#
Apprentice Program, Summer 2012 REU
Linear Algebra and Combinatorics

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| Synopsis
| Calendar
| Problem sets
| Notes
| Further reading

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A second set of **
supplementary problems**
has been posted (7/6).

A set of **
supplementary problems**
has been posted. These problems
are directly related to class and most of them have been stated in
class.

Note changes in the __schedules of Weeks 3, 4, 5__ (see "Calendar"
section below). Note especially that
during these weeks, the Tuesday afternoon sessions begin at 4:30pm.

The course will develop the usual topics of linear algebra and
illustrate them on highly unusual and often striking applications
to combinatorics, discrete geometry, and discrete probability.
Emphasis will be on creative problem solving and discovery.
The basic topics include permutations, determinants, linear
transformations, the characteristic polynomial, Euclidean spaces,
orthogonalization, the Spectral Theorem, linear algebra over finite
fields. Application areas to be highlighted include, time
permitting, extremal set theory, the spectral theory of graphs
(expansion, mixing of random walks, independence number, Shannon
capacity, etc.), k-wise independence of events, counting
zero-patterns of polynomial maps, and more.

The course is peppered with a potpourri of fun problems.

The TAs conducting the problem sessions are Rita Jimenez-Rolland
(week 1 only), Jonathan (Jonny) Gleason, Michael Smith,
Vaidehee Thatte, Bobby Wilson, Matthew Wright (starting week 2),
Casey Rodriguez (starting week 3).
Week 1: June 18-22 (MWF 9:30-noon classes by instructor, TTh 11-12, 5-6
problem sessions by TAs)

Week 2: June 25-29 (MWF 9:30-noon classes by instructor, TTh 11-12, 5-6
problem sessions by TAs)

Week 3: July 2-6 (All classes held by instructor: MF 9:30-12, TTh 11-12,
4:30-6. No class on Wed, July 4.)

Week 4: July 9-13 (Problem sessions by TAs MW 9:30-12, TTh 11-12, 4:30-6;
class by instructor Fri 9:30-12)

Week 5: July 16-20 (MWF 9:30-noon classes by instructor, TTh 11-12, 4:30-6
problem sessions by TAs)

Your principal resources are the **online problem sets** listed here.
Solutions are discussed in the problem sessions (schedule above).
Send email to the instructor about the "AHA" problems.
The problem sessions are an integral part of the course; you are
expected to attend and to participate by presenting your thoughts
about the problems.

There is some overlap among these problem sets.
Browse the
**
class notes of the 2011 apprentice program.**
While this year's course is not identical with
the 2011 course, there is a large overlap.

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- Instructor's online Discrete Mathematics Lecture Notes: