MAT 310 (Linear Algebra)

Fall 2006

Department of Mathematics, Stony Brook University

Welcome to MAT 310!

This is the final course in the linear algebra sequence. We cover all the material in MAT 211 (or AMS 210) as well as some material (for example the Cayley-Hamilton theorem and the Jordan canonical form) that will be new to most of you. The course will probably have quite a different emphasis from your previous courses on this subject: specific calculations will be of far less importance than understanding the statement of the main theorems and precisely why they are true. Because one of the aims of this course is to teach you how to write proofs, the homework and recitations are an integral part of the course.

This is the link to the CURRENT HOMEWORK. This page will also contain links to solutions.

Course Notes:

(posted Dec 17) The exam will be in the usual room. I will have office hours on Tuesday 10am -1pm.

(posted Dec 17) Here are solutions to the review sheet. p1 p2 p3 p4 Solutions to the HWs are also posted.

(posted Dec 13) Just to repeat: I will NOT be in the dept tomorrow-- I told one student today that I would be, but I forgot that I am going to the city. I have done some of the Final Review which is now posted HERE. I will update this on Thursday morning. (now done)

(posted Dec 13) I forgot to say in HW 11 Ex 2 that $V$ has dim $n$.

(posted Dec 10) The homework is now posted; sorry it is late. Vincent will be at Stony Brook on Wed Dec 13 and will be in his office most of the day. I will be away that day, though.

(posted Dec 5) There was a mistake in Ex 1(ii) in the HW this week. It is now corrected. Also, Vincent sent you all a rather incoherent message about recitations. The recitations this week as are usual. His message concerns next week when WED Dec 13 follows MONDAY's schedule. This means that there is no recitation on Wed 13. He invites all of you who are interested to come to his Thursday class instead.

(posted Nov 29) Either of the midterms (carefully rewitten) would be suitable for the proof part of the writing requirement. If you are interested in this, please submit your rewrite to me fairly soon (eg next week) so I can check it over. Also, your projects would do for another part of the writing requirement (and would do for the proof part if they contained enough proofs...) If you are interested in this, please write on your project when you submit it that you want me to consider it for the writing requirement.

(posted Nov 19) I will give back the exams in Tuesday's class. Most of you have been working really hard, and it shows in the results. Many of you did really well. There was a wide spread in the results: the distribution was: < 30: 9; 30-39: 4; 40-49: 3; 50-59 4; 60-69: 6; 70-79: 6; 80-89: 5; 90-110: 7. a total of 44 exams. Again, I will give the 16 students who got < 50 a chance to improve their grade. They must hand in a rewritten exam IN CLASS ON TUESDAY NOV 27 together with their old exam. I will add half the extra points to the exam grade up to a maximum of 50. (The exam is posted on the HW page: HW for next week is also posted there.) I will spend Tuesday's class discussing the exam and answering any questions there may be about the projects. On Tuesday Nov 27 I will start lecturing on the characteristic polynomial (Ch 8).

(posted Nov 12) I am leaving on the morning of Wed Nov 15 and so will not be able to hold my usual office hours then, sorry. I will be having office hours on Tuesday as usual (12-1 in UG office and 1-2 in my office.)

(posted Nov 11) Here are the projects. Project 1 concerns eigenvectors and eigenvalues; Project 2 is a minimization problem; Project 3 is about Fibonacci numbers; Project 4 is a basic project intended for students who are aiming for a C (or C+); Project 5 is about the Jordan normal form. The deadline for all projects is Thursday, December 14 at 5pm. You should give them to me in my office (or under the door, if I am not there.) The projects should be your own work and written in your own words. However, you can come to me or Vincent to discuss any questions you might have about them. Each student should do at most ONE project.

(posted Nov 11) Here is the review sheet for Midterm 2 (added at 8:45pm: slightly revised). We will discuss it in Tuesday's class, together with any other questions you have. Since there will also be review time in recitation this week, it might be best if on Tuesday I tried to answer your more fundamental questions to give you a basis for doing the review sheet. So please, if there any subject that you really have no clue about, do ask me to go over it.

(posted Nov 10) The HW solutions are now posted.

(posted Oct 31) I am leaving tomorrow (Wed) in the morning for a meeting in Washington. So I won't be able to manage tomorrow office hours, sorry. Here is the Worksheet for Thursday. Most of the problems on HW 8 will be very much like these. I haven't quite written it yet, but I plan just to change numbers etc. in many problems. So Thursday's class should be an opportunity for you to get a head start on the HW for next week.

