Teaching/Math 532 Spring 2007
The course is over! Thanks to everyone for a great semester.
Basics
- Instructor
- Prof. Graham Leuschke
- Contact
-
gjleusch@math.syr.edu - Time & Place
- MW 12:45—2:05, Carnegie 300
- Office Hours
- TR 10—11:30; W 2:30—4; by appointment; and any time my door is open (206C Carnegie)
- Text
- Elementary Linear Algebra, Applications Version, 9th ed., by Anton and Rorres
- Important documents
- course syllabus
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
Final Exam:
Monday, 7 May, 2:45—4:45, in Carnegie 300
Topic schedule (finally settled down)
| week | section(s) | topics | remarks | HW |
|---|---|---|---|---|
| Jan 15 | Ch. 1 | systems of equations, matrices | no class Mon | |
| Jan 22 | Ch. 2, 11.1, 11.5 | determinants, curve fitting, | HW01 | |
| Jan 29 | Ch. 3—4, 11.12 | Euclidean vector spaces | HW02 | |
| Feb 5 | 5.1—5.3 | abstract vector spaces | Exam I Wed 2/7 | HW03 |
| Feb 12 | 5.4—5.6 | bases & dimension, row/column and nullspaces | no class Wed (snow!) | |
| Feb 19 | 5.6—6.1 | rank/nullity, inner product spaces | HW04 | |
| Feb 26 | 6.2—6.3 | orthonormality, dreaded Gram-Schmidt | HW05 | |
| Mar 5 | 6.3—6.4 | QR-decompositions, least squares | Exam II Wed 3/7 | |
| Mar 12 | S P R | I N G B R | E A K | |
| Mar 19 | 9.3—9.4, 11.6 | approximation, regression lines, Markov chains | HW06 | |
| Mar 26 | 11.6, 11.9, 7.1 | Markov Chains and Leontieff models, eigenstuff | HW07 | |
| Apr 2 | 7.2, 6.6, 7.3 | Eigenstuff, diagonalization, orthogonal diagonalization | HW08 | |
| Apr 9 | outside source | search engines | Exam III Wed 4/11 | |
| Apr 16 | 9.5, 9.6, 9.7 | quadratic forms, conic sections, quadric surfaces | HW09 | |
| Apr 23 | 8.1, 8.2, 8.4 | linear transformations | ||
| Apr 30 | outside source | coding theory | no class Wed |
Links
- Π is Wrong!
- The Second Eigenvalue of the Google Matrix
- 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.)
- PageRank Uncovered [PDF] (A slightly slimy overview of Google’s PageRank, including tips for webmasters. See page 12 for the mathematics.)
- The World’ s Largest Matrix Computation
- Google Technology (“The heart of our software is PageRank™, a system for ranking web pages developed by our founders Larry Page and Sergey Brin at Stanford University.”)
- Another application of diagonalization: exponential functions of matrices and solving systems of linear differential equations
- Fourier Series and their Applications (a nice expository paper, well-written, with nice pictures at the end. It does use the fact that e^{it} = cos t + i sin t, though.)
- Applications of Fourier Series in Classical Guitar Technique
- an awesome application of Fourier series to elementary number theory (the fact that \sum_0^\infty 1/n^2 is \pi^2/6)
- 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.
- What are Fourier Series?
- Regression lines on your TI-83
- Gauss and Ceres
- Do you have a facebook?
- groovy interactive graphic (dreaded) Gram-Schmidt orthonormalization applet
- World Freehand Circle Drawing Champion
- Lagrange interpolation (an alternative description of our interpolating polynomials)
- Your search - mega-theorem of doom - did not match any documents.
- history and motivation of determinants
- 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.
- A Brief History of Linear Algebra and Matrix Theory from Marie Vitulli at Oregon
- The Nine Chapters on the Mathematical Art (Wikipedia)