Class 17, Wed., Nov. 19, 2014
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.
Turn in chapter 6 homework next Monday. Chapter 7 will be due during exam week. You may skip 6.1, #11, and also 6.3, # 2 (which involves differential equation solving techniques.)
Class 17, Wed., Nov. 19, 2014
We went over more on transformations, and also looked at why an n by n matrix with n distinct eigenvalues has eigenvectors that are independent. We also saw why the sum of the eigenvalues is the trace and the product is the determinant.
See updated homework below.
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 16, Mon., Nov. 17, 2014
We went over chapter 7.2 and differential equations application of eigenvectors from section 6.3.
We'll go over 6.4, 6.6, and 7.3 on Monday.
Ch. 7.1: 1,3,8a,9,14,21,24
Ch. 7.2: 1,5,11,15,21
Ch. 7.3: 1-3
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
Class 15, Wed., Nov. 12, 2014
Exam 2
Class 14, Wed., Nov. 5, 2014
We went over sections 6.1 and 6.2 on eigenvalues and eigenvectors
Class 13, Mon., Nov. 3, 2014
We went over more of chapter 5 and began chapter 6
Class 12, Wed., Oct. 29, 2014
We went over most of the rest of chapter 5 on determinants.
Homework for chapter 4 is due on Monday.
Please watch Gilbert Strang's video lecture on eigenvectors (lecture number 21, the start of chapter 6).
Please begin to watch the appropriate lecture BEFORE the class on that subject. We'll try to use this technique for the rest of the quarter!
You might also want to watch the lectures on chapter 5, especially the end of chapter 5, which we have not yet finished.
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
Class 11, Mon., Oct. 27, 2014
We went over material from chapter 4.2 and 4.4, we are skipping 4.3 for now.
Chapter 3 homework is due next Monday, Oct. 27
Ch. 4.4: # 1,2,3,5,10,13-15,17
Class 10, Wed., Oct. 22, 2014
We went over material from sections 4.1 and 4.2.
Chapter 3 homework is due next Monday, Oct. 27
Ch. 4.1: # 3,4,9,10,11,14,24
Ch. 4.2: # 1a,2a,3,11,21,22
Class 9, Mon., Oct. 20, 2014
We went over exam 1 and chapter 3.6.
Ch. 3.6: #1,2,5,6,11,27
Class 8, Wed., Oct. 15, 2014
We went over section 3.5, and had first exam.
Ch. 3.5: # 1-5,7,8,9,11,12,16,17,19,27,37
Class 7, Mon., Oct. 13, 2014
We went over section 3.4.
Exam on Thursday will go through section 3.4.
Ch. 3.4: # 1,3,4,5,12,16,17,24
Class 6, Wed., Oct. 8, 2014
We went over chapters 3.2 and most of 3.3.
Ch. 3.2: # 1-4,9,11,12,16,18
Ch. 3.3: # 1,2,3,7,8,9
Class 5, Mon., Oct. 6, 2014
We went over chapter 2 and 3.1
Ch. 3.1: # 2,5,6,7,10,17,18,19,23
Class 4, Wed., Oct. 1, 2014
We went over chapters 2.6 and most of 2.7.
Ch. 2.6: # 1,2,3,4,6,15,16
Ch. 2.7: # 1,2,4,14
Class 3, Mon., Sep. 29, 2014
We went over chapters 2.4 and 2.5.
Ch 2.5: # 2,3,5,7,12,14,23,26,30,35
Class 2, Wed., Sep. 24, 2014
We went over sections 2.1-2.3 and most of 2.4 .
Homework:
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
Class 1, Mon., Sep. 22, 2014
We went over sections 1.1 and 1.2, and began chapter 2.
Homework:
Ch. 1.1: # 9,11,12,15-18,24,28
Ch. 1.2: # 7,8,9,13,16,17,21,28,29
Later (we have not finished section 2.1):
Ch. 2.1: # 1,3,5,9,13,16-19,23,28,30-32
Some info from past classes:
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.