(posted Oct 31) There was a small typo in Ex 5 on HW 7 that I have just corrected.

(posted Oct 26) I just got an email saying that USG (the Undergrad student government) is starting a new program called PASS to make free one on one tutoring available to all students. You might want to check it out (though I'm not sure they would have tutors equipped to handle MAT 310... -- it would be better to come to my (or Vincent's) office hours...

(posted Oct 26) I added HW problems from Ch 5 and 6 to the syllabus. I will be away on Nov 2; Vincent will give another workshop on some topics from Ch 6.

(posted Oct 12) The average in the exam was 60%; with distribution: (90-100) 5; (80-89) 11; (70-79) 8; (60-69) 3; (50-59) 5; (40-49) 8; (30-39) 3; (0-29) 8. VERY rough grade equivalents are: A for 85 and above, B to A- for 70-84; C to B- for 50 to 69; D to C- for 40 to 49. For those of you who did not do so well the important thing is to keep working. I will allow the grade of your rewrite of the exam to improve your exam grade up to a maximum of 50. So, the rewrite will count as a HW, but also I will add 1/2 of the difference between the new grade and the old to your old grade, to give you a revised grade of no more than 50. (So this will NOT affect those of you who got over 50). For fairness, I will keep note of both the revised and the old midterm grades.

(posted Oct 11) Vincent I and will get the exam graded by class time on Thursday at the latest. (Some of you may get it back in recitation.) From my bit of grading, I think you have mostly done very well. The homework for this week is to rewrite the exam. You need not rewrite any question for which you got 90% or more on a question. Please hand in the rewrite as well as your original exam paper in the usual way next week. Thanks.

(posted Oct 11) Here are the two versions of the exam. Version 1 (tex file) and Version 2 (tex file). I corrected the typo in Q1. Also, I corrected two types that were pointed out to me in the list of theorems. You might want to look at the new list (posted below.)

(posted Oct 11) The lecture tomorrow will be on polynomials. Then we move on to Ch 5.

(Posted Oct 6) Solutions to HW 4 are now posted.

(posted Oct 5) Here is the final version of the review sheet, and also the final list of theorems. Please bring these to class today if you can.

(posted Oct 3) I will prepare a review sheet today or tomorrow to discuss in class on Thursday. I will post it on this page as soon as it is ready.

(posted Oct 3) I realised that part (ii) of Ex 3 was wrong and changed it.

(posted Sep 27) Here is the worksheet for the class on Thursday Sept 28.

(posted Sep 20) Here are some notes to amplify some parts of Ch 2 and Ch 3.

(posted Sep 20) I have extended my Wednesday office hours to 11:15 - 12:30. I also have office hours on Tuesday. The department wants me to hold some of these in the Undergraduate office. So I will be 12-1 in UG Office (P143) and 1-2:15 in my office (3-111).

(posted Sep 18) Someone asked me to post the tex file of the HW. I have now done this for HW 2. It is on the HW web page.

(posted Sep 12) In today's class some students pointed out some inaccuracies in HW 1. So I have slightly revised it, correcting Ex 2 (iii) and making Ex 6 more clear. I also added a bonus problem. (Note: if you ever think one of the HW problems is wrong etc, please email me and I'll see if it needs correcting.)

(posted Sep 12) I just sent an email message to all the students who gave me their address last week. Please email me at dusa at math.sunysb.edu if you are registered for the course and do NOT receive this email by the morning of Wed Sep 13. Those who got it need do nothing (unless you want me to take you off the list.) Thanks.

(posted Sep 12) I wrote out a model proof for you to guide you in doing your homework.

(posted Sep 12) I will be away on Sept 14. The lecture will be given by Professor Phillips. Topic: first half of Ch 2 especially the proof of 2.4. This is a crucial result.

(posted Sep 7) Here is the Exercise Sheet for this week's recitations. You are not expected to hand anything in. The material in Ex 3-5 is review for next week and is not relevant to this week's work.

(posted Aug 30) Please go to your first recitation, even though this will be before the first lecture. This will be a review class to remind you of some of the basics from MAT 211.

Instructor: Dusa McDuff

Instructor's Office Hours: held in Undergraduate Office (Math P143): Tu 12-1, and in Math Building 3-111: Tu 1:00-2:15, Wed 11:15-12:30 You are always welcome to contact me by email (dusa at math.sunysb.edu) either to ask a short question or to set up an appointment to see me.

