MAT 2240 — §101, Spring '15 (151)

Let us reflect that, having banished from our land that religious intolerance under which mankind so long bled and suffered, we have yet gained little if we countenance a political intolerance as despotic, as wicked, and capable of as bitter and bloody persecutions.

— Thomas Jefferson (1743-1826) in his First Inaugural Address.

Homework List

✈ Jump down to '♞ This Week.'

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Week 1

• Monday, Jan 12
  ◊ Read §1.1.
  
  
• Wednesday, Jan 14
  §1.1. Pg 10; #1, 2, 6, 11, 15, 17, 29, 31, 33, 34.
  §1.2. Pg 21; #1, 3, 9, 13.
  
  
• Friday, Jan 16
  §1.2. Pg 21; #19, 21, 29, 33.
  §1.3. Pg 32; #1, 3, 5.
  
  

Week 2

• Monday, Jan 19 — No class: Dr Martin Luther King, Jr, Day
  
  
• Wednesday, Jan 21
  
  1. Register/enroll for our MyMathLab course (Use these directions and access code [you can copy/paste the access code]). Our course is "bauldry74021".
  2. Work through the "Orientation" assignment. (Due by next Monday.)
  §1.3. Pg 32; #9, 11, 13, 15.
  
  
• Friday, Jan 23
  ¡Quiz today!
  §1.3. Pg 32; #19, 21, 26, LA 28 ("LA" is "Look at").
  
  

Week 3

• Monday, Jan 26
  §1.4. Pg 40; #1, 2, 4, 5, 7, 11, 13, 15, 17, 21.
  
  
• Wednesday, Jan 28
  §1.5. Pg 47; #1, 3, 5, 7, 11, 13, 14, 15, 17, 19, 21, 23, 28→31.
  
  
• Friday, Jan 30
  ◊ MyMathLab: Homework 1. Due by next Wednesday
  §1.7. Pg 60; #1, 3, 5, 9, 11, 15, 17.
  
  

Week 4

• Monday, Feb 2
  §1.8. Pg 68; #1, 2, 3, 5, 7, 8, 9, 11, 15, 16, 20, 21, 39.
  
  
• Wednesday, Feb 4
  §1.8. Pg 68; #1, 3, 7, 8, 9, 11, 16, 20.
  
  
• Friday, Feb 6
  ¡It's time to think about our first midterm!
  ¤Pg 87; #11, 12.
  
  

Week 5

• Monday, Feb 9
  §2.1. Pg 100; #1, 3, 7, 8, 9, 17, 21, 23, 35, 40.
  
  
• Wednesday, Feb 11
  §2.2. Pg 109; #1, 3, 5, 8, 9, 13, 21, 31, 33.
  
  
• Friday, Feb 13 — Paraskevidekatriaphobia!
  §2.2. Pg 109; #7, 11, 15, 19, 41.
  §2.3. Pg 115; #10, 13, 14.
  
  

Week 6

• Monday, Feb 16
  §2.3. Pg 115; #1, 3, 7, 10, 11, 13, 18, 19, 33, 36.
  
  
• Wednesday, Feb 18 — It's "Elm Farm Ollie Day!"
  ¤ Good review problems are in:
  • Chapter 1 Supplementary Exercises. Pg 88.
  • Chapter 2 Supplementary Exercises. Pg 160.
  
  
• Friday, Feb 20
  ☝ ¡If class is canceled for weather, then we will have our exam on Monday, Feb 23! ☝
  ◊ Test I is today — A chance to demonstrate your excellence!
  • You can bring one 8½"×11½" sheet of notes.
  • You can bring a calculator; check the batteries!
  ¤ Test I Topics List
  For Monday:
  ◊ Read §2.5.
  
  

Week 7

• Monday, Feb 23
  §2.5. Pg 129; #1, 3, 5, 9, 13.
  ¤ Maple has a command LUDecomposition
  
  1. Become a student of linear algebra in Maple.
  2. Generate a random \(5\times5\) matrix with: A:=RandomMatrix(5,5, generator=-2..2). (You can copy/paste commnds.)
  3. Find the \(L\,U\) factorization of \(A\) with: L,U:=LUDecomposition(A)[2..3]
  4. Test with: Equal(A, L.U)
  5. When \(A\ne L\,U\), enter: (A, L.U)      What happened?
  6. Repeat several times.
  
  
• Wednesday, Feb 25
  §2.8. Pg 151; #1→4, 5, 9, 11, 13, 23, 31, 37.
  
  
• Friday, Feb 27
  ¤ Group Project: Leontif Input-Output Analysis. Due Friday, Mar 6.
  §2.8. Pg 151; #7, 14, 17, 19, 20, 25, 35, 38.
  
  

Week 8

• Monday, Mar 2
  §2.9. Pg 157; #1, 3, 5, 7, 11, 13, 19, 21.
  
  
• Wednesday, Mar 4
  §3.1. Pg 167; #1, 7, 9, 13, 14, 25, 27, 29, 39, 45.
  ◊ For #45. Maple: A:=RandomMatrix(4,4, generator=-9..9). Two functions are Determinant and Transpose.
  
  
• Friday, Mar 6
  §3.2. Pg 175; #1, 3, 7, 10, 15, 17, 19, 23, 25, 46 (cf. §2.3, Ex 9, pg. 115).
  ◊ For #45. In Maple, define a function for the condition number of a matrix with: CNum := LinearAlgebra[ConditionNumber]:
     Then CNum(A) will give the condition number of the matrix \(A\).
  
  

Spring Break Week: Monday, Mar 9 → Friday, Mar 13. Let's be careful out there!
☝ Saturday, March 14, is \(\large\pi\)-Day of the Century! 3.14.15 @ 9:26:53.


Week 9

• Monday, Mar 16
  Chapter 2, Supplementary Exercises. Pg 160; #3, 4, 6. \(\big[\)Hint for #4: \(1-x^n=(1-x)\cdot(1+x+x^2+\cdots+x^{n-2}+x^{n-1})~\big]\)
  Chapter 3, Supplementary Exercises. Pg 186; #9, 10.
  
  
• Wednesday, Mar 18
  Chapter 3, Supplementary Exercises. Pg 186; #18, 19, 20.
  
  
• Friday, Mar 20
  Chapter 3, Supplementary Problem:
  
  1. Take the data we created today. \[ \begin{array}{ccc} n & \text{Time} & \text{Num Operations} \\ \hline 1 & 0. & 0 \\ 2 & 0.001 & 3 \\ 3 & 0. & 17 \\ 4 & 0.002 & 95 \\ 5 & 0.009 & 599 \\ 6 & 0.061 & 4319 \\ 7 & 0.462 & 35279 \\ 8 & 4.973 & 322559 \\ 9 & 74.509 & 3265919 \end{array} \] Form \[ \mathbf{X} = \left[\begin{array}{cc} 1 & 1 \\ 1 & 2 \\ \vdots & \vdots \\ 1 & 9 \end{array} \right] \text{ and } \mathbf{Y} = \left[\begin{array}{c} 0 \\ 3 \\ \vdots \\ 3265919 \end{array} \right] \]
  2. Find \(y=mx+b\), the line of best fit (least squares regression line), by solving the matrix equation below for \(b\) and \(m\). \[ \left(\mathbf{X}^{T} \mathbf{X}\right) \left[\begin{array}{c} b \\ m \end{array} \right] = \left(\mathbf{X}^{T} \mathbf{Y}\right) \]
  3. Describe why the line doesn't fit the data very well.
  4. What function family best fits the data? Why?
  5. Fit a line to the time data and discuss the fit.
  
  

Week 10

• Monday, Mar 23
  ¡Quiz today!
  
  
• Wednesday, Mar 25
  §4.1. Pg 195; #1, 5→8.
  
