Class notes are below the list of homework problems.
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.
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.
HOMEWORK FROM THE TEXT:
Ch. 1.1: # 9,11,12,15-18,24,28
Ch. 1.2: # 7,8,9,13,16,17,21,28,29
Ch. 2.1: # 1,3,5,9,13,16-19,23,28,30-32
Ch. 2.2: # 4,5,6,13,19,25,26
Ch. 2.3: # 3,5,7,10,13,17,18,25
Ch. 2.4: # 1,2,5,6,7,11,13,14,16,18,37
Ch 2.5: # 2,3,5,7,12,14,23,26,30,35
Ch. 2.6: # 1,2,3,4,6,15,16
Ch. 2.7: # 1,2,4,14
Ch. 3.1: # 2,5,6,7,10,17,18,19,23
Ch. 3.2: # 1-4,9,11,12,16,18
Ch. 3.3: # 1,2,3,7,8,9
Ch. 3.4: # 1,3,4,5,12,16,17,24
Ch. 3.5: # 1-5,7,8,9,11,12,16,17,19,27,37
Ch. 3.6: #1,2,5,6,11,27
Ch. 4.1: # 3,4,9,10,11,14,24
Ch. 4.2: # 1a,2a,3,11,21,22
Ch. 4.3: # 1-5,12,26 (NEW!)
Ch. 4.4: # 1,2,3,5,10,13-15,17
Ch. 5.1: # 1,3,4,7,8,9,13,24,28
Ch. 5.2: # 1,6,12
Ch. 5.3: # 1,3,4,17,18
Ch. 6.1: 2-5,8,9,11,14-18,20
Ch. 6.2: 1-5,7,8,11,12,14,15
Ch. 6.3: 1-3
Ch. 6.4: 1-5,18
Ch. 6.6: 1-8
Ch. 7.1: 1,3,8a,9,14,21,24
Ch. 7.2: 1,5,11,15,21
Ch. 7.3: 1-3
Class 20, Wed., Mar. 18, 2015
We learned about Markov Processes (section 8.3) and Google's Page Rank algorithm.
Here is a web site that I used for the background on Page Rank. Please study it! Also study 8.3.
Here is the handout we worked on in class on Google Page Rank.
Here's Brin and Page's original article on their search engine.
Turn in chapter 6 and 7 homework (only the sections we covered) during the final exam; I'll give them back to you right away during the exam.
In chapter 6 we skipped 6.5 and 6.7. In chapter 7 we only covered 7.1 to 7.3. We also covered some of 8.3.
Class 19, Mon., Mar. 16, 2015
We went over material linear transformations.
Class 18, Wed., Mar. 11, 2015
We went over material on linear transformation.
Class 17, Mon, Mar. 9, 2015
We learned about differential equations applications of eigenvalues (6.3) and symmetric matrices (6.4) and started on linear transformations (7.1).
Class 16, Wed., Mar. 4, 2015
We went over chapter 6.2 on diagonalizability.
Turn in chapter 5 homework on Monday, Mar. 9
Class 15, Mon., Mar. 2, 2015
Sub Edwin Njinimbam went over eigenvalues and eigenvectors in chapter 6.1 and started on 6.2
Class 14, Wed., Feb. 25, 2015
We had exam 2 and introduced eigenvalues and eigenvectors.
Class 13, Mon., Feb. 23, 2015
We went over all of chapter 5, except Cramer's rule.
Please turn in chapter 4 homework tomorrow after exam 2.
Please bring a scantron (half page long version) for the exam.
Exam includes from chapter 3.5 to 5.1, but includes knowing how to calculate 2 by 2 and 3 by 3 determinants.
Some things to study:
Solving Ax=b when solutions are infinite, non-existent
Basis, span, independence, dimension
The four subspaces associated with a matrix and their dimensions
Given several vectors, can you decide if they are dependent or independent?
How to project a vector onto another vector or a subspace
Orthonormal sets of vectors and orthonormal vectors
Rules for calculating determinants and ways to calculate 2 by 2 and 3 by 3 determinants
Gram-Schmidt
Least squares approximations
Class 12, Wed., Feb. 18, 2015
We went over Gram-Schmidt orthogonalization.
Second exam is next Wednesday.
Chapter 4 homework will be due on Wednesdaty, Feb. 25.
Class 11, Wed., Feb. 11, 2015
We went over more about projections, also least squares approximation lines (Chapter 4.3) seen as projections into a 2-dimensional subspace of R^n, where n is the number of data points.
Note that I've added some Chapter 4.3 homework problems.
Chapter 4 homework will be due on Wednesdaty, Feb. 25.
Class 10, Mon., Feb. 9, 2015
We went over more about dimension and important subspaces, as well as projections.
Class 9, Wed., Feb. 4, 2015
We went over more about bases, dimension, independence/dependence, spanning, etc.
We also started chapter 4 on projections.
Chapter 3 homework is due next Wednesday.
Class 8, Mon., Feb. 2, 2015
We went over exam 1 and more about dimension and independence.
Class 7, Wed., Jan. 28, 2015
We had exam 1.
Class 6, Mon., Jan. 26, 2015
We went over more on permutations.
We also went over sections 3.3 and 3.4.
First exam will go through section 3.4.
Chapter 2 homework will be collected on Wednesday following exam 1.
Class 5, Wed., Jan. 21, 2015
We went over section 2.6 on LU factorization and also 2.7 on transposes and permutation matrices.
Here is a "visual proof" of the formula for the sum of the first n squares.
Chapter 2 homework due Monday, first exam is next Wednesday.
Class 4, Wed., Jan. 14, 2015
We went over more material from chapter 3 on the column space and the null space, and learned how to write the solution to the equation Ax=b in the form of a vector plus a linear combination of vectors. No class on Monday for Martin Luther King holiday, but please watch the Strang videos and work on chapter 2 homework. We will go back and go over the end of chapter 2 sections next week.
Class 3, Mon, Jan. 12, 2015
The sub Edwin Njinimbam went over vector spaces and finding the inverse of a matrix, and gave a short quiz on matrix transformations of the plane.
Class 2, Wed., Jan. 7, 2015
We went over material up to chapter 2.4. We also learned about how a 2 by 2 matrix can modify the vectors in the plance by looking at what one does to a unit square with its lower right corner at the origin.
You'll cover sections 2.5 and 3.1 on Monday. When I return to class I'll go over section 2.6 and 2.7.
Do come to class on Monday, when Edwin Njinimbam will sub, you might find that there is a class assignment!!
Homework: Chapter 1 is to be turned in on Monday, Jan. 12. You should be working on chapter 2 homework already, and watching the Strang videos that accompany this material.
Class 1, Mon., Jan. 5, 2015
We went over chapter 1 on vectors, and the beginning of chapter 2.
Some info from past classes:
We went over some homework problems on eigenvalues, and learned about 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
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.