Linear Algebra Schedule, Fall 2019

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Overview: I've grouped the class meetings into seven blocks, two weeks each. You will have a quiz on the second Thursday of each block, mostly related to the homework [HW], lectures and reading for the previous 2-3 weeks, but usually nothing from the second Tuesday (from just before the quiz). For example, Quiz 2 will be at the end of Week 4 and will mainly cover topics from lectures 3 to 6. I should be able to return HW2 to you before Quiz 2. There may be a little overlap of topics on consecutive quizzes. The pattern just described applies to the first six blocks. The seventh is a bit longer, with a final exam and no quiz. The HW lists below are intended to be the minimal required for a strong student to get the main ideas. You should normally do at least 50 per cent more problems of your choosing (not to hand in) until you master each section.

I will probably adjust some dates and content from time to time, but will post such changes on this web page asap, and also announce any major ones in class. If you print out this page, recheck it or reprint it every 1-2 weeks. Refresh your browser if needed to update what you see here.

How to read the tables: As you can see from the tables below, we will cover roughly 1 section of our book per lecture. HW is usually due a week before each quiz so we can return it to you on time. But HW1 is due on Tues 9/3, on problems 1.1.1 thru 1.2.15. Quiz 1 is 9/5, and mainly covers the topics in HW1. It might have an easy problem from Ch 1.3 or 1.4 to check that you are keeping up with the lectures. But these 2 sections are mainly tested in Quiz 2; there may be some small overlap of quiz topics. This pattern repeats for each block, maybe with exceptions for holidays/emergencies/etc. Refer back to this page regularly in case of changes.

Don't worry too much about my abbreviations under "lecture topics" as those are mainly notes for myself. Contact me ASAP if you don't understand anything, or you see a conflict with a religious holiday, an inconsistency with the syllabus, or any other mistake. I usually give a little extra credit for such help.

Weeks 1 and 2

The first weeks should be the easiest. You will be learning to solve systems, which are routine calculations. But you may have to adjust to a math course which emphasizes vocabulary [and later on, theorems] much more than Calculus does. You should start using MATLAB asap, though this is not yet urgent. See my MATLAB page for tips and for the separate Matlab HW (MHW) lists. The first MHW is due soon after Ch.2.

Read Ch 1 [but I probably won't test you on Ch 1.6]. Learn the main concepts, which are usually highlighted (such as consistent system, equivalent systems, augmented matrix, triangular form, elem operations, row echelon form, G.elim'n, underdetermined, etc). Do HW1, and as many more problems as you feel you need. For more good quick learning, read over the other exercises, including Ch 1.1.9 and Ch. 1.2.16 to 19, even if you do not solve them. Start on HW2. Look over Leon's website and this one, and practice with my web page on proofwriting Part I, if needed. If you do not want your HW to count into your grade, you need to write me a note or email by Thursday 8/29 and get my confirmation.

Visit our Learning Assistant and grader for the course, Javier Castro, [ jcast497@fiu.edu TuTh 11:00am to approx 1pm, Green Library 5th floor.]. You are expected to see him about problems with the reading, HW, etc. I usually give a little extra credit to the students who participate regularly in those sessions. Some other help options are listed on my "help pages". For example, you can go to GL 129, Mondays-Thursdays 9am-8pm, Fridays 9am-5pm for general math help. Sometimes they can help with MAS 3105. You are welcome in DM419B during my office hours, no appt needed, and to email questions any time.

Remember that Quiz 1 will be mostly like HW 1, which is relatively easy. In previous terms, the Quiz 1 average has usually been over 70 percent. You can find sample quizzes (and keys) on my exam page. If you have any extra time after mastering Ch 1, I strongly suggest that you scan Chapters 2-6 (especially Chapter 3), to let those harder ideas sink in slowly. Note that we will cover just a bit of Ch.1.6 in class and the rest is optional.

There have been several questions in the past about HW problem, Ch 1.3 - 9, so here is a similar example. Some HW exercises may seem a bit tedious to do by hand. You can use MATLAB to save some time on those, but if so, leave a note to the grader about the missing work. Also, you will not have MATLAB during the quizzes, so be sure you can do such work by hand. Sometimes I post links that seem interesting on this page. Here is one about learning strategies. (it recommends flash cards, for example, but not highlighting or re-reading). A student found some HW solutions online (for the 8th edition, but the 9th is very similar). You can use these to check your HW answers, but don't copy them. I also found this wiki-book, if you want additional Linear Algebra reading or exercises.

