Linear Algebra

Mathematics V2010y
Prof. Michael Thaddeus
Spring 2007

Welcome to the course home page.

Course information will be available here.

Many frequently-asked questions are answered by the syllabus.

Our teaching assistant is Nels Hanson.
But you can also seek help from anyone in the Columbia Help Room.

FINAL GRADES:

Final grades have been submitted and should be available in a matter of hours.
Your grade on the final exam is visible on Courseworks.
I am out of town for the summer, so if you want to view your final exam, it will have to wait until the fall.
However, please do call or come by then if you want to see the exam or discuss the results.
Have an excellent summer!

PROBLEM SESSION:

Nels Hanson will conduct an optional problem session on Tuesdays from 2-4 pm in 405 Mathematics. First session: Tuesday, February 20.
He will continue to spend one hour in the Columbia Help Room, 406 Mathematics, from 11-12 on Wednesday.
You can seek assistance from anyone else in the Columbia Help Room as well.

HANDOUTS:

Here is the handout How Gaussian Elimination Works.

Here is the handout Glossary of Symbols.

Here is the handout on Stresses on Beams.
Here is the flat ceiling of the Sheldonian Theatre in Oxford, designed in the 1660s by Christopher Wren.
And here is the arrangement of beams whose stresses were worked out, in a tour de force of calculation, by Wren's colleague John Wallis.
(From the book Oxford Figures.)

Handout on Proving Statements in Linear Algebra.

The review slide on bases and dimension, from the lecture after spring break.

Handout on The Gram-Schmidt Orthonormalization Process.

A handout with some Key Concepts for Review.
Despite its length, this is not guaranteed to be comprehensive.
For instance, I just noticed I left out AB inverse equals B inverse A inverse...
Besides this sheet, the best way to prepare for the final is to review lecture notes, homework and quiz problems.

LINKS:

Ready to parlay your knowledge of linear algebra into fame and fortune?
Try reading "The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google" by Kurt Bryan and Tanya Leise.

The Declaration of Linear Independence, a classic of geeky humor by David Grabiner.
It's (slightly) funnier if you are familiar with the original Declaration of Independence.

MATRIX CALCULATORS:

Here are Java applets for doing 3x3 matrix multiplication and solving 3x3 linear systems, both written by Marcus Kazmierczak.
Use at your own risk. In particular, the linear system solver may return only one solution even though an infinite number of solutions exist.
You could also download his much fancier Java Applet Matrix Calculator.

Or check out the Online Row Reducer and the Linear Algebrator by Greg Landweber.

PRELIMINARY GRADES:

Quiz #8 has been graded and is available from the wire box outside 414 Mathematics. (Here are the answers.)
All 8 quiz grades and the total of your 5 best can now be seen on Courseworks.
Please check our arithmetic. Ignore the percent value, which is calculated by Courseworks and is meaningless.
Here is a rough indication of your letter grade going into the final: out of 150 points,
0-15 = F, 15-30 = D, 30-45 = C-, 45-59 = C, 59-72 = C+, 72-86 = B-, 86-99 = B, 99-113 = B+, 113-126 = A-, 126-140 = A, 140-150 = A+.
Disclaimer: this is a rough guideline only! Besides, the final counts for 50%, so your grade could go up or down dramatically! Study hard!

REVIEW SESSION:

Prof. Thaddeus will conduct a review session on Sunday, May 6 from 2-4 pm in 203 Mathematics.
There is no set agenda, so bring questions!

PRACTICE FINAL:

Here is a practice final exam, with accompanying diagrams.
This was the actual final exam in a previous incarnation of the course.
And here are the answers.

QUIZ ANSWERS:

Answers to Quiz #1 (corrected version)

Answers to Quiz #8

HOMEWORK ASSIGNMENTS:

Assignment #1, due January 29; Answers

Assignment #2, due January 31; Answers (corrected version)