Math 309 - Intermediate Linear Algebra - Spring 2016

General Information:

Meeting Time:MWF, 9:00 - 9:50
Location: Millington 100
Instructor:Ryan Vinroot
Office: Jones 130
Office Hours: Wed 1-2 and Thurs 3-5 (also by appointment).
Announcements:All announcements and course information will be on this webpage. In particular, I will not be using Blackboard.
Textbook:Linear Algebra, Fourth Edition, by Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence
Midterm - 30%, Homework and Quizzes - 30%, Final Exam - 35%, Class Participation - 5%. The grading scale will be based on the standard 10-point scale, as follows:
A: 93-100, A-: 90-92, B+: 87-89, B: 83-86, B-: 80-82, C+: 77-79, C: 73-76, C-: 70-72, D+: 67-69, D: 63-66, D-: 60-62, F: 0-59.
Attendance & Lecture Policy: It is expected that you attend all lectures, with exceptions minimized. It is greatly appreciated when you are on time. Please do your best to stay awake and attentive during lecture, please do not email or text during lecture, and keep all cell phones/hand held devices/laptops put away during lecture. While it is understandable that you may miss a lecture here and there, or be sleepy in class once in awhile, repeated absences, late arrivals, naps, or general non-attentiveness will negatively affect your class participation score.
Any legitimate absence for a test or quiz must be discussed with me (or the Dean of Students office) *prior* to the test or quiz date.
Calculator Policy: Calculators will not be needed or allowed on quizzes or exams. Calculators could potentially be useful on some homework problems, but there is no requirement to buy any particular calculator for this purpose.
Prerequisites: Linear Algebra (Math 211) and Foundations of Mathematics (Math 214). Both of these are absolutely crucial for background. You may find this course extremely difficult if you did not get at least a B- in both of these courses.
Course Summary: A more suitable title for this course might be The Theory of Vector Spaces. The main goals of this course are to (1) prove a lot of the results from Math 211 in the context of abstract vector spaces, (2) generalize and expand these results for abstract vectors spaces, and (3) study the theory of canonical forms and inner products. In particular, this course will be very proof-theoretic (making Math 214 absolutely crucial), and a parallel goal will be for you to develop your proof-writing skills in the context of vector spaces. All of the techniques you learned in Math 211 are crucial as well, as they serve as basic examples on which the more general theory we will develop is based.

We will begin the course by reminding ourselves of the abstract definition of a vector space, and we will immediately broaden our view of vector spaces by realizing that the scalars need not be the set of real numbers, but can also be the complex numbers, the rational numbers, or in fact any field (in the algebraic sense). We will cover Chapters 1-3 in the first third of the course, which covers a lot of the familiar topics from Math 211 (such as bases, dimension, linear transformations, and invertibility). We will prove all of the claims in the sections we cover, and we will introduce and prove new concepts and results as well (such as dual bases, in Sec. 2.6). There will be less concentration on examples in these chapters, because the most important examples are covered in Math 211. Examples we will discuss will concentrate on those which go beyond those covered in Math 211.

In the second third of the course, we will review determinants (Section 4.4), and realize the determinant as the unique (up to scalar) alternating multilinear form on the space of square matrices (Section 4.5). We will then review the basic idea of eigenvalues, and introduce a few new concepts (Sections 5.1, 5.2, and 5.4).

After material from Chapter 5, we will move immediately to the theory of canonical forms in Chapter 7. The rest of the course will dedicated to the study of Jordan and rational canonical forms, and to get as far as possible through the theory of inner product spaces in Chapter 6.

Dates & Course Announcements:

Midterm and Final Exams:

As agreed, your midterm grade will be determined by your 3 highest quiz scores, plus your highest HW score. The final exam is scheduled to be on Fri, May 6, 9 AM-12 Noon.