If you have time, problems 29-32 of Ch.1.5 are good practice with True-False and justification. But these are not required for the HW.

Optional - check out this FIU program, if you have taken MAC 2311 - not associated with MAS 3105.

Updates for Dorian: FIU will be closed on 9/3, so no class, no HW due that day. I have bumped the hw, quiz and lecture topics forward approx one meeting day in the 9/5 to 9/12 period, expecting that we can catch up to the original schedule by 9/17. If not I may need to make another update then, possibly omitting Ch.2.3 on Cramer's Rule. See below for another update.

 

Day Date I give you You give me Lecture topics HW
1 8/27 Web site   1.1- Systems, G.Elim 1ab, 2, 3, 4, 6ab, 7
2 8/29     1.2- RE form 1, 2abc, 3abc, 4, 5achi,12, 13, 14, 15
3 9/3 Class Cancelled for Dorian none none
4 9/5   HW1, thru 1.2 1.3- Matrix Arith 1.3 - 1, 2, 3, 4, 6, 9, 10

 

Weeks 3 and 4

A previous student found a proof on the internet, that the RREF of every matrix is unique. This is not required reading, but it is interesting, and is used implicitly in our book.

Update 2 (9/7/19): I have moved Ch.1.4 from 9/5 to 9/10, so Ch.1.4 will not be on Quiz 1. I revised the HW2 list to stop at Ch.1.4.  I added Javier's hours above (TR 11am GL, 5th Floor.)

Misc Announcements:

You should be working on the MATLAB HW from Chapter 1 by now (see page 80), and starting to complain about closed labs, dead printers, arcane exercises, etc. Do it early! Starting with Quiz 2, I may ask some very easy questions about MATLAB. As long as you are keeping up with the schedule, you shouldn't really have to study for these. A student found this web site for learning MATLAB (free registration required), which you can explore, if you need it, but probably not. The MATLAB software itself also has built-in Help, tutorials, etc. You can also get help from me. This is due Tuesday 9/24.

If you aren't getting your proofs right yet, this is something you should work on asap, perhaps with me or with your LA. Remember to include WORDS but (usually) not examples. If you feel lost on proof-writing, try my help page drills thru Part III or come by my office hours for help. There are several good books on proofs (eg Velleman's) that you can buy online or at a local bookstore." Problems 1.5.23 to 27 are good for additional practice.

Problem 2.2.20 sometimes causes trouble (but is interesting - see also 2.2.21). Problem 3.1.7 is easy if you can set it up correctly - you might assume that the space has 2 "zeros", called a and b, for example.  You can probably find help with these on this web site if you look ( try the help pages, or answer keys to old quizzes, or ask me).

I have changed some HW3 numbers on 9/17/19, so make sure you are using the updated lists. For now, I may have to omit LU and induction examples from the lectures, but I hope to return to these topics as time permits. For the basics of induction, you could try a Discrete Math textbook.

For Quiz 2, read Chs 1.3 - 2.2 and review the lecture notes thru Tues 9/17. Note that Ch.1.3 is tested twice, on Quiz 1 lightly and on Quiz 2 more heavily. Focus on the main definitions and theorems. Prepare to prove the "tfae" Thm 1.5.2, and Thms 2.2.2 and 2.2.3. - assuming I have gotten that far in my lectures. The words are as important as the calculations. You may not need to know all three proofs, but you do need to prepare. If you need help with the proof of Thm 2.2.3, you can look here.

Review HW2, and do more problems as needed. Practice with the Chapter Tests; see page 84. Always try to justify your True-False answers, at least for yourself (it is sometimes required on my quizzes, but usually not). Some students like to practice the TF on my exam page (let me know if they don't work well).

