|
| Professional |
| Classes |
| Hobbies |
| Useful Links |
Applied Linear Algebra
Questions or Comments?
- Send me email (click here and delete my initials at end).
- Homepage: http://www.math.uconn.edu/~troby
- Office: MSB 212; Phone: 860-486-8385
- Office hours (TENTATIVE): Tues/Thurs 11:30–12:25 and 3:20–4:00 in MSB 212 and by appointment. I'm happy to answer questions or schedule appointments by email, which I check frequently.
Class Information
COORDINATES: Classes meet Tuesdays and Thursdays
2:00-3:15 in MSB 307 (MOVING
TO MSB 215 ON
THURSDAY, 29 AUGUST). The registrar calls this Section 002, #3022.
PREREQUISITES: MATH 1132, 1152, OR 2142.
TEXT: David C. Lay: Linear Algebra and Its Applications, 4th Ed., available in the bookstore. Let me know if you have any trouble getting it.
WEB RESOURCES: The homepage for this course is http://www.math.uconn.edu/~troby/Math2210F13/. The author also has a useful site with review sheets and downloadable data here.
SOFTWARE: In most areas of mathematics it is frequently helpful to use computer software not only for computations, but also to explore examples, search for patterns, or test conjectures. For linear algebra there are several extensive and sophisticated commercial software packages, including MATLAB, Maple, and Mathematica. Matlab is particularly good at linear algebra for applications. All of these can be expensive, depending on your site license.
An excellent alternative to the above is the free open-source computer algebra system Sage. There are many commands for linear algebra, and a textbook (linked below) has been written that makes significant use of Sage examples. Sage also provides a full-fledged programming environment via the Python programming language, but you don't need to be a programmer to use it. I highly recommend trying it out online, and installing a copy on your computer.
Our sysadmin has provided a local copy of the downloads for Sage.
GRADING: Your grade will be based on two midterm exams, a final exam, homework, and quizzes.
The breakdown of points is:
| Midterms | Final | Quizzes | Homework
|
|---|---|---|---|
| 20% each | 30% | 20% | 10% |
EXAMS: The exam dates are already scheduled, so please mark your calendars now (midterms in class on 3 October and 5 November, final (tentatively) on 10 December 2013, 1:00-3:00). All exams (like math itself at this level) are cumulative. No makeups will be given; instead if you have an approved reason for missing an exam, the final will count for the appropriately higher percentage.
QUIZZES: Quizzes will be given each Thursday (except midterm exam days), covering (a) sections from the previous week (at the level of HW exercises) and (b) the reading assigned for the current week (at the level of True/False exercises). Your lowest two quiz scores will be dropped.
HOMEWORK: Homework will be assigned most weeks, and is DUE at class the following TUESDAY. Since I may discuss the homework problems in class the day they are due, late assignments will be accepted only under the most extreme circumstances. (Please let me know as soon as possible if you find yourself with a situation that might qualify.) The lowest written homework score will be dropped in any event. (I've color coded the schedule by week to help clarify what the HW is for a given week.)
You may find some homework problems to be challenging, leading you to spend lots of time working on them and sometimes get frustrated. This is natural. I encourage you to work with other people in person or electronically. It's OK to get significant help from any resource, but in the end, please write your own solution in your own words. Copying someone else's work without credit is plagiarism and will be dealt with according to university policy. It also is a poor learning strategy.
ACADEMIC INTEGRITY: Please make sure you are familiar with and abide by The Student Code governing Academic Integrity in Undergraduate Education and Research. For quizzes and exams you may not discuss the material with anyone other than the instructor or offical proctor, and no calculators, phones, slide rules or other devices designed to aid communication or computation may be used unless otherwise specifically indicated on the exam.
CONTENT: Linear Algebra is a beautiful and important subject, rich in applications within mathematics and to many other disciplines. For many of you this is the first course to begin bridging the gap between concrete computations and abstract reasoning. Understanding the notions of vector spaces, linear (in)dependence, dimension, and linear transformations will help you make sense of matrix manipulations at a deeper level, clarifying the underlying structure.
ACCESSIBILITY & DISABILITY ISSUES: Please contact me and UConn's Center for Students with Disabilities as soon as possible if you have any accessibility issues, have a (documented) disability and wish to discuss academic accommodations, or if you would need assistance in the event of an emergency.
LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.
We will often spend classtime doing things in groups, presenting mathematics to one another, or having interactive discussions. There will not be time to "cover" all material in a lecture format so you will need to read and learn some topics on your own from the book (or otherwise).
SCHEDULE: I will update the following schedule over the course of the semester. Generally we will cover three sections per week, which means splitting a section between two lectures. Lecture notes are linked section by section: I recommend you review them before or after lecture, allowing you to spend lecture time focussing on the material rather than copying things down. If you have a religious observance that conflicts with your participation in the course, please meet with me within the first two weeks of the term to discuss any appropriate accommodations.
