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The apprentice problem sets have been consolidated into a single file and separated from the class notes (see below).

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.

**Notes: Class #19 - Fri July 22****Notes: Class #18 - Thu July 21****Notes: Class #17 - Wed July 20****Notes: Class #16 - Tue July 19****Notes: Class #15 - Mon July 18****Notes: Class #14 - Fri July 15****Notes: Class #13 - Thu July 14****Notes: Class #12 - Wed July 13****Notes: Class #11 - Tue July 12****Notes: Class #10 - Mon July 11****Notes: Class #9 - Fri July 8****Notes: Class #8 - Thu July 7****Notes: Class #7 - Wed July 6****Notes: Class #6 - Tue July 5****Notes: Class #5 - Fri July 1****Notes: Class #4 - Thu June 30****Notes: Class #3 - Wed June 29****Notes: Class #2 - Mon June 28****Notes: Class #1 - Mon June 27**

**Apprentice Problems 1-193**. Solutions discussed each Wednesday.

- Instructor's online Discrete Mathematics Lecture Notes:
- For your amusement: 2007 Puzzle Problem sheets: