Math 43, Fall 2008

Survey of Linear Algebra

Christmas-Saucon 332, phone 83756, e-mail dmd1
Office hours: M 9:30-10:30, T Th 2:30-3:30

The text is "Linear Algebra: A Modern Introduction," by Poole, second edition. Your grade will be determined from the following, scaled at the end of the semester.

100--Quizzes and homework
100--First hour exam
100--Second hour exam
100--Third hour exam
200--Final exam

Quizzes will be unannounced, 5-10 minutes at the end of class once or twice most weeks. They will be composed of problems extremely similar to homework problems assigned two or three lectures earlier. A small number of homework problems will be collected and graded once a week. Solutions to suggested (resp. assigned) problems will be made available on Blackboard under Assignments two days after they are assigned (resp. the day after they are due). No make-up quizzes will be given. If you have a compelling reason for missing a quiz, present the reason in writing to your instructor, who may possibly give you an excused absence, which will result in your receiving an average score on the quiz. It will not be enough to write "I missed class because I didn't feel well." You will have to provide some documentation. The main type of excused absence could be if you are on a Lehigh sports team that has an away game. Half-credit will be given for just handing in a quiz; this is your reward for attendance. Late homework will not be accepted; if it is not handed in on the assigned date and time, a score of zero will be given. Quiz and homework scores will be in the same category. The lowest three scores will be dropped, and the remaining scores averaged.

The hour exams occur during lecture hour. If you miss an hour exam for some compelling reason, then contact your instructor within 24 hours of the exam to explain why you missed the exam. If he accepts your absence as excused, you will be entitled to take a makeup exam at 4:10 six days after the regular exam was given. No one who takes the regular exam may take the makeup exam. The final exam will cover material from the entire semester, with a heavy emphasis on material subsequent to the second hour exam. You will have three hours for it, but it will only be twice as long as the hour exams.

Accommodations for Students with Disabilities: If you have a disability for which you are or may be requesting accommodations, please contact both your instructor and the Office of Academic Support Services, University Center 212 (610-758-4152) as early as possible in the semester. You must have documentation from the Academic Support Services office before accommodations can be granted.

Schedule of lectures and homework problems.

