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.