Dr. Sarah's Math 2240 Class Highlights
### Dr. Sarah's Math 2240
Class Highlights Summer 2002 Page

**Tues May 28** Fill out stiff sheets, hand out
syllabus, intro to course via
section 1.1 from book.
Intro to
Maple via Maple worksheet
(html version)
and then LAMP via Chapter 1, Module 1.

**Wed May 29**
Put 1.1 number 69 up on board.
Look at student's papers of
section 1.1 homework and ask for questions to be posted later on
WebCT.
Review LAMP module Chapter 1, Module 1 (the html version on WebCT).
Section 1.2 by hand and on Maple, including
1.2 number 31.
Start section 1.3.
Do Lamp 1.3 section 1 on fitting a curve to data. Do
1.3 number 21.

**Thur May 30**
Place 1.2 #35 up on the board,
and review Gauss-Jordan.
Do 1.3 number 23 - students do this by hand (contest).
Begin 2.1 via digital image examples and applications.
Review webpages and problem set guidelines.
Students work in lab.

**Fri May 31**
2.1, 2.2, and begin 2.3
(Motivate matrix mult via p. 54 number 51 and introduction to proofs)

**Mon Jun 3**
Prove that a system of linear equations has no solutions, exactly 1 solution,
or infinitely many solutions.
3x3 example of using Gauss-Jordan to find an inverse of the matrix.
Discuss
uniqueness of solutions given by an invertible coefficient matrix
and proof.
Prove that cancellation works with an invertible matrix.
Begin 2.5 via LAMP demo on Markov Chains.
Chapter 2 Module 3 c3m4_v3.mws sections 1, 2,
(3 up to but not including
3A - ie jump to Section 4 and
skip example 3A on Random Walks, skip Interpretation of
Matrix W, and skip Exercise 3.1), 4.
If time remains, work on Problem Set 2.

**Tues Jun 4**
Review Markov chains (note see p. 90-93 of the text for similar ideas
but different terminology),
continue 2.5 via applications of matrices to cryptography and
least squares regression line.
Show diagram of 1932 invention that coded 6x6 matrices.
3.1, 3.2, 3.3 including
proof that a square matrix is invertible iff det is not 0
and p. 137 #57.

**Wed Jun 5**
Show diagram of 1932 invention that coded 6x6 matrices.
Finish chapter 3 via LAMP Chapter 3, Module 7. c3m7_v3.mws.
If time remains, then work on problem set 2 or 3.

**Thur June 6**
Review LAMP Chapter 3, Module 7. Begin Chapter 4 (4.1) via
vectors in R^2 and R^n, linear combinations of vectors algebraically.
Application of vectors in R^n (coffee problem from LAMP) and
linear combination of vectors geometrically.
LAMP c2m2_v3.mws and practice problems 4.1 numbers 31 and 33.

**Fri June 7**
Begin 4.2

**Mon June 10** Test 1, Finish 4.2

**Tues June 11** 4.3

**Wed June 12** 4.4 and begin 4.5

**Thur June 13** Finish 4.5 and 4.6

**Fri June 14** 7.1 and begin 7.2.

**Mon Jun 17** Test 2 on Chapters 1-4.

LAMP c6m1_v3.mws
Chapter 6 Module 1, Section 2: The Geometry of Eigenvectors,

LAMP c6m2_v3.mws Chapter 6 Module 2, Section 2: Evectors Command

**Tues Jun 18**
Finish 7.2.
Begin 6.1 def of linear transformation, properties, and examples 7 and 8,
6.5.
LAMP c6m3_v3.mws
Chapter 6 Module 3 Eigenvector Analysis of Discrete Dynamical Systems

**Wed Jun 19**
LAMP Ch 4 Module 1 Geometry of Matrix Transformations of the Plane
With a partner, begin working on

Chapter 4 Module 1 Problem 1: Guess the transformation

Chapter 4 Module 1 Problem 9: Square roots, cube roots, ...

Chapter 6 Module 4
Problem 7: Projection matrices

Chapter 6 Module 4 Problem 8 Parts a and b: Shear matrices

Save your work for continued exploration on Monday.

**Thur June 20**
Free time to work on Final project

**Fri June 21** Free time to work on Final project

**Mon June 24**
With a partner, continue working on

Chapter 4 Module 1 Problem 1: Guess the transformation

Chapter 4 Module 1 Problem 9: Square roots, cube roots, ...

Chapter 6 Module 4
Problem 7: Projection matrices

Chapter 6 Module 4
Problem 8 Parts a and b: Shear matrices

and then go over answers.

LAMP Ch 4 Module 2
Section 1 Geometry of Matrix Transformations of 3-Space.

**Tues June 25**
LAMP Ch 4 Module 3 Computer Graphics
With a partner, work on Problems 1, 3 and 6.

**Hints on Problem 1**:
Look at Section 1 example 1c, but use rotation by -Pi/6.
We also need to shrink the triangle as it goes around, so, instead of
letting M equal U.R.T, you need to add in a dilation matrix A somewhere
(using, for example, the command
A:=Diagmat([1/2,1/2,1]); and
M:= the product of the 4 matrixes A, U, R, and T in some order that makes
sense, and
Movie(M,triangle,frames=18); but adjusting the dilation so that
it matches the problem.)

**Hints on Problem 3**:
Try a rotation matrix composed with a translation matrix.

Extra Credit for Flying along a curve in 3-Space DUE Thursday.

**Wed June 26** Final Exam

**Thur June 27** Final Project Presentations