Lecture 1: Monday, August 25: 1.1
- Suggested problems: pp 13-14: 5c, 9, 14, 18.
- Hand in Sept 5: p.14 #20.
Lecture 2: Wed Aug 27: 1.2
- Suggested problems: pp 26-27: 8, 22, 25, 30, 36, 42, 60.
- Hand in Sept 5: p.27 #58. (Hint: use dot product for norm-squared.)
Lecture 3: Fri Aug 29: 1.3
- Suggested problems: pp 41-43: 6, 8b, 12, 14, 16, 22, 30, 32.
- Hand in Sept 5: p 42 #26.
Lecture 4: Mon Sept 1: 2.1.
- Suggested problems: pp 64-65: 12, 16, 21, 28, 30.
- Hand in Sept 5: p 64 #32.
Lecture 5: Wed Sept 3: 2.2
- Suggested problems: p 83: 12, 16, 22, 24, 25.
- Hand in Sept 12: p 84 #26 (show your work).
Lecture 6: Fri Sept 5: 2.2
- Suggested problems: pp 84-85: 31, 42, 46.
- Hand in Sept 12: p 84 #34 with the 35 in lower right changed to 34.
Lecture 7: Mon Sept 8: 2.3
- Suggested problems: pp 99-100: 4, 8, 10, 16.
- Hand in Sept 12: p 100: #12.
Lecture 8: Wed Sept 10: 2.3, 2.4 (just Allocation of Resources)
- Suggested problems: pp 100-101: 24, 28, 35, 40. p.113 #2 (Show that there are no solutions. How much would you need to change the amount of Food C so that there are solutions? What would be the general solution if this change were made?)
- Hand in Sept 19: p 114: #6. (Note: the Special Blend is as in Exercise 5.)
Lecture 9: Fri Sept 12: 2.5 (just Gauss-Seidel method)
- Suggested problems: p. 130: 8 (Iterate until differences are less than 0.1. Omit Jacobi method), 14.
- Hand in Sept 19: p 130: 10 (Iterate until differences are less than 0.01. Omit Jacobi method).
Lecture 10: Mon Sept 15: 3.1
- Suggested problems: pp 150-151: 4, 6, 8, 20, 26, 32, 36.
- Hand in Sept 19: p 150: 14
Lecture 11: Wed Sept 17: 3.2
- Suggested problems: pp 159-160: 8, 14, 24, 26.
- Hand in Oct 3: p 160: 22
Lecture 12: Fri Sept 19: 3.3
- Suggested problems: pp 176-177: 6, 24, 26, 38, 40, 54
- Hand in Oct 3: p. 177: 52
Mon Sept 22: review
Wed Sept 24: Exam covering lectures 1-10
Lecture 13: Fri Sept 26: 3.4
- Suggested problems: pp 187-188: 8, 10.
- Hand in Oct 3: p 251: 12 with second and third rows interchanged
Lecture 14: Mon Sept 29: 3.5
- Suggested problems: pp 207-208: 2, 6, 10, 11, 16
- Hand in Oct 3: p 207: 12.
Lecture 15: Wed Oct 1: 3.5
- Suggested problems: p 208: 20, 38, 48, 50
- Hand in Oct 10: p 208: 19 with 1 in upper right corner changed to 0
Lecture 16: Fri Oct 3: 4.1
- Suggested problems: pp 259-260: 6, 12, 14, 20
- Hand in Oct 10: p 261: 26 with -2 replaced by 4.
Lecture 17: Mon Oct 6: 4.2
- Suggested problems: pp 280-281: 2, 14, 16, 22
- Hand in Oct 10: p 280: 13 with 6 replaced by 3
Lecture 18: Wed Oct 8: 4.2
- Suggested problems: pp 281-282: 34, 40, 50, 60
- Hand in Oct 17: p 282: 58 with 3 replaced by a variable A, which can represent any number
Lecture 19: Fri Oct 10: 4.3
- Suggested problems: pp 295-296: 4, 6, 12, 16
- Hand in Oct 17: p 295: 8 with first and third rows interchanged
Lecture 20: Wed Oct 15: 4.4
- Suggested problems: pp 306-307: 4, 6, 8
- Hand in Oct 31: p 307: 12
Lecture 21: Fri Oct 17: 4.4
- Suggested problems: p 307: 16, 20, 24
- Hand in Oct 31: p 307: 22
Lecture 22: Mon Oct 20: 3.7 (Markov chains)
- Suggested problems: p 244: 6, 8, 9
- Hand in Oct 31: p 244: 10 with initial .6,.2,.2 changed to .6,.4,0. In (c), just do two generations.
Wed Oct 22: Exam covering lectures 11-19
Lecture 23: Fri Oct 24: 4.6 (Markov chains pp 322-326)
- Suggested problems: p 356: 4, 7
- Hand in Oct 31: p 356: 9. Answers should be fractions, not decimals.
Lecture 24: Mon Oct 27: 3.7 (Population growth)
- Suggested problems: pp 245-246: 20, 24 (Remember that L keeps track of females)
- Hand in Nov 7: p 245: 22 with .1 changed to .2. (Hint: what happens after three generations?)
Lecture 25: Wed Oct 29: 4.6 Population growth pp 327-329
- Suggested problem: p 356: 14 (Hint: the eigenvalue is an integer), 20.
- Hand in Nov 7: p 356: 19
Lecture 26: Fri Oct 31: Handout on genetics
- Suggested problem: #1 from genetics handout
- Hand in Nov 7: #1 from genetics handout modified so that they always fertilize with aa.
Lecture 27: Mon Nov 3: Genetics handout
- Hand in Nov 7: Modified version of #2. Fertilize with AA, then aa, then repeat, fertilizing again with AA, aa, etc. (Hint: Use a matrix for changes over a 2-generation interval.)
Lecture 28: Wed Nov 5: 3.6
- Suggested problems: p 222: 8, 10, 20
- Hand in Nov 14: p 222: 22
Lecture 29: Fri Nov 7: Matrix of Linear Transformation, Handout
- Suggested problems: see handout
- Hand in Nov 14: see handout
Lecture 30: Mon Nov 10: 4.5 (just Power Method)
- Suggested problems: p 320: 6, 10 (use k=5)
- Hand in Nov 14: p 320: 24
Lecture 31: Wed Nov 12: 5.1
- Suggested problems: pp 373-374: 6, 10, 14, 20
- Hand in Nov 24: p 429: 2
Lecture 32: Fri Nov 14: 5.2
- Suggested problems: p 384: 6, 8, 18
- Hand in Nov 24: p 384: 14
Mon Nov 17: Review
Wed Nov 19: Exam on Lectures 20-30
Lecture 33: Fri Nov 21: 5.3
- Suggested problems: p 392: 6, 10, 16, 18
- Hand in Dec 5: p 430: 16
Lecture 34: Mon Nov 24: 5.4
- Suggested problems: pp 404-405: 2, 6, 20, 22
- Hand in Dec 5: p 404: 8
Lecture 35: Mon Dec 1: 7.3
- Suggested problems: p 595: 8 (Also, graph the points and the line); p 596: 20 (Also, compute Ax for your solution and compare with b)
- Hand in Dec 5: p 596: 12 (Also, graph the points and the line.)
Lecture 36: Wed Dec 3: 7.3
- Hand in Dec 5: p 596: 26 (Also, compare values.)
Lecture 37: Fri Dec 5: Review or Google algorithm, handout
?: Final exam