Fall 2015: Math 351, Linear Algebra

Math 351, Linear Algebra

Time: T/TH 1030-1145, 1200-115

Location: UNIV 101

Office hours: Wednesday 1230-300 PM, Thursday 800-1000 AM, and by appointment.

Book: I do not plan to have an official textbook for the class. There are many resources for linear algebra that are freely available on-line. I do plan to have class notes that will be updated throughout the term for the class. I will have links to webpages (mostly wikipedia) that give lengthier discussions of the various topics we cover. You should utilize the free information that abounds.

Problem sets: I will post weekly problem sets here in .pdf format. The problem sets will be due on Thursdays. I will try to post the problem sets a week before they are due.

Grades: I assign grades based on your rank within the class. I usually employ 3-4 schemes for producing a ranking. They are based on exams and homework. I give you the best grade among the different schemes. You may care about grades. The university may care about grades. I do not care about grades.

The class: The aim of the class is to introduce you to rigorous mathematics. Linear algebra is a foundational subject for most mathematics. The problem sets are the best guide to a subject. They will have new concepts and I hope will challenge you all. The lectures will be formal "theorem-proof" style.

Class News:

Problem sets will be due in class on Thursdays. The first problem set will be due Thursday September 10. It will be posted below with the class lectures.
September 9. Correction: Problem 2 should be "alpha x + beta y in Im(L)" at the very end. The current version of Pset 1 has been corrected.
September 9. Pset 2 posted.
September 14. No office hours on Wednesday (Sept 16).
September 20. Posted Notes on problems 1-3 on Pset 2.
September 21. Posted Pset 3. Note the Tuesday due date. Pset 4 will be due on that Thursday and will be posted by Thursday.
September 21. The red text in the class notes indicates that there is a link to an external page that can be opened by clicking on the red text. They largely refer to Wikipedia pages.
September 22. Pset 4 posted and due on Thursday October 1. It is slightly longer than I said it would be but the problems are all very "easy". [Never trust things in quotes.]
Midterm 1 is scheduled for October 8 in class.
September 25. I will have extended office hours on October 3 from 1200-300PM. I reserve the right to go home if I do not have any students.
September 25. I have added a fair amount of new material to the class notes. I would strongly advise reading over the full set of notes but a focus on Lecture 4+epsilon through Lecture 6. Also, I have, more or less, completed the class lecture notes up through quotients in a fairly complete story. The notes are still dense but I hope they give a bit more of a picture of the landscape.
September 26. Additional office hours 800-1000 AM on Tuesday September 29.
September 30. Review notes for Midterm 1 posted. Note contains an old 351 exam.
September 30. Practice Midterm 1 has been posted. The format is identical though the problems are different. I currently (1931 EST Sep302015) view your exam to be easier than the practice exam. I may very well change your exam (to make it more difficult). Also, if you want solutions to the practice problems, then you should solve the problems. I am here to assist and will have extra office hours this Saturday (see 4 posts above), next Tuesday 800-1000AM, next Wednesday 1230-330 PM (slightly expanded), and the usual 800-1000 AM next Thursday. I will give as little or as much as I want in terms of assistance. Do remember I like to solve problems since that is my "other" job here at the university.
October 2. Posted a short note on dependence, independence, and spanning.
October 7. Posted another review note (Review2) for midterm 1.
October 26-27. Fixed typos on Problem 2 (c) and 4(c) of Pset 5.
October 29. Midterm 2 is scheduled for November 12 in class.
October 29. If you were unable to turn in Pset 5 today, you can turn it in during class on Tuesday.
October 29. Pset 6 posted.
November 9. Short review note for Midterm 2 posted. Midterm 2 looks to be more difficult than Midterm 1 by a fairly wide margin. Any perfect score on the exam will earn 100 USD. It is still straightforward but it is unlikely that anyone will garner full marks. We will have a lottery as before.
November 9. Midterm 3 is scheduled for December 3 in class. That is the final exam for our class.
November 10. Practice problems for Midterm 2 posted. Enjoy.
November 17. Class notes updated. Will likely update them again. Make sure to check you're using the most up-to-date version.
November 27. Pset 7 posted.
November 30. Updated the review note for Midterm 3. Make sure to read it!
December 1. To put your minds at ease, Problem 1 (c) on Pset 7 is not something I expect you can solve. It can be done but not without some effort (and math beyond what I expect you to know).
December 2. We will have class on Tuesday. I will hand the exams back and they will have your final grade. If you cannot attend lecture and want to have a chance to discuss your final grade, send me an e-mail before Tuesday. I will not discuss your final grade if you do not pick up your exam or e-mail me before hand.

Lectures:

Lecture 0. August 25. An informal lecture of sets and functions.
Lecture 1. August 27. The vector space R^2.
Lecture 2. September 1. The vector spaces R^n and some examples. (Mark Pengitore will lecture)
Lecture 3. September 3. Real vector spaces.
Lecture 3.5. September 8. Examples and philosophy.
Lecture 4. September 10. Product spaces and projections.
September 15. No class.
Lecture 4 + epsilon. September 17. Problem set 2 and vector space philosophy.
Lecture 4 + 2 epsilon. September 22. Dependent and independent directions.
Lecture 5. September 24. Spanning sets, independent sets, and Goldilocks.
Lecture 5 + epsilon. September 29. Bases exist and the how-to guide to building them.
Lecture 6. October 1. Dimension.
October 6. Review for Mid-term 1.
October 8. Midterm 1. You only need a few devices for writing. I will supply everything else.
October 13. No class. Fall Break.
October 15. Midterm 1 handed back and gone over.
Lecture 7. October 20. Finite dimensional real vector spaces.
Lecture 8-9. October 22. Linear functions between finite dimensional vector spaces.
Lecture 10. October 27, Linear systems.
October 29. No class (Ty was sick).
Lecture 11. November 3. Solving linear systems and matrices.
November 5. No class (Ben was sick).
November 10. Matrices and review for midterm 2.
November 12. Midterm 2.
November 17. Midterm 2 hand back and exam stats.
Lecture 12. November 19. More on linear functions and matrices
Lecture 13. November 24. Determinants and Gram-Schmidt
November 26. No class.
December 1. Gram-Schmidt and review for Midterm 3.
December 3. Midterm 3.
December 8. Hand back Midterm 3. Give final grades.