Dr. Sarah's Math 2240 Web Page - Fall 2007

Jump down to tomorrow's homework which is located above the red lines
Date     WORK DUE at the beginning of class or lab unless otherwise noted!
Dec 12 - Wed
  • Final Project Poster Sessions from 12-2:30. Be sure that your poster (one per group) is facing so that it is taller than it is wider and is at most 2 feet wide. Bring your own beverage. If you want to bring something to share, feel free - Dr. Sarah will provide some food. peer evaluation, self evaluation
  • __________ ________________________________________________________________________
    __________ ________________________________________________________________________
    Dec 4 - Tues
  • Final project abstract due by 11am to the WebCT bulletin board forum for you and Dr. Sarah (NOT email!) as an attachment that I can read (text, Word, rtf, or Maple)
  • Come prepared to present your abstract orally in class.
  • A maximum of two people per topic (either as a group or individual projects) will be granted on the WebCT bulletin board.

    Chemometrics: Kyle and Nick
    Cramer's Rule: David Bond
    Cryptology: David Fleischhauer and Melissa
    Fractals: Kenneth
    Hebb's Rule: Eamonn
    Image compression: Nate
    Internet Search Engines: Kristen and Dale
    Linear Programming: Graeme
    NFL's quarterback rating: David Secrist and Jacob
    Population Estimates: Michael
    Programming matrix algebra and determinants using Kronecker's method: Jeremy and Mark
    Rotation Matrices, Gimbal lock, and the Space Shuttle: Will
    Thermal Equilibrium: Brett and Zach
  • Nov 29 - Thur
  • Test 3 study guide
  • Nov 28 - Wed
  • Jason Sain will hold a review session from 4:00 to 5:00 in Walker 302.
  • Nov 27 - Tues
  • Study for test 3 and write down any questions you have.
  • Work on the final project abstract under the December 4th date.
  • Nov 20 - Tues
  • Problem Set 6 - See Problem Set Guidelines and Sample Problem Set Write-Ups
    Note: You may work with one other person and turn in one per group of three
    Problem 1:  7.1   #14 by hand and on Maple via the Eigenvectors(A); command also compare your answers and resolve any apparent conflicts or differences within Maple text comments.
    Problem 2:  Rotation matrices in R2   Recall that the general rotation matrix which rotates vectors in the counterclockwise direction by angle theta is given by
    M:=Matrix([[cos(theta),-sin(theta)],[sin(theta),cos(theta)]]);
      Part A:   Apply the Eigenvalues(M); command. Notice that there are real eigenvalues for certain values of theta only. What are these values of theta and what eigenvalues do they produce? Also find a basis for the corresponding eigenspaces. (Recall that I = the square root of negative one does not exist as a real number and that cos(theta) is less than or equal to 1 always.)
      Part B:   Use only a geometric explanation to explain why most rotation matrices have no eigenvalues or eigenvectors.
    Problem 3-5:  7.2   7, 18, and 24
    Problem 6:  Foxes and Rabbits (Predator-prey model)
    Suppose a system of foxes and rabbits is given as:


