6/3 Administration. Probabilistic test for primality. 8/3 Primality finished. Pollard's rho-method for factorization. 14/3 Quadratic sieve for factoring, mentioned some other methods. 15/3 Discrete logarithms. Shanks giant step, baby step method which implied an algoritm that works in time about $\sqrt {q_s}$ where q_s is the largest prime factor in p-1. Introduced the general idea about collecting equations. 22/3 Computing linear equations to compute discrete logarithms mod p. A short description of finite fields. A check that previous algorithms can be used to compute finite logarithms in GF[2^n]. An initial description of Coppersmiths method for finding descrete logarithms in GF[2^n]. 28/3 An final description of Coppersmiths method for finding descrete logarithms in GF[2^n]. 29/3 Factoring polynomials in finite fields. Berlekamps method. First for small fields and then large fields. Implications for solving polynomial equations. In particular the special case of taking squareroots mod p. 5/4 Factoring polynomials over the integers. Proof of some lemmas (factors are integral, bounds on their coefficient). Resultants and their relation to a nontrivial GCD. General outline of how to attack the complete problem. I.e. to find a factorization mod $p^k$ and to find a multiple of a factor with small coefficients. 18/4 Hensel lifting of a factorization. Some general discussion of lattices in dimension 2 and discussion how to extend it to higher dimensions. 19/4 Lovasz basis reduction and how it finishes the algorithm for factoring integer polynomials in worst casee polynomial time. 25/4 Finding the equation given an approximation of an algebraic number. Fast multiplication using FFT. 26/4 Finished the details of fast multiplication. Planarity testing of graphs. 2/5 Finished planarity testing of graphs. Some ideas for finding median in linear time. 3/5 Finding medians in linear time. 9/5 Heuristics for TSP, in particular Lin-Kernighan. Descriptions and some reports on experiments. 10,16,17/5 Fast matrix multiplication in time O(n^{2.67}).