I've color coded the schedule by week to help clarify what the HW is for a given week.
| 2210Q LECTURE AND ASSIGNMENT SCHEDULE | |||
|---|---|---|---|
| Section | |
|
HW Problems |
| §1.1 | 8/27 T | Intro to Linear Alg & Systems of Eqns. | 1, 2, 3, 10, 12, 13, 15, 16, 21, 24, 25, 31, 32 |
| §1.2 | 8/29 R | Row Reduction & Echelon Forms | 2, 10, 13, 14, 19, 21, 24, 29, 31 |
| §1.3 | 8/29 R | Vector Equations | 3, 6, 7, 9, 12, 14, 15, 21, 22, 23, 25 |
| §1.4 | 9/3 T | Matrix Equations | 1, 4, 7, 9, 11, 13, 17, 19, 22, 23, 25, 31 |
| §1.5 | 9/5 R | Solution Sets of Linear Systems | 2, 6, 11, 15, 18, 19, 22, 23, 27, 30 |
| §1.7 | 9/10 T | Linear Independence | 1, 2, 5, 7, 9, 15, 16, 20, 21, 32, 35 |
| §1.8 | 9/10 T | Linear Transformations | 2, 4, 8, 9, 13, 15, 17, 21, 26, 31 |
| §1.9 | 9/12 R | Matrix of Linear Transformation | 1, 2, 5, 13, 15, 20, 23, 26, 32, 34 |
| §2.1 | 9/17 T | Matrix Operations and Inverses | 2, 5, 7, 10, 15, 20, 22, 27, 28 |
| §2.2 | 9/19 R | Inverse of a Matrix | 3, 6, 7, 9, 11, 13, 15, 23, 24, 29, 32, 37 |
| §2.3 | 9/24 T | Characterizations of Invertible Matrices | 1, 3, 5, 8, 11, 13, 15, 17, 26, 28, 35, 40(challenge!) |
| §2.4 | 9/24 T | Partitioned matrices | 1, 4, 9, 10, 11, 13, 16, 19 |
| Ch. 1 | 9/24 T | Supplementary Exercises | 6, 7, 10 ,18, 22, 23 |
| §2.5 | 9/26 R | Matrix Factorizations | 2, 5, 7, 21, 23b, 24 |
| §3.1 | 9/26 R | Intro to Determinants | 4, 8, 11, 13, 20, 21, 31, 32, 37, 39 |
| §3.2 | 9/26 R | Properties of Determinants | 2, 3, 8, 10, 16, 17, 20, 26, 27, 32, 34, 40 |
| §1.1–2.5 | 10/1 T | Catchup & Review Day | Do Practice Midterm by today! |
| THURSDAY 3 OCTOBER: FIRST MIDTERM EXAM (through §2.4) | |||
| §3.3 | 10/8 T | Cramer's Rule & Volumes | 4, 5, 6, 13, 16, 22, 23, 26, 29, 30; HW 2.5–3.2 due |
| §4.1 | 10/8 T | Vector Space & Subspaces | 1, 3, 8, 12, 13, 15, 17, 22, 23, 31, 32 |
| §4.2 | 10/10 R | Null Spaces, Column Spaces & Lin. Transf. | 3, 6, 11, 14, 17, 19, 21, 24, 25, 32, 33, 34, 36 |
| §4.3 | 10/15 T | Bases and Lin Ind. Sets | 3, 4, 8, 10, 14, 15, 21, 23, 24, 29, 30, 31; Quiz #5 due |
| §4.4 | 10/17 R | Coordinate Systems | 2, 3, 5, 7, 10, 11, 13, 15, 17, 21, 23, 32 |
| §4.5 | 10/22 T | Dimension of a VS | 1, 4, 8, 11, 14, 21, 23, 26, 28, 29 |
| §4.6 | 10/22 T | Rank | 2, 5, 7, 10, 13, 19, 24, 27, 28; Midterm #1 Rewrite due |
| §4.7 | 10/24 R | Change of Basis | 1, 3, 5, 7, 9, 11, 13, 15 |
| §5.1 | 10/29 T | Eigenvectors & Eigenvalues | 2, 6, 7, 11, 13, 15, 19, 21, 23, 24, 25, 27, 31 |
| §5.2 | 10/29 T | Characteristic Equation | 2, 5, 9, 12, 15, 19, 20, 21 |
| §1.1–5.2 | 10/31 R | Catchup & Review Day | Do Practice Midterm 2 by today |
| TUESDAY 5 NOVEMBER SECOND MIDTERM EXAM (through §5.2) | |||
| §5.3 | 11/7 R | Diagonalization | 1, 4, 5, 9, 11, 15, 17, 21, 24, 26 |
| §5.4 | 11/12 T | Eigenvectors & Linear Transformations | 1, 3, 6, 7, 10 ,15, 16, 23, 25 |
| §6.1 | 11/12 T | Inner Product & Orthogonality | 3, 5, 10, 16, 18, 19, 23, 25, 27, 29 |
| THURSDAY 14 NOVEMBER CLASS UNEXPECTEDLY CANCELLED | |||
| §6.2 | 11/19 R | Orthogonal Sets | 3, 6, 8, 9, 11, 14, 20, 21, 23, 26, 27, 28, 29 |
| §6.3 | 11/21 R | Orthogonal Projections | 1, 6, 7, 9, 11, 13, 17, 21, 23, 24 |
| 25-29 NOVEMBER THANKSGIVING BREAK NO CLASSES | |||
| §6.4 | 12/3 T | Gram-Schmidt Process | 1, 3, 7, 9, 11, 17, 19 |
| §6.5 | 12/3 T | Least-Squares Problems | 3, 5, 7, 9, 11, 17, 19, 21 |
| §7.1 | 12/3 T | Diagonalization of Symmetric Matrices | 1, 3, 5, 8, 10, 13, 17, 19, 25, 29 |
| §1.1-7.1 | 12/5 R | Catchup & Review Day | |
| MONDAY 9 DECEMBER 7:30PM: REVIEW SESSION IN MSB 215: Do Practice Final by today! | |||
| TUESDAY 10 DECEMBER 1:00-3:00 FINAL EXAM IN MSB 215 | |||
Web Resources
- Rob Beezer has a free open-source textbook in linear algebra that you might find to be a useful supplement. You can download a print edition, or view the online hyperlinked version.