Exam Calendar (Tentative):
Exam Date Time/Due Location
Final Exam Fri, May 6 9 AM-12 Noon Millington 100

Class Announcements:
  • All relevant announcements will be listed here. Check back frequently (don't forget to refresh your browser) for updates.
  • Important Dates and Class Holidays:
    • Fri, Jan 29: ADD/DROP DEADLINE
    • Sat, Mar 5 - Sun, Mar 13: NO CLASS (Spring Break)
    • Fri, Mar 18: WITHDRAW DEADLINE
    • Fri, May 6, 9 AM - 12 Noon: FINAL EXAM
  • (1/20) My office hours during the first short week of class are as follows: Wed Jan 20: 1-2 and 4-5, Thurs Jan 21: 2-3, Fri Jan 22: 2-3.
  • (1/20) Between our first and second meetings of class, you need to read the following sections in the book: Sections 1.1 and 1.2, and Appendices A, B, and C.
  • (1/20) Quiz 1 will be on Monday, Jan 25, at the beginning of class. It will cover Section 1.2 and Appendix C.
  • (1/21) I have to shift (but extend) my office hours today (Thurs, Jan 21). They will be 2:30-4.
  • (1/25) Quiz 1 is shifted to Wed, Jan 27, due to class being canceled on Monday. Also, HW1 is now due on Mon, Feb 1.
  • (1/25) My office hours today, Mon, Jan 25, will be 2:30-4.
  • (1/27) My office hours for the rest of this week are: Wed, Jan 27 (today), 1-2, and Thurs, Jan 28, 3-5.
  • (2/1) My regular weekly office hours will be Wed 1-2 and Thurs 3-5, and I will have an extra office hour either on Fridays (if HW is due on Mon) or on Mondays (if HW is due on Fri).
  • (2/8) Quiz 2 will be in two weeks, on Mon, Feb 22.
  • (2/10) I have to shift my office hours to 3:30-4:30 today (Wed), instead of 1-2. I apologize for any inconvenience. I will have my normal 3-5 office hours on this Thurs.
  • (2/19) I will have an extra office hour today (Fri, Feb 19), 2:30-3:30. Remember that Quiz 2 is on Mon, Feb 22.
  • (2/22) I will have an extra office hour today (Mon, Feb 22), 1-2.
  • (2/29) I will have "open door" office hours tomorrow, Tues Mar 1, between 10 and 3. Come by any time during those hours and knock on my door.
  • (3/14) I will have walk-in office hours tomorrow, Tues Mar 15, between 10:30 and 2:30. Come knock on my door during those times for any questions. I will have my normally scheduled office hours today as well.
  • (3/18) Quiz 3 will be next Friday, Mar 25. Quiz 3 will cover Sections 2.1-2.4, but with a conentration on Sec. 2.4 (Isomorphisms).
  • (3/28) I will have additional office hours this Tues, Mar 29, 12:30-3:00.
  • (4/4) I will have additional office hours today, Mon, Apr 4, 1-2, and tomorrow, Tues, Apr 5, 10-12.
  • (4/4) Quiz 4 will be next Mon, Apr 11. It will cover Sec. 4.2 on determinants. A nice summary of the results covered is given in Sec. 4.4, through the bottom of p. 235 (all except for the last line).
  • (4/5) Quiz 4 will instead be next Wed, Apr 13. It will cover the same material as previously planned.
  • (4/6) So that you can prepare for your own time management, the following is the schedule for the final HWs and quizzes for this semester:
    Quiz 4: Wed, Apr 13
    HW8: Due Mon, Apr 18
    Quiz 5: Fri, Apr 22
    HW9: Due Mon, Apr 25
  • (4/18) The last homework has been posted, and it is due next Mon, Apr 25. The last quiz will be this Fri, Apr 22.
  • (4/20) My office hours today will be shifted, but extended, 2-3:30. My office hours on Thurs, Apr 21, will be 10-11:30 in addition to the regular 3-5.
  • (4/27) My office hours this week are as follows: Today (Wed, Apr 27) 4-5, and tomorrow (Thurs, Apr 28) 10-11 and 3-5.
  • (4/28) My office hours during the first week of exams, leading up to our final exam (Fri, May 6, 9 AM, Millington 100) will be as follows:
    Mon, May 2: 12:30-4
    Tues, May 3: 11-2 and 3-5
    Wed, May 4: 10-2 and 3-5
    Thur, May 5: 12:30-4
    I give the final exam for my other course on Thurs, May 5, 9-12, so I will not be available then.

