Our Teaching Page
has important information for my students.
(It has the
Notes, Exams and Links
from all of my previous courses.)
The Teaching Page has my schedule,
LOR guidelines,
and Usually Useful Pamphlets.
One of them is the
Checklist (pdf)
which gives pointers on competant mathematical writing.
Further information is at our
class-archive URL
(I email this private URL directly to students).
In all of my courses, attendance is absolutely required (excepting illness and religious holidays). In the unfortunate event that you miss a class, you are responsible to get all Notes / Announcements / TheWholeNineYards from a classmate, or several. All my classes have a substantial class-participation grade.
Work through W: Determinant. In progress is Properties of Determinants.
Please read the first few paragraphs of: Bilinear_map and Bilinear_form, as well as Multilinear_map and Alternating_multilinear_map.
Have read the beginning of W: Characteristic_polynomial. The defn we'll use is in the Cayley-Hamilton pamphlet (pdf).
An example of computing an eigenbasis.We will also discuss Jordan Canonical Form (JCF), In particular, I would like you to know the stmt and proof of the Block Upper-Triangular--matrix Lemma [just page 4 in JCF].
This demo page illustrates these linear transformations: Dilations, Rotations and Shears. It also shows the affine transformation of Translation.
Please peruse the Wikipedia pages that define Group, Ring, Field as well as Set builder notation.
Quantifiers ∀ and ∃ (“for all” and “there exists”) are like nitroglycerin, in that one little mis-step leads to the whole thing blowing up in your face.
There is no partial credit when it comes to Explosives and Quantifiers.
-JLF King
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.)
Author: | Friedberg, Insel, Spence | ISBN: | 978-0134860244 |
Year: | 2019 | Publisher: | Pearson |
...is due, slid u n d e r my office door (Little Hall 402, Northeast corner) no later than [Time & Date].
This IOP (pdf), 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.
Spring 2022, LinA:
(Jake Park TA-ed for this course, and was tremendously helpful.)The delightful Class-V (pdf) is online.
Part (X2d) of IOP-x asks for four KxK matrices A,B,C,D, where Det of block-matrix [ A B ] [ C D ] fails-to-equal Det(AD - CB). It is insufficient just to produce non-commuting A and C. You need to produce also B and D, and to compute that the determinants are unequal. Indeed, [extra credit] it is possible to have non-commuting A and C, and still have equality of the determinants.
Spring 2016, LinA:
We had the pleasant Class-B, (a mini-test of prerequisite knowledge) on Friday, 08Jan2016.
The mini-test counted for little, about
2%—4% of course grade, and selects some topics from:
:: High-school knowledge
(formula for a line between two points, the Quadratic Formula,
intersecting a line with a parabola, etc.), and some
:: Sets&Logic ideas
(Equivalence relations, partial orders, binary operators,
induction, pigeon-hole principle, cardinality, powerset operator, etc.)
:: Mathematical maturity
(Do you remember your basic calculus stuff? Do you remember how
to sum a geometric series?)
Eager students rushed to post solns, especially to the more interesting conundra, such as (C1b).
On Tuesday, 05Apr2016 we relaxed to the music of Class-E, the last in-class exam of the semester.
Various math czars who help out.
Computer | Time | EL-Probs | Phone-list |
---|---|---|---|
John | Avery | Meghan | Sarah |
Author: | Friedberg, Insel, Spence | ISBN: | 978-0130084514 |
Year: | 2003 | Publisher: | Prentice Hall |
Autumn 2015, LinA:
Shouts of joy greeted the two-tone Class-A as crowds gathered to cheer the elegance of the exam. The essay question asked for a proof of the Rank-Nullity Theorem.
Newspaper headlines across the country, Class-B a success. Avid readers looking forward to the next installment.
Various math czars who help out.
Computer | Chalk | EL-Probs | Time | Phone-list |
---|---|---|---|---|
James | Nick | Benjamin | Brodie | Allison |
Autumn 2011, LinA:
My students (well, Thom) created a LinAlg facebook page.Various math czars who help out.
EL-Probs | Computer | Time | Chalk | Blackboard | Phone-list |
---|---|---|---|---|---|
Jenn | Brandon | Rachel | Dillon | Suzy | Katherine |
The highly-anticipated and outrageously cheerful Class-B (pdf) entranced the cognoscenti with its clever use of rotation matrices, delighting Linear aficionados with mini-questions exploring linearly-independent sets.
Spontaneous cries of “Encore!” and “Author! Author!” were heard echoing about the hall. Critics effused over the exam's clean lines and minimalistic two-tone format. A Smash Hit!, was the consensus...
Lots better than getting hit by a truck!to
Somewhat better than getting hit by a truck!
Autumn 2010, LinA:
A Good Time was had by all.
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).
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
link.
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).
Various math czars who help out.
Time | Chalk | Blackboard | Computer/Proj |
---|---|---|---|
Kaitlin | James | Sean | James |
Autumn 2005, LinA:
Author: | Friedberg, Insel, Spence | ISBN: | 0-13-008451-4l |
Year: | 2003 | Publisher: | Prentice Hall |