 

Day Date I give you You give me Lecture topics HW
5 9/10 Quiz 1 thru 1.3   1.4- Matrix Algebra
1.5 - Elem.Mat's
1.4 - 1, 3, 4, 7, 10, 16, 29
1.5 - 1, 2, 3, 5, 6, 10abef, 12, 18, 22
6 9/12   HW 2, thru Ch.1.4. 1.6 - P Matrices
2.1 - Det(A)
1.6 - 1 [and read over Ch.1.6]
2.1 - 1, 2, 3abcg, 4, 8, 10
7 9/17     2.2 - Det(A) and E's
2.3 - Cramer's Rule
2.2 - 1, 5, 6, 7, 13, 15, 20
1, 2abc, 3, 5, 6, 14
8 9/19 Quiz 2 thru 2.2   3.1- Vector spaces 3.1 - 1, 3 (has 8 parts), 7, 11

 

Weeks 5 and 6

The course enters more abstract territory this week, so pay more attention to vocabulary and precise definitions. If interested, see this old HW3 grading page.

Note that MHW1 is due 9/24, on Chs 1-2. For full credit, keep it organized - keep the problems in order, highlight or circle the problem numbers, put headers at the top of your pages, etc. Write out any required explanations, these usually not just computer exercises.  The MATLAB program is on many machines in PC 413 (and probably others, such as VH 133) and on FIU's elabs. See my MATLAB page for more on this. Let me know asap of any technical / access problems.

Quiz 3  will not include induction proofs. It will cover mainly HW3, and Chs 2.2 thru 3.3. Know the proofs of Thm 2.3.1, Thm 3.2.1 and Thm 3.3.2. (just the first half). You can also practice 2-3 TF quizzes on my exam page and see my Ch 2 and Ch. 3 help pages. Note that Ch 2.2 may be on both Quiz 2 and Quiz 3. Reminder: Our LA is there to help you with HW and other questions. He can usually hold review sessions before the quizzes, but you may have to ask him in advance. And remember to do more than the assigned HW!

 

Day Date I give you You give me Lecture topics HW
9 9/24   MHW1 more 3.1
3.2 subsp's, span, N(A)
[no more]
1, 3, 4, 12, 18, 20
10 9/26   HW3 thru 3.1 3.3 LD, basis 1, 2, 3, 8, 14, 15, 19
11 10/1 return MHW1   3.4- basis, w pfs 1, 2, 3, 5, 7, 11, 14
12 10/3 Quiz 3 thru 3.3   3.5, transition m's 1, 2, 5, 6, 9

 

Weeks 7 and 8

Quiz 4 covers HW 4 and the lectures / reading for 3.2 thru 4.1. Be able to use the Wronskian for problems like HW 3.3.6 and 7. If you are having trouble with proofs, see my hints for HW4. Know the main definitions, and the proofs of Thms 3.4.3, 3.6.1 and 3.6.5.

Quiz 4 may include an induction pf from Ch 2 if we have covered that in the lectures by 10/15 (see page 90 and the Ch 2.2 exercises).

After grading MHW1 a few years back, I wrote a short summary, which might help you when reviewing yours, or doing MHW2.

We will go over a standard type of application soon that I call the Rabbit example [probably on 10/22], which ties together many ideas from Chs 3 to 6. It is not in the book, though Ex1 pg 283 is related. Make sure you understand it (except the part about finding the eigenvectors, which we will cover later in Ch.6). I will refer back to this example repeatedly.

 

Day Date I give you You give me Lecture topics HW
13 10/8     3.6, Rowspace 1, 4, 5, 12, 22, 25
14 10/10   HW 4 thru 3.5 4.1, Transforms 1, 2, 3, 4, 7, 14, 17, 20, 21
15 10/15 HW 4 back   4.2, Mat. Rep. 1, 2, 5, 6, 14, 17
16 10/17 Quiz 4 thru 4.1   4.3 Similarity 1, 2, 5, 7, 9, 11

 

Weeks 9 and 10

Quiz 5 covers HW 5, MHW2 and recent topics such as the Rabbit example, and possibly Ch.5.2. Understand what each theorem says. Know the proofs of Thms 3.6.6, 4.1.1 and 5.1.1. There are TF quizzes for you on the exam page. The HW in Ch 4.3 has some good proofs ( try 4.3 - 12, 13 and 14). Review the "Rabbit Ex" from the lectures (see also the link above the Week 7 Table); a quiz problem might refer to it.