Homework & Quizzes:

Homework problems and quizzes will be a very important part of the course, and there will be homework assigned most weeks. Completion of all homework problems is required, and your grade on a homework assignment will be based on completeness, as well as on the details of the solutions of the problems graded. Solutions should be written carefully and neatly, with attention paid to the completeness and clarity of your proofs and steps. You may work with other students when you are figuring out how to do homework problems. However, you should be alone when you write up these solutions. That is, working with other students is only allowed when discussing the problems, but not when you are writing the solutions themselves. You should not, under any circumstances, attempt to look up solutions or hints to problems online. I will consider this plagiarism, an honor offense. You are always welcome to come to my office hours or to email me if you need any hints or help on homework problems.

Homework is due at the beginning of class on the due date of the assignment. Homework turned in by 5 PM on the due date, but after the start of class, will be allowed once without penalty, and after once will be marked of 10%. Homework turned in after 5 PM the due date will be marked off 20% for each day late. Any homework turned in late can be turned in on my office door, and please write down the date and time you turned in the work on your paper. If there are serious reasons for you not getting homework in on time (severe illness, injury, or family issues, for example), you should go through the Dean of Students office so that they can let me know. Please feel free to ask me about this policy if it is not clear.

Homework (and Quiz, see below) scores will each be out of 50 points. Some of the assigned HW problems will be scored in detail, others for completeness. Your lowest HW and lowest Quiz scores will be dropped at the end of the semester.
Assignment Problems Due Date
1 1.2 #7, 8, 12, 18, 21
1.3 #19, 20
Mon, Feb 1
2 1.3 #13, 15, 23, 31(a,b)
1.4 #10, 13, 1.5 #9
Mon, Feb 8
3 1.3 #12, 1.6 #16, 22, 29(a), 31, 32
1.7 #4
Mon, Feb 15
4 2.1 #13, 14, 15, 28
2.2 #4 (also prove T is linear), 8, 13
Fri, Feb 26
5a 2.3 #3, 12(a), 13, 2.4 #16 Fri, Mar 4
5b 2.3 #12(b,c), 2.4 #9, 2.5 #5, 10 Fri, Mar 18
6 2.4 #19, 2.6 #6, 7, 13(a,b), 17
3.1 #2, 3.2 #14
Wed, Mar 30
7 3.2 #4, 7, 8
4.1 #3, 9, 4.2 #20, 25
Wed, Apr 6
8 4.2 #4, 29
4.3 #12, 15, 17, 20, 21
Mon, Apr 18
9 4.5 #16, 17
6.8 #2, 5(a,b), 6
Mon, Apr 25
Final Review
1.2 #13, 17, 1.3 #14, 30, 1.4 #12, 14
1.5 #3(a-f), 11, 14, 1.6 #6, 12, 23
1.7 - Understand Theorems 1.12, 1.13
2.1 #4, 6, 20, 33, 2.2 #5, 10
2.3 #4, 11, 2.4 #3, 15, 18
2.4 #3, 15, 18, 2.5 #6(a,b), 11
2.6 #3, 15, 3.1 #3, 3.2 #5, 17
4.1 #6, 4.2 #3, 10, 26, 4.3 #11, 13, 24
4.5 - Understand definitions from notes and the book, and Theorem 4.12
6.8 #4(a-d), 5(c), also understand notes from class
Not Due

Quizzes: There will be several (between 4 and 6) quizzes during the semester, and each will count the same weight as a homework score. Quizzes will be announced the week before they are given, along with what material they will cover. Quizzes will typically be given at the beginning of class. There will be no make-up quizzes, unless your absence is discussed with me prior to the quiz, or there is a serious issue which is reported through the Dean of Students. The quiz solutions will be posted below throughout the semester, following each quiz:
  • Quiz 1 solutions.
  • Quiz 2 solutions.
  • Quiz 3 solutions.
  • Quiz 4 solutions.
  • Quiz 5 solutions.