Green Sheet
Strang text (3rd edition) homework list
Video Lectures
The textbook author Gilbert Strang has an excellent series of video lectures following the text online here.
Watch the first couple of his lectures prior to the first week of classes. We'll continue this practice during the quarter, and this will make the class more productive. Please watch the appropriate lecture BEFORE the class on that subject. You will have simple online quizzes with only a few questions for each lecture, which will count as part of your grade. The site allows you to watch these lectures at faster or slower than normal speeds.
Research Experiences for Undergraduates (REUs)
You may be interested in being part of a summer research project funded by the National Science Foundation, entitled Research Experiences for Undergraduates (REUs). Many of these provide stipends and support for travel and lodging. There are literally hundreds of such programs in a variety of science disciplines, including mathematics, and are a great opportunity to get experience in doing research. See this site for information. Most applications are due in February and March, but each sets its own deadlines.
Class 17, Wed., Mar. 2
We looked more closely at eigenvalues and eigenvectors: why is the product of the e'values equal to the determinant, why is the sum of the e'values equal to the trace? Reports are due on Monday, March 14.
Class 16, Mon., Feb. 29
We went over how to diagonalize a matrix.
Class 15, Wed., Feb. 24
We went over new material on eigenvalues and eigenvectors. You'll have new video quizzes assigned for next week.
Class 14, Mon., Feb. 22
We went over rest of materal on determinants. Here's a site with some proofs that the determinant equals area.
Class 13, Wed., Feb. 17
We went over more on Gram-Schmidt and also material on determinants. Exam 2 is next Wednesday, Feb. 24.
Class 12, Mon., Feb. 15
We went over Gram-Schmidt material.
Class 11, Wed., Feb. 10
We went over more from chapter 4 on orthogonal matrices and Gram-Schmidt orthogonalization.
Homework for chapter 4 is due on Monday, Feb. 22, and we will start on chapter 5 on Wednesday.
Class 10, Mon.., Feb. 8
We went over material from chapter 4 on projections.
Homework for chapter 3 is due on Wednesday, Feb. 10.
Class 9, Wed.., Feb. 3
We went over more material on dimension and the four subspaces.
I've assigned several more video quizzes. On Monday we will cover material from chapter 4 on orthogonality, projections, etc.
Class 8, Mon., Feb. 1
We went over material on linear independence and dependence, span, basis, and dimension.
Class 7, Wed., Jan. 27
We went over more material on column and null spaces, and had exam 1.
You should be working on chapter 3 homework.
I have assigned two more video quizzes, numbers 8 and 9, due Monday.
Class 6, Mon., Jan. 25
I've added a list of items to study for exam 1 here: Study guides for exams.
Class 5, Wed., Jan. 20
We went over material on transposes and inverses, as well as new material from chapter 3 on vector spaces.
Homework for chapter 2 is due either next Monday or Wednesday, whichever day you want to turn it in.
Please go over this new material on column space and null space, as it is central to what we will be doing.
There are two new quizzes assigned, for video lectures 6 and 7.
Class 4, Wed., Jan. 13
The substitute Edwin Njinimbam went over material on inverses and LU decomposition and gave a quiz on 2 by 2 matrix multiplication.
Class 3, Mon., Jan. 11, 2016
We went over material on matrix multiplication, LU factorization, and using elementary matrices and permuttion matrices for row operations. You have one more video quiz, number five, assigned for Wednesday.
Class 2, Wed., Jan., 6, 2016
We went over more material on matrices and their use to represent systems of equations. We also noted that matrix multiplication is not commutative. You should now be working on chapter 2 homework, though I have not yet announced the due date since so many of you do not yet have the textbook.
Class 1, Mon., Jan., 4, 2016
We will go over chapter 1 on vectors, and the beginning of chapter 2.
Watch Strang's lectures 1 and 2 before class.
Chapter 1 is review of vectors. However, I am assigning as homework
Ch. 1.1, # 9,11,12,14,15-18,24,26, 28
Ch. 1.2, # 7,8,9,13,16,17,21,24,28,29
To give us some problems to discuss.
These WILL NOT BE COLLECTED in class or count as a homework assignment since they are review.
We also saw how to represent a system of linear equations in row and column form, as well as in matrix form.
Class 2, Wed., Jan. 6, 2016
We will review the several ways to understand matrix multiplication, see that it is non-commutative but is associative, and go over row reduction and back substitution. We will see how matrix multiplication can affect the unit square in the plane. Watch video lectures 3 and 4.
Class 3, Mon., Jan. 11, 2016
We will go over material in chapter 2, especially on elementary matrices as a means of "encoding" row operations and row reducing a matrix.
Some info from past classes:
Information on Google PageRank and its calculation using eigenvalues and Markov processes. Here's a page with a high PageRank, that describes the mathematics of PageRank. Here's Brin and Page's original article on their search engine.
The AMATYC exam practice problems are at:
http://www.amatyc.org/?page=SMLPastQuestions
There are now a number of free copies of linear algebra texts available online. For example, a copy of the "2012-Feb-29" version of the Hefferon text is posted at this Dropbox site:
https://www.dropbox.com/s/wqu5yamk3diuxmw/Hefferon.Feb.2012.pdf
Here are some handouts that might be helpful to you. Please read!
Augmented matrices.
Linear Algebra vocabulary.
Here is the vocabulary list.
Here is the vocabulary list with definitions.