The course is over!Final grades have been submitted to MySlice. Thanks to everyone for a great semester, and enjoy your break.

## Basic Info

- Instructor
- Prof. Graham Leuschke

email:`gjleusch@math.syr.edu`

AIM:`leuschkeg`

Google:`leuschke@gmail`

- Time & Place
- TR 9:30–10:50 in Carn 300
- Textbook
- Carl D. Meyer,
*Matrix Analysis and Applied Linear Algebra* - Office Hours
- MW 1:30–4:30; by appointment; and any time my door is open (317G Carnegie)
- Important documents
- syllabus

## Announcements

Here is last year’s final exam. As always, it should be used with caution: we did not cover exactly the same material this year. Also, this year’s final will have a large section consisting of definitions and formulas, like Exam II.

Exam II was in class on Thursday 29 November. It covered up through orthogonal projections and reflections, that is, Sections 5.1–5.6, plus the PageRank material. Here is last fall’s Exam II for your reference. **Note** that we did not cover exactly the same material this year. **Also** I announced in class that about half the points on this exam will be “theoretical” questions: definitions and formulas, rather than computations.

Exam I was in class on Tuesday 9 October. It covered up through least-squares, that is, all of the material we covered from Chapters 1–4. Here is last fall’s Exam I for your reference. **Note** that we did not cover exactly the same material before the first exam this semester as last year.

It has been said that ‘the human mind has never invented a labor-saving machine equal to algebra.’ If this be true, it is but natural and proper that an age like our own, characterized by the multiplication of labor-saving machinery, should be distinguished by the unexampled development of this most refined and most beautiful of machines.

Josiah Willard Gibbs, 1887

## Problem Sets

- HW #1, due Thursday 6 Sept
- HW #2, due Thursday 13 Sept. Here is a solution to problem #2, and here are the calculations in 3-digit floating-point arithmetic for problem #4 (a.k.a. #1.1.5).
- HW #3, due Thursday 20 Sept (corrected)
- HW #4, due Thursday 27 Sept
- HW #5, due Thursday 4 Oct
- HW #6, due Thursday 18 Oct
- HW #7, due Thursday 25 Oct
- HW #8, due Thursday 8 Nov
- HW #9, due Thursday 15 Nov (OMIT problem 1(c))

## Links

- interactive data-fitting (least-squares/regression lines). Place a bunch of points more-or-less on a line, watch the line snap to them. Then move one waaaaay off the line, and see how robust the regression line is.
- Mathematics at Google: “There is a wide variety of Mathematics used at Google. For example Linear Algebra in the PageRank algorithm, used to rank web pages in search results. Or Game Theory, used in ad auctions, or Graph Theory in Google Maps. At Google there are literally dozens of products which use interesting Mathematics. These are not just research prototypes, but real Google products; in which Mathematics play a crucial role. In this presentation, I introduce several applications of Mathematics at Google.”
- an online linear algebra toolkit
- an application where rank-one updates and their inverses arise
- The Anatomy of a Large-Scale Hypertextual Web Search Engine [PDF] (Sergey Brin and Larry Page’s original paper describing the PageRank algorithm. Surprisingly readable.
- The Use of the Linear Algebra by Web Search Engines [PDF] (Again, surprisingly readable. Has sections on PageRank and Jon Kleinberg’s HITS [“hubs and authorities”] algorithm. Co-written by our textbook’s author.)
- The second-order linear differential equation we studied on 4 September is essentially the same thing as a Sturm-Liouville equation. Examples include the Bessel equation and the Legendre equation.
- What Every Computer Scientist Should Know About Floating-Point Arithmetic (a slightly different approach than ours)
- The Nine Chapters on the Mathematical Art (wikipedia)
- A Brief History of Linear Algebra and Matrix Theory from Marie Vitulli at Oregon (dead link: http://darkwing.uoregon.edu/~vitulli/441.sp04/LinAlgHistory.html)
- James Joseph Sylvester (1814-1897) first coined the term ”matrix”: “a rectangular array of terms out of which different systems of determinants may be engendered, as from the womb of a common parent.” (”Matrix” is the Latin word for ”womb.” Sylvester was also responsible for the mathematical terms ”syzygy”, ”meicatecticizant,” and ”tamisage.” His articles are still great fun to read.) Here’s some more on Sylvester.
- Carl Friedrich Gauss (Wikipedia) was the greatest mathematician of all time (OF ALL TIME), but he did not invent Gaussian elimination.
- history and motivation of determinants (nothing about why you should *avoid* them, but we’ll see that later)
- A complete explanation of the operation counts in Gaussian elimination. Also Gauss-Jordan and finding the inverse.
- World Freehand Circle Drawing Champion because why not