Class 20, Wed., Mar. 19, 2014
We went over dimension analysis again.
Class 19, Mon., Mar. 17, 2014
We went over more about geometry and linear transformations.
Class 18, Wed., Mar. 12, 2014
We did a bit more with eigenvectors, also learned more about linear algebra and geometry. Please turn in chapter 4 homework on Monday.
Class 17, Mon., Mar. 10, 2014
We learned more about eignevalues and eigenvectors, and also learned about isometries, linear transformations that preserve distance - in the plane the only isometries are rotations and reflections.
Revision of chapter 5 homework:
5.II.1: 1.5,1.6, 1.7a, 1.10, 1.12, 1.14
5.II.2: 2,7, 2,10, 2.15a,b, 2.17, 2.18
5.II.3: 3.22a,c,d, 3.24, 3.25, 3.29, 3.31, 3.40
Revision of Chapter 4 homework:
4.I.1: 1.1a,b, 1.3, 1.6a, 1.8, 1.10, 1.12, 1.16, 1.18
4.I.2: 2.8a,b, 2.14, 2.15, 2.17
4.I.3: 3.15a, 3.24, 3.28
4.II.1: 1.10-1.13
Cramer's rule (end of chapter): 1a, 2, 4
Class 16, Wed., Mar. 5, 2014
We learned about Fibonacci numbers and saw how we could use the process of diagonalization to find a formula for Fibonacci numbers.
Class 15, Mon., Mar. 3, 2014
We went over the exam and more about determinant.
The AMATYC exam is this Friday, consult the notes posted around math classrooms for details, see
http://www.amatyc.org/?page=SMLPastQuestions
for sample questions.
Class 14, Wed., Feb. 26, 2014
We had exam 2, and went over some determinant properties.
Class 13, Mon., Feb. 24, 2014
We went over more about transition matrices.
Class 12, Wed., Feb. 19, 2014
We went over more of the ideas about change of basis, and went through the material in section 3.V.
One of the things we learned about was matrix equivalency, which as we saw, shows that every linear mapping from one finite dimensional space to another may be represented - using suitable bases - by a matrix with an identity submatrix in the upper left corner
and zeroes elsewhere; this is quite an important concept, since such matrices are clearly either one-to-one, or projections. Problem V.2.27 (in my edition) is about similarity, a closely related idea which we'll see in chapter 5 is also quite important.
Exam 2 will be Wednesday, Feb. 26, after we've finished chapter 3.
Class 11, Wed., Feb. 12, 2014
We went over in more detail kernel, range, dimension, basis and span.
We went over chapter 3.III, some material from 3.IV, and just started 3.V on change of basis.
Chapter 3 homework not due till week after next, as we will not finish chapter 3 till next week.
Class 10, Mon., Feb. 10, 2014
We went over chapter 3.III.2. Chapter 3 homework will not be due till next week.
Please study definitions and vocabulary!!
Class 9, Wed., Feb. 5, 2014
We went over material from chapter 3.I and 3.II.
Here are some handouts that might be helpful to you. Please read!
Augmented matrices.
Linear Algebra vocabulary.
Homework for chapter 3:
3.I.1: 1.11a, 1.12a, 1.14a,d, 1.20, 1.32
3.I.2: 2.9a, 2.10a, 2.13, 2.18
3.II.1: 1.17a, 1.18c,d, 1.19a, 1.23, 1.24, 1.27, 1.33
3.II.2: 2.22, 2.23a, 2.24a, 2.25, 2.28, 2.33
3.III.1: 1.12a, 1.14, 1.16, 1.18c, 1.23, 1.26
3.III.2: 2.12, 2.13, 2.16, 2.19, 2.22
3.IV.1: 1.12, 1.16
3.IV.2: 2.20, 2.31
3.IV.3: 3.25, 3.26, 3.32, 3.39, 3.40, 3.4
3.IV.4: 4.16, 4.20, 4.26, 4.28
3.V.1: 1.7, 1.8c, 1.11c,
1.22a
3.V.2: 2.10a,2.15, 2.19, 2.27
3.VI.1.7a, 1.8a
3.VI.2 2.11a, 2.12
Class 8, Mon., Feb. 3, 2014
We went over the first exam, and went over material from the link on matrices.
Class 7, Wed., Jan. 29, 2014
We reviewed and had exam 1.
I've located a copy of the "2012-Feb-29" version of the Hefferon text and posted it at this Dropbox site:
https://www.dropbox.com/s/wqu5yamk3diuxmw/Hefferon.Feb.2012.pdf
Please use this for homework assignments.
Interestingly, Hefferon emailed me that he did not have copies of the older versions himself! I found this one at the Way Back Machine site.
Please read the material on matrices at
http://joshua.smcvt.edu/linearalgebra/MatrixArithmetic.PDF
and do the homework problems: 1e,3b,7,8,11b,c,13,14,18
Class 6, Mon., Jan. 27, 2014
We went over material from Ch. 2.III.3.
We will skip chapter 2.III.4.
We learned about matrix multiplication.
We also learned how to represent a directed graph with an adjacency matrix, and use powers of the matrix to find numbers of paths of different lengths.
We had a very brief introduction to binary codes. (Here is a link to some more on such codes. Here's another.)
The first exam is on Wednesday. It will cover chapters 1 and 2, except not chapter 2.III.4.
Turn in homework for chapter 2 this Wednesday, Jan. 29, after the exam.
Bring a scantron to the exam.
Class 5, Wed., Jan. 22, 2014
We went over material through Chapter 2.III.2.
The first exam is on Wednesday. It will cover chapters 1 and 2.
Turn in homework for chapter 2 on Wednesday after the exam.
Bring a scantron to the exam.
PLEASE study the vocabulary!! (see the handout below)
Homework for chapter 2:
(note that not all checked problems are included, and there are a few that are unchecked problems)
2.I.1: 1.18a, 1.19a, 1.21b, 1.22b, 1.24, 1,28b, 1.29, 1.30, 1.40
2.I.2: 2.20c, 2.22b, 2.24d,e, 2.25d, 2.26d, 2.28a, 2.35, 2.43, 2.46
2.II.1: 1.18b, 1.19c, 1.20b, 1.21d, 1.25, 1.33, 1.36, 1.40
2.III.1: 1.16d, 1.17b, 1.21c, 1.23a, 1.24b, 1.29, 1.32a
2.III.2: 2.15,
2.19a,b, 2.23, 2.25, 2.32
2.III.3: 3.17b, 3.18b, 3.20, 3.21c,
3.24, 3.27, 3.32, 3.37
2.III.4:
4.20e, 4.21b, 4.23, 4.33, 4.34, 4.37 (Skip this section)
Class 4, Wed., Jan. 15, 2014
Sub went over material on vector spaces from chapter 2. Please turn in chapter 1 homework on Wednesday, Jan. 21.
You also had a quiz on linear systems.
Class 3, Mon, Jan. 13, 2014
We went over more chapter 1 material.
Class 2, Wed., Jan. 8, 2014
We went over material up to chapter 1.III.1. Please work on problems up to this point.
Class 1, Mon., Jan 6
We went over sections Ch. 1.I.1, 1.I.2, and 1.I.3. Please review the sections Ch. 1.II.1 and 1.II.2 on vectors on your own.
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.