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