- Here's an Online Mind Reader. Can you figure out how it works?
- The MIT 18.06 (Linear Algebra) website has lots of resources, including Mathlets (small web-based teaching tools) (called "Demos" under the Extras link.) for your learning pleasure.
- This
website (found via Google) has a brief one-page blurb on computing
Google's pagerank algorithm.
- A Gaussian Elimination (row reduction) applet from Terry Tao's website
- A linear transformation applet for the plane from Smith College
- Here's another Online Row Reducer from Greg Landwebber's Cohomology.com website.
Anonymous Feedback
Use this form to send me anonymous feedback or to answer the question: How can I improve your learning in this class? I will respond to any constructive suggestions or comments in the space below the form.
Feedback & Responses
- This is a test.
This is only a test.
- It would be helpful if you didn't just skip sections that you planned to cover otherwise. If you are gone from class, teach the section at a different time. Don't expect us to learn it by ourselves and then have homework due on it. It isn't fair. I'm not getting my money's worth out of your teaching.
- I feel that it would be more helpful to not skip sections. If we don't get
to section 7.3 or 7.4 it won't be the end of the world. However, when we try to
learn a new section after rushing through or entirely skipping a previous
section, the new one doesn't make sense. I would rather fully understand fewer
sections than trying to get through 7.4, which seems impossible at this point.
Thanks for your feedback, which I just got now after today's class (though you sent it before class, when I was teaching something else). I agree that skipping sections is not a good strategy, and if we don't make it to the SVD, that's not the end of the world. (Many sections of this course don't get that far, though it's certainly a worthwhile goal.) As I hope was clear during class, I am happy to slow down when there are questions or clear points of confusion that should be addressed.
I'll think more carefully over Thanksgiving break about how far we can reasonably expect to get. And I hope your final comment was really a conditional: "If I skip sections or rush through, then you won't be getting your money's worth" rather than the absolute statement it appeared to be. If not, please say more about that.
- Would you mine talking about the Final exam so we can study during the
thanksgiving break..
Unfortunately, this feedback was posted at 12:53 on Thursday, when I was already teaching my earlier class. Perhaps I said enough in class anyway, but it was a good reminder for me to get the Practice Final (see below) posted. Please take a look at it and let me know if you have other questions!
NEWS, NOTES, AND HANDOUTS
[27 Aug] We will be moving class to MSB 215 for the rest of the semester, starting on the second day of class, Thursday 29 August, so we can take advantage of a hi-tech room.
[26 Sept] I've modified the schedule so that (a) Exam 1 only covers through §2.4 and (b) HW on §2.5, 3.1, and 3.2 is due after the midterm. Please spend this weekend on the practice midterm.
[22 Nov] I've modified the schedule based on the day we missed. All HW for §5.3–6.3 is due on Tuesday 12/3, along with rewrites for Exam #2. I've also posted the practice final (see links below and on the schedule above).
[5 Dec] Question #8 on the practice final covers a section we didn't get to (§7.3) this semester. Feel free to just ignore it.
[7 Dec] I updated the Practice Final to take out things we didn't cover; if you have an older version (e.g., what I handed out on Thursday), then omit #8 on constrained maximization. Also, replace "p. 269" with "p.236" in #7, and eliminate the quadratic form and constrained extrema clause of 11(e). I'll make the solutions available sometime on Sunday.
[7 Dec] Note the review session added to the schedule for MONDAY 9 DECEMBER starting at 7:30 PM. Assume it's in MSB 215, but we might need to move to a nearby room, e.g., MSB 203.
[8 Dec] I'll be in my office on Tuesday 12/10 from 11:30-12:45 to answer any questions from 2210Q students. Our exam starts at 1:00 that afternoon.
Handouts
- Practice Midterm 1
- Rules for Rewrites
- Practice Midterm 2
- Practice Final [UPDATED!]
- Solutions to Practice Final
Back to my home page.