Western Washington University, Fall 2015

Math 204: Elementary Linear Algebra

Class Meetings: MTRF 2 – 2:50 pm, Bond Hall 317

Instructor: Dr. Stephanie Treneer Email: stephanie.treneer[at]wwu.edu Office: 206 Bond Hall, (360) 650-3468 Office Hours: 12:00-12:50 pm MTRF, or by appointment Prerequisites: Math 125 or 135. Math 224 is recommended. Textbook: Linear Algebra and its Applications, David C. Lay, 3rd ed. We will cover most of chapters 1 through 5. Calculator: You may find it useful to have a calculator which allows you to row reduce matrices (e.g. a TI 85 or higher).

Course Overview: Solving systems of equations is an important and difficult problem in mathematics. Even figuring out if a single equation has any nontrivial solutions can be extremely difficult. If the system consists of linear equations, there is an algorithm to find its solutions. In this course, we will study this algorithm, which will help us solve many problems in both algebra and geometry. The techniques we develop apply not only to solutions of linear systems, but also to many different mathematical systems, such as complex numbers, real-valued functions, lines through the origin in the plane, etc. When we abstract the properties that allow us to apply our techniques to these systems, we get what is called a vector space. The benefit of working with vector spaces is that everything we deduce about them automatically applies to all the diverse systems we want to understand. In the latter part of the class we will study vector spaces in general.

Course Objectives: The successful student will demonstrate: 1. Ability to translate between systems of linear equations, vector equations, and matrix equations, and perform elementary row operations to reduce the matrix to standard forms.

2. Understanding of linear combination and span.

3. Determination of the existence and uniqueness of a solution to a system of linear equations in terms of the columns and rows of its matrix.

4. Ability to represent the solution set of a system of linear equations in parametric vector form and understand the geometry of the solution set.

5. Understanding of linear dependence and independence of sets of vectors.

6. Understanding of linear transformations defined algebraically and geometrically, and ability to find the standard matrix of a linear transformation.

7. Understanding and computation of the inverse and transpose of a matrix.

8. Understanding and computation of the determinant of a matrix and its connection with invertibility.

9. Understanding of the notions of a vector space and its subspaces and knowledge of their defining properties.

10. Knowledge of the definitions of a basis for and the dimension of a vector space, and ability to compute coordinates in terms of a given basis and to find the change of basis transformation between two given bases.

11. Ability to find bases for the row, column, and null spaces of a matrix, find their dimensions, and knowledge of the Rank Theorem.

12. Ability to find eigenvalues and eigenvectors of a matrix.

13. Knowledge of all aspects of the Invertible Matrix Theorem.

14. Knowledge of the Diagonalization Theorem and ability to diagonalize a matrix. The achievement of these goals will be measured by exams and quizzes.

Homework: Several problems will be assigned from each section, but will not be collected. Here is a full list of the problems. In order to keep up with and understand the course material, you should do all these problems yourself. We will go over some of the problems in class, and you are welcome to ask questions about the homework, either in class or in office hours. You are encouraged to do more than these problems, especially if you encounter a topic that you find more difficult.

Quizzes and Exams: There will be a quiz or exam every Friday except for the first and last weeks of the quarter. Quizzes will be given in the first 20 minutes of class, and will include questions similar to ones from class and homework. There will be two midterm exams, and a final exam. The midterm exams are scheduled for October 16 and November 13. Makeup midterm exams will only be considered in the case of illness or emergency, and you must let me know of your situation prior to the exam. The final exam is on Thursday, December 10, at 8 am. It will be comprehensive. The date and time of the final can’t be changed, so you should plan your winter break travel so as not to interfere with the exam.

Grading: Your grade for the course will be based on exams and quizzes as follows:

25% each Best two of Exam 1, Exam 2, and Quiz Average 15% Worst of Exam 1, Exam 2, and Quiz Average 35% Final Exam

I tend to give challenging exams, so my grading scale is usually more generous than the standard scale of A 90-100%, B 80-89%, C 70-79%, etc.

Some advice for succeeding in the course: This is a fast-paced course, with many challenging concepts and new vocabulary. It is very important to keep up with the material by reading the book carefully and doing all of the homework problems in a timely manner. To do well on the exams, you will need to understand the concepts, not just memorize the methods. Sources of help: Please talk with me about any questions or concerns you may have about the course, and make use of my office hours. In addition to my office hours, there is help available in the Math Center (211A Bond Hall). This is staffed by Math Fellows who are trained to help with homework questions, and is also great place to meet other students to work with.

Academic Integrity: Don’t cheat! Please consult this collection of integrity resources for further information.

Accommodation: If you are in need of special accommodation for this course, you should first visit disAbility Resources for Students (DRS, Old Main 120) to register your eligibility, and then submit the necessary requests online. Please also feel free to talk with me early in the quarter to let me know how I can be of assistance.