CLASS  NOTES

Entire Set of Notes:   dvi   ps   pdf   tex

1. Introduction, Primality Testing, Algebra Review                                                  9/04/02  Sarnak   dvi   ps
2. Notation, Euclid's Algorithm, Lagrange's Theorem, Riemann Zeta Function              9/04/02  Miller     dvi   ps
3. Legendre Symbols, Gary Miller's Primality Test and GRH                                       9/11/02  Sarnak   dvi   ps
4. Cosets, Quotient Groups, and an Introduction to Probability                                    9/11/02  Miller     dvi   ps
5. Efficient Algorithms, Probability, Alg+Transcendental, Pidgeon Hole, Chebychev     9/18/02  Miller     dvi   ps
6. Quadratic Reciprocity (Miller), Central Limit Theorem & Graph Problems (Sarnak) 9/18/02  M, S      dvi   ps
7. More of an Introduction to Graph Theory                                                                9/25/02  Sarnak   dvi   ps
8. Linear Algebra Review, especially Spectral Theorem for Real Symmetric Matrices   9/25/02  M, B      dvi   ps
9. Central Limit Theorem, Spectral Theorem  for Real Symmetric, Spectral Gaps        10/02/02 Sarnak   dvi   ps  
10. Properties of Eigenvalues of Adjacency Matrices of Random Graphs                      10/09/02 Sarnak   dvi   ps
11. Spacings of Eigenvalues of Real Symmetric Matrices; Semi-Circle Law                   10/09/02 Miller    dvi   ps
12. More Graphs, Maps mod p, Fourier Series and {n alpha}                                       10/16/02 M, S     dvi   ps
13. Notes on Constructing Transcendentals and Poissonian Behavior                             10/16/02 Miller    dvi   ps   pdf
14. More Graphs, Randomness of x to x^{-1} mod p                                                   10/23/02 Sarnak  dvi   ps
15. Introduction to the Hardy-Littlewood Circle Method                                               10/23/02 Miller    dvi   ps   pdf
16. Articles on Kloosterman: Heath-Brown  and  Sarnak
17. Multiplicative Fns, Kloosterman Bounds, p-adic Numbers, Review of 3 Problems   10/30/02 Sarnak  dvi   ps
18. Notes on Kloosterman Sums (Handout)                                                                  11/05/02 Barnett dvi   ps
19. Random Graphs, Autocorrelations, and Correlations and Densities (RMT)              11/06/02 Sarnak  dvi   ps
20. The Circle Method and Germaine Primes                                                                11/18/02 Miller    dvi   ps   pdf
21. Increasing Length Subsequences and Tracy-Widom                                                11/20/02 Sarnak  dvi   ps

REFERENCES

1. Week 1 (9/04/02):  Euclidean Algorithm   Fermat's Little Theorem   Primality Testing   Carmichael Numbers   Infinitude of Primes   Riemann Zeta Function   Zeta(2) = pi^2/6
2. Week 2 (9/11/02):  Wilson's Theorem   Legendre Symbol   Quadratic Reciprocity   Eisenstein's Proof   Jacobi Symbol   Probability   Poisson Distribution
3. Gary Miller's Test   Chinese Remainder Theorem   Prime Number Theorem   Cyclic Groups   Abelian Groups   Structure Theorem for Abelian Groups   Quotient Group
4. Sampling Random Graphs (Sergei Maslov) -- Matlab Code

General References:  Math World    Introduction to Number Theory