COURSE: MATH 300-001 -- Linear Algebra

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, 12:30 - 1:20 p.m., Kinard 308

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: Mondays and Wednesdays  2:00 p.m. - 3:30 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 also required.

HOMEWORK: Homework assignments will be made during each class session; you are expected to complete these assignments by the next class session.  It is strongly urged that you do use Mathematica to do the assigned problems.  Mathematica notebooks with data for many homework problems may be found on the course website. If, after attempting an assignment, you either do not understand the material or have difficulty with certain problems, you are encouraged to get help from your instructor.

HOMEWORK SETS: Each Monday a selected subset of these problems will be posted on the course website.  You should do these problems in the Mathematica notebook provided (or copy your work into that notebook) and e-mail the completed notebook to me by noon on Tuesday.  Each homework set will be worth 10 points.

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 630 points possible; 300 from the tests, 130 from the homework sets, and 200 from the final.  An approximate grading scale for each test and homework set will be determined after it is 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: Friday, October 23.  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:  Wednesday, December 9 at 11:30 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

W 8/26

1.1

Systems of Linear Equations

2

F 8/28

1.2

Row Reduction and Echelon Forms

3

M 8/31

1.3

Vector Equations

4

W 9/2

1.4

The Matrix Equation Ax=b

5

F 9/4

1.5

Solution Sets of Linear Systems

6

M 9/7

1.6

Applications of Linear Systems

7

W 9/9

1.7

Linear Independence

8

F 9/11

1.8

Introduction to Linear Transformations

9

M 9/14

1.9

The Matrix of a Linear Transformation

10

W 9/16

NO CLASS

11

F 9/18

NO CLASS

12

M 9/20

1.10

Linear Models in Business, Science, and Engineering

13

W 9/23

2.1

Matrix Operations

14

F 9/25

2.2

The Inverse of a Matrix

15

M 9/28

2.3

Characterizations of Invertible Matrices

16

W 9/30

2.4

Partitioned Matrices

17

F 10/2

TEST 1

18

M 10/5

2.5

Matrix Factorizations

19

W 10/7

2.6

The Leontief Input-Output Model

20

F 10/9

2.7

Applications to Computer Graphics

21

M 10/12

2.8

Subspaces of Rn

22

W 10/14

2.8,2.9

Subspaces of Rn; Dimension and Rank

23

F 10/16

2.9

Dimension and Rank

24

M 10/19

NO CLASS

25

W 10/21

3.1

Introduction to Determinants

26

F 10/23

3.2

Properties of Determinants

27

M 10/26

4.9

Applications to Markov Chains

28

W 10/28

4.9

Applications to Markov Chains -- PageRank

29

F 10/30

5.1

Eigenvectors and Eigenvalues

30

M 11/2

TEST 2

31

W 11/4

5.2

The Characteristic Equation

32

F 11/6

5.3

Diagonalization

33

M 11/9

5.4

Eigenvectors and Linear Transformations

34

W 11/11

5.5

Complex Eigenvalues

35

F 11/13

5.6

Discrete Dynamical Systems

36

M 11/16

6.1

Inner Product, Length, and Orthogonality

37

W 11/18

6.2

Orthogonal Sets

38

F 11/20

6.3

Orthogonal Projections

39

M 11/23

6.4

The Gram-Schmidt Process

40

W 11/25

NO CLASS

41

F 11/27

NO CLASS

42

M 11/30

6.5

Least-Squares Problems

43

W 12/2

6.6

Applications to Linear Models

44

F 12/4

 

TEST 3

45

M 12/7

 

Review and Evaluation