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F2010: MAS4105 3247 Linear Algebra 1, 7th, MWF:LIT237, Tu:LIT207

# (Abstract) Linear Algebra

Our Teaching Page has useful information for students in all of my classes. It has my schedule, LOR guidelines, and Usually Useful Pamphlets. One of them is the Checklist (pdf) which gives pointers on what I consider to be good mathematical writing. Further information is at our class-archive URL (I email this private URL directly to students).

• Available are all the quizzes so far, and some potential future quiz/text questions (pdf). [Tuesday, 30Nov2010]
• Students pointed out that Class-D (pdf) was too short --Have you no respect us, Prof. King?-- but was the nonetheless fun.

Time permitting, tomorrow (Wedn.) we'll have a bonus-quiz whose score I'll directly add to the exam score.

It might be “Find the closest point on this line to this point” [in 2 dim'al, or N dim'al space –use Proj() and Orth()]. It might be computing Proj() w.r.t an IP defined by a positive-definite matrix. It might be computing Orth() w.r.t the complex dot-product (which is conjugate-linear in its first argument). Make sure that you can do all of the short-answer questions on Class-D, and the problems on the above quizzes so far link.

• There was no class on Friday, 15Oct, as this is UF's “Homecoming day ”.
• Class-C (pdf) took place on Wednesday, 13Oct, to joyful shouts of acclaim and fascination.

Characteristically, Polly Nomial was very determinant to make an appearance, which she did along with her friend x.

Unlike polite Polly, question (C1) had attitude: What are ya tryin' ta Prove?!, buddy, it seemed to say. It also seemed clueless …not quite spacey —subspacey, might be a better term. Fortunately, we were able to resolve the (C1) conundrum (pdf).

Prob (C2), a basis for Range(L_S): One method uses RREF(S) (txt). Another method uses RREF(Transpose(S)) (txt).

• Here are some examples of change-of-basis, applied to rotation matrices.
• The outrageously cheerful Class-B (pdf) [on Wedn., 22Sept] concentrated on the RREF algorithm, with a sub-emphasis on linearly-independent sets. The critics effused over the exam's clean lines and minimalistic two-tone format. Gaiety and applause greeted the novelty of ending with a True-False query. Our reporter concludes: A Good Time was had by all.
• The prereq exam, Class-A (pdf), seemed to be easy for folks.
##### Some of the material we've covered
• Weeks 1 & 2:

In browsers that support CSS3 (Firefox does, and is available in our classroom) this demo page illustrates these linear transformations: Dilations, Rotations and Shears. It also shows the affine transformation of Translation.

Please have perused the Wikipedia pages that define Group, Ring, Field as well as Set builder notation.

We have learned the Euclidean algorithm in the form of the Lightning bolt algorithm (LBolt). We saw an example of a Game isomorphism between TicTacToe and the “Game of 15”.

We had the Prereq exam, which tested The Math-Greek alphabet (pdf), basic proof techniques (e.g, induction), simple logical properties (e.g, what is a contrapositive), and High-school knowledge (e.g, quadratic formula).

### General Info

Our LinA class has a LISTSERV archive. I will email to each student how to post-to and read-from the Archive. (The archive is at a private URL, only for the use of the folks in our class.)

Our Lina syllabus [Friday, 22Oct2010] has tentative exam dates, as well as the first homework and reading assignment. It also mentions the Class photo Day.

Our main textbook is Linear Algebra (4th edition).
 Author: Friedberg, Insel, Spence ISBN: 978-0130084514 Year: 2003 Publisher: Prentice Hall

It is available from the publisher and from online booksellers.

Various math czars who help out.

Time Chalk H-Probs Blackboard Computer/Proj
Kaitlin James ? Sean James

If this is useful to you, here are my webpages for Linear Algebra, 2005, as well as Computational Linear Algebra from 2007 (Spring and Autumn), 2002 and 1998. All of my previous course “Notes, Exams and Links” are available from the Teaching Page.

#### End-of-semester Individual Linear-Algebra project

The Optional individual-project E (pdf), was due, slid u n d e r my office door (Little Hall 402, Northeast corner) , no later than noon, Friday, 10Dec2010.

The project must be carefully typed, but diagrams may be hand-drawn.

At all times have a paper copy you can hand-in; I do NOT accept electronic versions. Print out a copy each day, so that you always have the latest version to hand-in; this, in case your printer or computer fails. (You are too old for My dog ate my homework.)

Please follow the guidelines on the Checklist  (pdf, 3pages) to earn full credit.