Apprentice Program, Summer 2010 REU
Linear Algebra and Combinatorics
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| Synopsis
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Press your browser's
"refresh" button to get the current problem sets
("puzzles15.pdf" and "linex15.pdf").
Old News
The problem set has been split into two: "Puzzle Problems" and
"Linear Algebra Exercises."
Some of the old "Puzzles Problems"
have been reclassified as "Linear Algebra Exercises," but
not all that is related to linear algebra was reclassified,
so some of the Puzzle Problems continue to be related to
linear algebra. (Press "Problem sets" on the banner.)
Kate's June 29 notes and the first two chapters of the instructor's
lecture notes have been posted (click "Notes" on the banner).
The course will develop the usual topics of linear algebra, and
illustrate them on unusual and often striking applications to
combinatorics and the theory of algorithms. Emphasis will be on
creative problem solving and discovery. The basic topics include
polynomials, finite fields, permutations, determinants, linear
transformations, the characteristic polynomial, Euclidean spaces,
orthogonalization, the Spectral Theorem. Application areas to be
highlighted include extremal set theory, the spectral theory of
graphs, and the algorithmic "geometry of numbers"
(Lovász's Lattice reduction).
Problem sets
(FINAL UPDATE: Fri, July 23, 8:30pm. REFRESH your browser)
These are the problems assigned in class. The sets are continually
updated.
The problems now posted include those stated in class on July 23.
Lecture Notes compiled from current and past years' apprentice
lectures will be posted. Here are the first two chapters:
These notes are hot off the press; typos and mistakes are likely.
Please report any to the instructor.
Here are Kate's notes from the June 29 class:
While the rest of the notes are under
construction, you are invited to consult
prior years' notes.