announcements
December 23, 2008
Here are possible solutions to the final exam.
December 22, 2008
Final grades have been submitted. I have the final exams, and you will be able to pick them up from me after the holidays. I'll post solutions for the final exam soon. Thanks for a great semester. Also, if you'd still like to send me comments on the book, please do so soon.
December 15, 2008
The review session is Monday 5-6:30 in room 199 Cupples I.
December 12, 2008
The exam will be cumulative, but weighted toward the material from the later part of the class. Specifically, we have covered the following topics in class:
- Basic properties of vector spaces; linear independence, basis.
- Basic properties of linear maps; matrix representations, change of basis.
- Linear transformations: determinants, eigenvalues and eigenvectors, diagonalizability, Jordan canonical form.
- Inner products: Gram-Schmidt, orthogonal projections, unitary and orthogonal matrices, Schur's Theorem, normal operators, self-adjoint operators.
December 3, 2008
The notes have been updated. In particular, note that exercise 1.6(b) has been modified. The other major change is that I've corrected the formulas in section 1.4, and added material on how the matrix changes when you change basis. This additional material affected some later sections, resulting in modifications in section 2.2 and the removal of exercise 2.2.
December 2, 2008
I've posted the last homework assignment. It's due on Monday (the last day of class), but it's a little bit longer than usual, so I recommend that you start working on it early.
November 21, 2008
Here are the notes on inner products, which we will be following for the remainder of the course. Please keep in mind that I will probably be making changes and corrections as we proceed, so when you're using the notes make sure that you have current version.
November 17, 2008
Solutions to the midterm are here.
November 10, 2008
Here are practice problems for the midterm. It would be best if you do them and the suggested problems from IV.1 before Wednesday's lecture and come with questions.
November 10, 2008
The midterm will be in class on Friday, November 14. It will cover the following topics: eigenvalues and eigenvectors, diagonalization, nilpotent operators and the canonical form for them, and minimum polynomials. The relevant sections in the book are Chapter 5, Sections II, III, and IV.1. Of course, material from earlier in the semester will appear indirectly, and you will be expected to be comfortable with that material as well.
October 15, 2008
Solutions to the midterm are here. Remember that, for several of the problems, there was not a unique solution, so you should view my solutions as being one possible way, but not necessarily the only way, to answer the questions.
October 10, 2008
I've updated the advanced notes to include last Tuesday's topics.
October 7, 2008
The optional advanced session will be tonight 5-6pm. We still don't have an official room assignment yet, but it should be okay to use 216 Cupples I again. There's a seminar in there that goes until 5, so you won't be able to go into the room early.
October 7, 2008
The first midterm is here. It is a take-home midterm, due Monday, October 13. Here are some guidelines for the midterm:
- Please make an effort to write complete and readable solutions to the problems. Even though your solutions will contain symbols and equations, they should sound like complete sentences when you read them aloud; for example, "a plus b equals c." In addition, you should accompany computations with sentences that explain what you are doing at each non-trivial step, as well as sentences that explain the "big picture" of what the computation is trying to accomplish. A good rule of thumb is that you should write your solutions so that any of your classmates would be able to read them and understand them without additional explanation.
- When working on the exam, you may refer to your notes, the textbook, other books, and online references such as Wikipedia. You may not communicate with other people about the problems, and that includes using online forums like Yahoo answers.
- Whenever you are asked to prove something, a tricky question that arises is "What am I allowed to assume?" In general, you are allowed to quote statements that are proven in the book or that we proved in class, except when the statement is essentially the same as what the question is asking you to prove. If you are unsure about a particular problem, you are welcome to ask me for clarification. When you quote a theorem or lemma from the book, you can refer to it by number, but remember to specify the chapter number and the roman numeral in addition to the number of the theorem or lemma. When you quote a statement from class, you should state the result in its entirety.
October 1, 2008
because of the debate, I've extended the deadline of HW#5 to Monday.
October 1, 2008
Here are notes for yesterday's advanced session. In particular, I want to draw attention to Example 1.6, which I didn't talk about in class, but I think many of you would find interesting.
September 30, 2008
The optional advanced session will be tonight 5-6pm. It's too late to get a room officially assigned, so we'll meet at 216 Cupples I, and hopefully the room will be free for us to use. If we have to move elsewhere, I'll leave a note on the door.
September 5, 2008
The second homework assignment is now up.
September 3, 2008
Note that my office hours have changed.
September 1, 2008
The first homework assignment is now up on the "homework and reading assignments" page.
July 24, 2008
Hello, welcome to Math 429. For basic information, see the syllabus. Please bookmark this page, since I will use it to make announcements.