  
• Friday, Mar 27
  ◊ Project day. Hill Codes
  
  

Week 11

• Monday, Mar 30
  ◊ Project day. Hill Codes
  
  
• Wednesday, Apr 1 — Hilaria!
  §5.1. Pg 271; #1, 5, 7, 9, 13, 17, 21, 23, 25, 29, 39.
  
  
• Friday, Apr 3
  §5.1. Pg 271; #3 (use both methods), 15, 40.
  ¤ Finish today's computation deciding which car to buy using AHP. (AHP Notes)
  
  

Week 12

• Monday, Apr 6
  ¤ No classes — Easter Holiday.
  
  
• Wednesday, Apr 8
  §5.2. Pg 279; #1→9 odd, 17, 18, 28.
  
  
  
• Friday, Apr 10
  ¤ Gershgorin Circles. (Note in Eigenvalues/Eigenvectors notes.)
  1. Plot the Gershgorin circles for the matrix \(A = \begin{bmatrix} \phantom{-}1 & 2 & 3 \\ -1 & 3 & 5 \\ -2 & 0 & 0 \end{bmatrix}\).
  2. Set \(B = \begin{bmatrix} 9 & \phantom{-}1 & -1 \\ 1 & -1 & \phantom{-}1 \\ 1 & \phantom{-}1 & -8\end{bmatrix}\).
     
     
     1. Plot \(B\)'s Gershgorin circles.
     2. Add the eigenvalues to your plot.
     3. How much can \(b_{1,3}\) be decreased from \(-1\) before circles start to overlap?
     4. How much can \(b_{3,1}\) be increased from \(1\) before circles start to overlap?
     5. What happens to the eigenvalues when the circles overlap?
     
     
  3. Create a matrix where the circles are nested.
  
  ¤ Power Method. (Note in Eigenvalues/Eigenvectors notes.)
  1. Use the Power Method to find the dominant eigenvalue/eigenvector pair:
     1. for the matrix \(A\) above. How many steps are needed?
     2. for the matrix \(B\) above. How many steps are needed?
  
  

Week 13

• Monday, Apr 13
  §5.6. Pg 309; #1, 3, 7, 15, LA 17.
  
  
• Wednesday, Apr 15 — Tax Day
  §6.1. Pg 336; #1, 3, 5, 9, 17, 18, 19.
  §6.4. Pg 358; #1, 5, 9, 24.
  
  
• Friday, Apr 17
  ¤ No classes before 1:00 pm. — Chancellor Everts' Installation
  
  

Week 14

• Monday, Apr 20
  ¡Quiz today!
  ◊ Reread the Gram-Schmidt process. §
  
  
• Wednesday, Apr 22
  ◊ Review and prepare your note sheets for the test.
  
  
• Friday, Apr 24
  ◊ Test II is today — A chance to demonstrate your excellence!
  • You can bring two 8½"×11" sheets of notes.
  • You can bring a calculator; check the batteries!
  ¤ Test II Topics List
  
  

Week 15

• Monday, Apr 27
  ¤ Test I Topics List
  → Chapter 1 Supplemental Problems: pg 88.
  → Chapter 2 Supplemental Problems: pg 160.
  
  
• Wednesday, Apr 29
  ¤ Test II Topics List
  → Chapter 3 Supplemental Problems: pg 185.
  → Chapter 4 Supplemental Problems: pg 262.
  
  
• Friday, May 1
  ¤ Review sheets and practice exams from the authors.
  → Chapter 5 Supplemental Problems: pg 326.
  → Chapter 6 Supplemental Problems: pg 390.
  
  

¤ Exam Week    ♞  (This Week)

• Friday, May 8
  ◊ Final Exam — 3:00 - 5:30 pm.
  
  ¤ The final is the last opportunity to demonstrate your excellence!
  • You can bring any notes — but no books!
  • You can use a calculator — check the batteries!
  • Bring a spare pencil/pen/eraser.
  
  

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“On two occasions I have been asked, ‘Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?’ I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.”

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