      Part A: Write out the Eigenvector decomposition of the iterate x_k, where the foxes F_k are the first component of this state vector, and the rabbits R_k the second.
      Part B: Use the decomposition to explain what will happen to the vector x_k in the longterm, and what kind of vector(s) it will travel along to achieve that longterm behavior.
    Extra Credit: Determine a value of the [2, 2] entry that leads to constant levels of the fox and rabbit populations, so that eventually neither population is changing. What is the ratio of the sizes of the populations in this case?
  • Nov 15 - Thur
  • Meet in 205.
  • Continue working on the final project and the last problem set.
  • Nov 13 - Tues
  • Begin working on the final project. See the project link under the December 12th date and the abstract link under the December 4th date. Your project topic and group must be approved by Dr. Sarah on the WebCT bulletin board. Topics will be assigned on a first-come, first-served basis.
  • Begin working on the last problem set.
  • Nov 8 - Thur
  • Begin working on the final project. See the project link under the December 12th date and the abstract link under the December 4th date. Your project topic and group must be approved by Dr. Sarah on the WebCT bulletin board. Topics will be assigned on a first-come, first-served basis.
  • Nov 1 - Thur
  • Test 2 on Chapters 1-3 and 4. study guide
  • Test 1 revisions due for possible +5. Turn in with the original test 1.
  • Oct 30 - Tues
  • Look over WebCT solutions and review for test 2 and write down any questions you have.
  • Oct 25 - Thur
  • Meet in 205
  • Problem Set 5 - See Problem Set Guidelines and Sample Problem Set Write-Ups Hints and Commands for PS 5
    Note: You may work with two other people and turn in one per group.
    Problem 1: 4.4   16
    Problems 2-3: 4.5   24, 48
    Problem 4: Cement Mixing Continued (**ALL IN MAPLE**) This problem is worth more than the others
    Problems 5-6: 4.6   24, 27
  • Oct 23 - Tues
  • Practice Problems (to turn in)
    4.4   11, 53
    4.5   22
  • Work on Problem Set 5
  • Oct 18 - Thur
  • Meet in 205.
  • Work on homework and the problem set for next week.
  • Oct 16 - Tues
  • Problem Set 4 See Problem Set Guidelines and Sample Problem Set Write-Ups, and Hints and Commands for Problem Set 4
    Note: You may work with two other people and turn in one per group.
    Problems 1-2: 4.1 36 and 44
    Problem 3:  Cement Mixing (*ALL IN MAPLE*) *This problem is worth more than the others.
    Problems 4-7: For all of the following vector space and subspace problems: If it is a vector space or subspace, then just state that it is, but if it is not, then write out the complete proof that one axiom is violated as in class:
    4.2   22
    Natural Numbers   Prove that the natural numbers is not a vector space using axiom 6.
    True or False:   The line x+y=0 is a vector space.
    Solutions to the plane 2x-3y+4z=5, ie {(x,y,z) in R^3 so that 2x-3y+4z=5}   Prove that this is not a subspace of R3 using axiom 1.
    Problem 8: 4.3   (14 part D be sure to leave n as general as in class - do not define it as 2x2)
    Note: If pipeline is down, use the direct WebCT access at the top of this page. If that is down too, you may contact me at greenwaldsj@gmail.com
  • Oct 4 - Thur
  • Practice Problems (to turn in)
    4.1 7, 35, 43, 49, 52
    4.2 21
  • Oct 2 - Tues
  • Practice Problems (to turn in)
    4.1 7, 35, 43, 49, 52
  • Begin working on problem set 4.
  • Sep 27 - Thur
  • Test 1 on Chapters 1, 2 and 3 study guide. Test is in 205.
  • Sep 25 - Tues
  • Problem Set 3 See Problem Set Guidelines, Sample Problem Set Write-Ups and Hints and Commands for Problem Set 3
    Note: You may work with at most two other people and turn in one per group.
    Problem 1: 2.5   24
    Problem 2: Healthy/Sick Workers (all on Maple including text comments) *This problem is worth more than the others.
    Problem 3: 3.1   47 part a
    Problem 4: 3.2   32 part c
    Problem 5-7: 3.3   (28 by-hand and on Maple), (34 if a unique solution to Sx=b exists, find it by using the method x=S^(-1) b), and (50 parts a & c)
  • Sep 20 - Thur
  • Practice Problems (to turn in). Do not worry about getting the same answer as the back of the book (although it would be nice!) but do concentrate instead on making sure you understand the determinant methods. Do not worry about explaining your work.
    3.1   33 by-hand using the co-factor expansion method.
    3.2   25 by-hand using some combination of row operations and the co-factor exapansion method.
    3.3   31
  • Sep 18 - Tues
  • Practice Problems 2.5 number 10 set-up the stochastic matrix and calculate month 1 only. Then analyze what happens in the long term for this system using only the definition of a stochastic matrix that is regular
  • Begin working on Problem set 3.
  • Begin reviewing for test 1.
  • Sept 13 - Thur
  • Problem Set 2 - - See Maple Commands and Hints for PS 2, Problem Set Guidelines and Sample Problem Set Write-Ups
    Note: You may work with at most two other people and turn in one per group but each person must complete and turn in Problem 5 themselves (in their own words).
    Problem 1: 2.1   30
    Problem 2: 2.2   (34 parts a, b & c)
    Problem 3: Show that the following statements about matrices are false by producing counterexamples and showing work:
          Statement a) A2=0 implies that A = 0
          Statement b) A2=I implies that A=I or A=-I
          Statement c) A2 has entries that are all greater than or equal to 0.
    Problems 4-7: 2.3   12, (14 by hand and on Maple), (28 part a - look at the matrix system as Ax=b and then apply the inverse method of solution), and     (40 part d)
  • Sept 11 - Tues
  • Practice Problems in 2.1 and 2.2: (to turn in). Do not worry about getting the same answer as the back of the book (although it would be nice!) but do concentrate instead on making sure you understand the methods. Do not worry about explaining your work.
    2.1   (7 use matrix algebra and equality to obtain a system of 4 equations in the 3 unknowns and then solve), (by-hand: 9, 32)
    2.2   (by-hand: 17, 18), (35 use matrix algebra to combine the elements, set it equal to the other side, use matrix equality to obtain equations, and solve.)
  • Work on Problem Set 2
  • Sept 4 - Tues
  • Read through Sample Problem Set Write-Ups
  • Problem Set 1 - See Problem Set Guidelines, Sample Problem Set Write-Ups, and Problem Set 1 Maple Commands and Hints. I also encourage you to ask me questions about anything you don't understand in office hours or on the WebCT bulletin board. Your explanations must distinguish your work as your own.
    Note: You may work with at most two other people and turn in one per group but each person must complete and turn in Problem 3 themselves (in their own words).
    Problems 1-2: 1.1 60 b and c, 74,
    Problems 3-5: 1.2   (30 by hand and also on Maple), 32, (44 find all values of k and justify),
    Problems 6-7: 1.3   24 a and b, 26
  • Aug 30 - Thur
  • Compare your 1.1 practice problems with solutions on WebCT. A similar style of explanation is necessary for problem set 1 but not for practice problems.
  • Do these by-hand since you need to get efficient at the by-hand method. No need to write in complete sentences.
    1.2   15, 25, 27, (43 find all the values of k and justify why these are all of them), and 49. Do not worry about getting the same answer as the back of the book (although it would be nice!) but do concentrate instead on making sure you understand the method of Gaussian Elimination.
  • Read through Problem Set Guidelines and Problem Set 1 Maple Commands and Hints Continue working on problem set 1 under the due date of 9/4.
  • Aug 28 - Tues
  • Practice Problems to turn in - the answers to odd problems are in the back of the book and there is a student solution manual in mathlab (M-Th, 2-5)
    1.1   7, 15, 19, (59 parts b and c - if it is false, provide a counterexample), and 73.
  • Begin working on problem set 1 under the due date of 9/4.
  • Aug 23 - Thur
  • Read through the online syllabus carefully and write down any questions you have - the university considers this a binding contract between us.
  • Begin working on practice problems for Tuesday and problem set 1 under 9/4.