Review MHW2 before you hand it in, for the Quiz and to check it is gradable. Make the problems easy to find, by keeping them in order, highlighting the problems numbers, and/or putting headers at the top of your pages. I have posted some hints for the Ch 5.2 HW. Also, some sample proofs related to Chs 4.1 thru 5.1.

I think the drop deadline is 11/4/19, but you should check this yourself. See me if you need advice. I probably can post an answer key and scale for Q5 by then. 

We now a final exam time (see the bottom of this page)

Day Date I give you You give me Lecture topics HW
17 10/22   MHW2 5.1 and Rabbits 1, 2, 4, 5, 8, 9, 10
18 10/24   HW5 thru 5.1 5.1 proj, planes, perps [no more]
19 10/29 return HW5   5.2 R(A^T), sums 1, 2, 3, 4, 13
20 10/31 Quiz 5 thru 5.1   5.3 - LSqs 1, 2, 3, 5

 

Weeks 11 and 12

Note on reading Ch 5: We will move fairly quickly through Ch 5.3 to 5.6, because many parts are optional at FIU. You can afford to skim quickly over the applications in the gray boxes and the heavy trig in Ch 5.5. You can omit Ch 5.7. We'll probably skip the MGSP on pg 267. Focus on the HW and the main theorems [the ones in the lectures, such as Thms 5.3.2, 5.6.2 and 5.6.3]. Then read Ch 6.1 (etc) carefully, as usual.

Quiz 6 mainly covers HW 6 and the lectures / reading thru early 5.6. Understand what each theorem in these sections says. Know the proofs of Thms  5.1.2,  5.2.1 and  5.3.2,  and of the "normal equations" on pgs 227-228. Review exercise 5.2.13. The TF  practice for Quiz 6 [and for Quiz 5] on the exam page may help, too. Review MHW2 briefly for this quiz.

 

Day Date I give you You give me Lecture topics HW
21 11/5 Return Q5 and MHW2   5.4 - IPs 3,7
22 11/7   HW6 thru 5.4 5.5 - ONB's 1, 2, 3, 15, 16, 21
23 11/12 return HW6   5.6 - A=QR, proj'ns 1, 2, 5, 7
24 11/14 Quiz 6 thru 5.6   more 5.6  

  

 

Weeks 13, 14, 15

The final is 12/12/19 (see below) and counts 30 points - about half of it will be on topics after Ch 5.5 (like a "Quiz 7") and about half will be review. It cannot be dropped; see the policy page about this, about incompletes, etc. Be sure to do the listed HW problems from Ch. 6.4, even though I won't collect them. Omit Ch 5.7 and 6.2.

See the final exam review page. I may need to update it a bit, but the list of proofs there is correct - 2.2.3, 6.1.1, 6.3.1, 6.3.2 and 6.4.4. Probably you should include Thms 5.6.2 and 5.6.3, though I may test you on those indirectly, rather than ask for the exact proofs. I will not require a proof of Schur's Thm from 6.4, but it could appear as extra credit or as an option.

Note that all work and other business is due on 12/3. [regrading requests, medical excuses, etc]. Check that I have your quiz and HW grades recorded correctly. See also my final lecture topics, and the exam page. You are welcome to come by to check your grades. I plan to have normal office hours on 12/5, but you'll probably need an appt to see me after that.

I will not be able to return your MHW3 before the final, so you may want to make a copy to study from. Note that the Ch6 MHW3 uses the eigshow utility. You may have to download this using notes from our MHW web page. You do not have to print out the displays from that unless you want to. I doubt that you can do these problems with alternative software.

Day Date I give you You give me Lecture topics HW
25 11/19     6.1 Eigenv's 1abcfgk, 2, 3, 4, 6, 8
26 11/21     6.3 Diagonals 1, 2, 3, 4, 6, 9, 23
27 11/26   HW7 thru 6.3 6.4 Hermitian 1, 2, 3, 4, 5
  11/28 TDay   [No Class]  
28 12/3 HW7 back MHW3, etc* 6.4 some pfs none
29 12/5     Review none

*Everything is due by 12/3 - any late HW7s, any promised medical excuses, regrading requests, etc

Final Exam -  Thurs, 12/12/19, 2:15pm to 4:15pm in CASE Room 132

 

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