Linear Algebra
Instructor
- Chuck Iverson
- Office Hours: MESA/Learning Center
- Office: 18-108
- Office Phone: (650) 306-3253
- Email: iverson@smccd.edu
- Web Page: http://www.civerson.com
Class Location and Meeting Times
- Building 16, Room 108
- 12:45-2:00 pm MW
Prerequisite
- Physics 250 and Math 252, both with a grade of C or better
Materials
- Linear Algebra (3rd Edition) by Poole (ISBN 978-0-538-73545-2)
- WebAssign: https://www.webassign.net/login.html
Grading
- Homework (25%)
- Exams and Quizzes (70%)
- Class Participation (5%)
Course Description
Study of vectors, systems of linear equations, the algebra of matrices, determinants, eigenvalues and eigenvectors, vector spaces, inner products and least-squares.
Sample Student Learning Objectives
- Correctly solve a system of equations using matrices and Gaussian elimination.
- Correctly find the eigenvectors and eigenvalues of a matrix.
- Correctly use the Gram-Schmidt process to create an orthogonal basis for a vector space.
Homework
Reading the textbook and doing the assigned exercises are the most important work students can do between classes to insure understanding of concepts and to develop skill in applying problem solving techniques. Consequently, exercises contribute significantly to the final grade. All homework is done online through WebAssign: https://www.webassign.net/login.html. The class key to enroll in WebAssign is: canadacollege 4906 3447. One by-arrangement hour of tutorials and exercises in the Math Lab is also required per week.
Class Notes and Assignments
http://www.civerson.com/M270/
Exams and Quizzes
Frequent quizzes, three midterm exams and a final exam will be given during the semester. Each midterm exam will cover two to three chapters. You may have one sheet of notes for each exam. See the tentative schedule below for the dates of the exams.
Quizzes may be given during the first 15 minutes of each class, based on the material discussed in the previous class. The average of your top ten quiz scores will count as one exam score.
Make-Up Exams
A make-up exam will be offered to any student who scores less than his or her homework average on a particular exam. Before taking a make-up exam, a student must meet with me to review his or her original exam. A make-up exam score will be limited to a student's current homework average. A make-up exam score will replace an original exam score only if the make-up exam score is higher.
Software
We'll be using Matlab (or SysquakeLE), Graphing Calculator and GeoGebra extensively in class to aid your understanding, to simplify routine calculations and to allow us to examine more interesting topics. It's not necessary to have these programs at home, but it may be useful. SysquakeLE (http://www.calerga.com/download/index.html) is cross-platform, free and duplicates many of Matlab's facilities for use in this class. Graphing Calculator, in particular, is an immensely helpful and easy-to-use math program that can be used through all math courses offered at Cañada College, and it will help you to visualize what's going on with vectors, lines and surfaces in two and three dimensions. To encourage students in mathematics, the creator of the program offers special student rates: $20 for a one-year rental or $60 (educational discount -- equivalent to two large pizzas, but so much better for you): http://www.pacifict.com/Order.html. I personally use this program every day. I recently learned about GeoGebra (http://www.geogebra.org/cms/), another free and very useful program.
Expectations
I can help you succeed in this class, but I can't succeed for you. In this class you're expected to be responsible for your own academic success.
- That means you are expected to attend class and to arrive on time (2 lates equals 1 absence, more than 4 absences leads to a drop).
- If you're going to miss class, you should notify me ahead of time, either by phone or email.
- You are expected to contribute to class discussions and to ask questions when something is not clear.
- You are expected to do your homework assignments before the class when they are due and to seek help from me or your classmates or a tutor if you are having difficulty completing them.
- You should check the class notes and assignments link (top right of this page) if you miss class. All class assignments, exam solutions, sample code and special notes will be posted at this web site after class.
- You are expected to see me during office hours for additional help or to take make-up exams.
Instructor's Fall 2011 Class Schedule
My class schedule, below, shows when and where I'm on campus. The best way to contact me if I'm not on campus is via email. I check my email several times a day. I have my email automatically sorted by the first 4 characters in the subject field. For this class, the subject line of the email should begin with M270.
Tentative Topic Schedule
| Monday | Wednesday |
|---|---|
| 8/17 - 1.0 Racetrack Game 1.1 Geometry and Algebra of Vectors 1.2 Length and Angle: Dot Product |
|
| 8/22 - 1.3 Lines and Planes 1.4 Code Vectors and Modular Arithmetic |
8/24 - 2.0 Triviality 2.1 Introduction to Systems of Linear Equations 2.2 Direct Methods for Solving Linear Systems |
| 8/29 - 2.2 Direct Methods for Solving Linear Systems | 8/31 - 2.3 Spanning Sets and Linear Independence 2.4 Applications |
| 9/05 - Labor Day Holiday | 9/07 - Review of Chapters 1-2 |
| 9/12 - Exam on Chapters 1-2 | 9/14 - 3.0 Matrices in Action 3.1 Matrix Operations 3.2 Matrix Algebra |
| 9/19 - 3.3 Inverse of a Matrix | 9/20 - 3.4 The LU Factorization |
| 9/26 - 3.5 Subspaces, Basis, Dimension and Rank | 9/28 - 3.6 Introduction to Linear Transformations 3.7 Applications |
| 10/03 - 4.0 A Dynamical System on Graphs 4.1 Introduction to Eigenvalues and Eigenvectors |
10/05 - 4.2 Determinants 4.3 Eigenvalues and Eigenvectors of n x n Matrices |
| 10/10 - 4.4 Similarity and Diagonalization 4.6 Applications |
10/12 - Review of Chapters 3-4 |
| 10/17 - Exam on Chapters 3-4 | 10/19 - 5.0 Shadows on a Wall 5.1 Orthogonality in R^n 5.2 Orthogonal Complements and Orthogonal Projections |
| 10/24 - 5.3 The Gram-Schmidt Process and the QR Factorization | 10/26 - 5.4 Orthogonal Diagonalization of Symmetric Matrices 5.5 Applications |
| 10/31 - 6.0 Fibonacci in (Vector) Space 6.1 Vector Spaces and Subspaces |
11/02 - 6.2 Linear Independence, Basis and Dimension 6.3 Change of Basis |
| 11/07 - 6.4 Linear Transformations | 11/09 - 6.5 The Kernel and Range of a Linear Transformation |
| 11/14 - 6.6 The Matrix of a Linear Transformation 6.7 Applications |
11/16 - Review of Chapters 5-6 |
| 11/21 - Exam on Chapters 5-6 | 11/23 - 7.0 Taxicab Geometry 7.1 Inner Product Spaces |
| 11/28 - 7.2 Norms and Distance Functions | 11/30 - 7.3 Least Squares Approximation |
| 12/05 - 7.4 Singular Value Decomposition 7.5 Applications |
12/07 - Review of Chapter 7 |
| 12/12 - No Class | 12/14 - 2:10-4:40 Final Exam |