TA: Vincent Graziano

TA's Office: Math Building 2-116

TA's Office Hours: TBA

Textbook: S. Axler, Linear Algebra done right, 2nd Ed., Springer Undergraduate Text

(one copy is available on reserve in the Math/Physics/Astronomy Library; later on in the semester there should be two)

Course Format:

The course meets for lecture Tuesdays and Thursdays in Harriman Hall 108 from 2:20 pm to 3:40 pm. You will get most out of these classes if you prepare beforehand by reading the relevant section in the textbook before class. My aim in these lectures will be to explain and illustrate the arguments in the book. I am always glad to answer questions during class. (If you have more questions, please talk to me after class or come to my office hours.)

There are recitations on Wednesday or Thursday. Their main aim is to help you understand the lecture and do the homework. The syllabus below suggests problems from the book for you to try on your own, but this is not the assigned homework. I will write out homework sets for you each week that you can access from this page. Homework should be handed in to the TA Vincent Graziano in recitation. He will tell you exactly when it is due. Late homework will be penalized (and if it is too late, e.g. after the solutions are posted, it will not be accepted.) He will also tell you exactly how the homework grade will be computed.

It is fine for you to work with others on your homework. But the work you hand in must be written in your own words. Do not copy other's work or let your own work be copied; both parties are penalized for copying.

Some links of interest There are many places online where you can get useful information, eg MathWorld and Wikipedia. Here are some other suggestions.

A useful online linear algebra text with many worked examples and exercises with solutions.

An online linear algebra tutorial by our own Avi Goldstein. Some of this is too computational to be very relevant, but there are many helpful worked examples.

A discussion of the many applications of linear algebra. We will not have time to discuss detailed applications, so you might want to look at this to see the range of possibilities.

A nice expository paper on the use of linear algebra in search engines.

Examinations:

There will be two in-class midterms (on October 10 and November 16 ). The final, which will be cumulative, is on December 19, 5:00-7:30 pm . It is your responsibility to make sure that you can manage these times; tell me of any problems well beforehand. Incomplete grades will be granted only if documented circumstances beyond your control prevent you from completing 50% or more of all class assignments.

Optional projects:

These will be similar in spirit to the projects done in Fall 05, i.e. written papers of less than 5 pages. You may submit work on at most two of them; the best will be graded and will add at most an extra 10% to your grade. Further details will be given out later (by Nov 21 at the latest).

Grading:

Your grade will be based on your examination performance, homework and project (if any), weighted as follows:

Exam I	20%
Exam II	20%
Final Exam	30%
Homework	30%
Project	10% extra

DSS advisory:

If you have a physical, psychological, medical, or learning disability that may affect your course work, please contact Disability Support Services (DSS) office: ECC (Educational Communications Center) Building, room 128, telephone (631) 632-6748/TDD. DSS will determine with you what accommodations are necessary and appropriate. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated. All information and documentation of disability is confidential. Students requiring emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information, go to the following web site http://www.ehs.sunysb.edu and search Fire safety and Evacuation and Disabilities.

Schedule (tentative):

The following is the basic syllabus. Please read the relevant parts of the book before class.

Days	Sections covered	Suggested exercises
Sep 7, 12	Ch 1	p 19: 2-5, 7, 8, 11, 13
Sep 14, 19	Ch 2	p 35: 1, 2, 5, 6, 9, 11, 13, 14
Sep 21 - Oct 3	Ch 3	p 59: 1-3, 5, 7, 9, 10, 12, 15, 16, 19, 20, 22, 26.
Sep 28		a workshop instead of lecture
Oct 5	review
Oct 10	Midterm I	on Ch 1,2,3.
Oct 12	Ch 4	p 73, 1-3
Oct 17, 19, 24	Ch 5	4, 5, 7,8,9,10,15,16,18,19,21,23
Oct 26 -Nov 7	Ch 6	1,2,3,4,7,8*,9,10,11,13,15,18, 21,24,27,29,30
Nov 9	Ch 7 (part)
Nov 14	review
Nov 16	Midterm II	on Ch 4,5,6
Nov 21	ch 7 ctd	projects given out and discussed
Nov 28, 30, Dec 5	ch 8 (parts)	TBA
Dec 7, 12	ch 10 (parts)	TBA
Dec 14	review
Dec 19	Final Exam	(Cumulative)