20 |
W 2/24 |
2.7 |
Applications to Computer Graphics |
|
21 |
F 2/26 |
2.8 |
Subspaces of Rn |
|
22 |
M 3/1 |
2.8,2.9 |
Subspaces of Rn;
Dimension and Rank |
|
23 |
W 3/3 |
2.9 |
Dimension and Rank |
|
24 |
F 3/5 |
|
Introduction to Determinants |
|
25 |
M 3/8 |
3.2 |
Properties of Determinants |
|
26 |
W 3/10 |
4.9 |
Applications to Markov Chains |
|
27 |
F 3/12 |
4.9 |
Applications to Markov Chains -- PageRank |
|
28 |
M 3/15 |
|
|
|
29 |
W 3/17 |
|
|
|
30 |
F 3/19 |
|
|
|
31 |
M 3/22 |
5.1 |
Eigenvectors and Eigenvalues |
|
32 |
W 3/24 |
5.2 |
The Characteristic Equation |
|
33 |
F 3/26 |
|
TEST 2 |
|
34 |
M
3/29 |
5.3 |
Diagonalization |
|
35 |
W
3/31 |
5.4 |
Eigenvectors and Linear Transformations |
|
36 |
F 4/2 |
5.5 |
Complex Eigenvalues |
|
37 |
M 4/5 |
5.6 |
Discrete Dynamical Systems |
|
38 |
W 4/7 |
6.1 |
Inner Product, Length, and Orthogonality |
|
39 |
F 4/9 |
6.2 |
Orthogonal Sets |
|
40 |
M 4/12 |
6.3 |
Orthogonal Projections |
|
41 |
W 4/14 |
6.4 |
The Gram-Schmidt Process |
|
42 |
F 4/16 |
6.5 |
Least-Squares Problems |
|
43 |
M 4/19 |
6.6 |
Applications to Linear Models |
|
44 |
W 4/21 |
|
|
|
45 |
F 4/23 |
|
TEST 3 |
|
46 |
M 4/26 |
|
Review and Evaluation |