Course Content Fall 2017


                                                                                                                                                                Basic Course Information

Math 4242 is a 4 credit course. Here is the official mathematics department description of this course:

Lecture:  
050 LEC , 1:25 P.M. - 2:15 P.M. , M,W,F Appleby 319 , TCEASTBANK .
Instructor: Professor S.Sperber.
Email: sperber@math.umn.edu
Office: 457 Vincent Hall
Phone: 612-625-4374
Office Hours: Mondays 2:30-3:30, Thursdays 11:30-12:20
Textbook: IMPORTANT: The selected text is ridiculously (outrageously) expensive. Please make every effort to avoid the cost of buying this text new. Other useful options: used texts are MUCH cheaper. Rental possibilities are available. Finally a PDF download seems to be available on the web.
Textbook: Gilbert Strang, Linear Algebra and its Applications, 4th edition, ISBN-13: 978-0030105678, ISBN-10: 0030105676 I believe the author has a series of video lectures which one can access from his webpage: http://www-math.mit.edu/~gs/

                                                                                                                                 Organization of Course and Grading Policy

  • There will be two mid-semester in-class exams of 50 minute duration. Exams will be in-class, on Wednesday, October 11 and on Wednesday, November 15.
  • There is also a (cumulative) two hour final examination on Monday December 18 from 8-10AM.
  • THE ROOM FOR THE FINAL EXAMINATION IS our current classroom Appleby 319.
  • Homework will be collected weekly, every Wednesday starting September 13 and some, if not all, of your work on each problem set will be graded.This grade will be the major component of the 20% of the "homework and class participation" portion of your Final grade
  • The final grade will be determined according to the following guide:

  • mid-semester exams 40%
  • final 40%
  • homework and class participation 20%

  •                                                                                            
    Sample Test

    Hints and answers to sample test 2:

  • Problem 1a. Add C1 to C2; Add -2C1 to C3; Add -1C1 to C1; Get Row 1= (1,0,0,0) Row 2 = (0, !, !,2) Row 3 = (1,2,-1,-1) Row 4 =(0,-1,1.-1). Add (-1)C2 to C3; Add -2C2 to C4; Get Row 1 = (1,0,0,0); Row 2 = (0,1,0,0); Row 3 = (1,2,-3, -5); Row 4 = (0,-1,2,1); Add (-5/3)C3 to C4 Get K with row 1=(1,0,0,0), Row 2= (0,1,0,0), Row 3 = (1,2,-3,0), Row 4 = (0,-1,2, -(7/3)) So det(A) = det(K) = 7
  • Problem 1b. det (B^3) = det(B)^3. det B = -6 det A So det B = -42 and det (B^3) = (-42)^3
  • Problem 2. Call basis {u,v,w}. Then c(u) = (0, -3, -1)^t, c(v) = (3,-3, -2)^t and c(w) = (4,-2,-2)^t. Find coordinates of c(u), c(v) and c(w) in terms of basis {u,v,w} In the case of c(u), c(u) = 3u -2v -1w. Similarly c(v) = 6u -v -2w and c(w) = 6u -2w. So matrix of linear map c with respect to basis {u, v, w} has first row = (3,6,6), second row = (-2, -1, 0) and third row = (-1, -2, -2).
  • Problem 3. Let A^t = the 2 by 5 matrix whose first row is (-2,-1,0,1,2) and second row is (1,1,1,1,1). Let y be the column vector (1,0,3,2,2)^t. Then must solve (A^tA)(m,b)^t= A^t y. Get. m = 2/5, b = 8/5.
  • Problem 4. x_1 = 1/3, x_2 = 3/2, x_3 = -7/6
  • Problem 5.a. tilde(q_1) = 1 + x. length (tilde(q_1) = sqrt(integral from -1 to 1 of (1+x)^2) = sqrt(8/3). So q_1 = sqt(3/8)(1 + x). tilde(q_2) = b - (b, q_1) q_1. Here, I get (b, q_1) = 2sqrt 3/ 3 sqrt 2. So tilde(q_2)= (1/2) - (1/2)x -x^2. Then find length(tilde(q_2). Set q_2 = tilde(q_2)/length(tilde(q_2)).
  • 5.b. First row f R is ((a, q_1), (b, q_1)). Second row is (0, (b, q_2)).