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Course Outline
TA: Goldwyn Miller.
Topics covered in the class
Jan. 7: Introduction & Addition principle, Pigeonhole principle.
Jan. 12: Generalized pigeonhole principle, counting pairs, multiplication rule.
Jan. 14: Euler's Theorem, ordered selections with repetition, ordered selections without repetitions, permutations
Jan. 19: binomial numbers, properties of binomial numbers, unordered selection with repetition.
Jan. 21: count the number of integer solutions, sieve principle.
Jan. 26: derrangements, compute Euler function.
Jan. 28: designs
Feb. 2: t-designs, Partition of a set,
Feb. 4: distributions, multinomial coefficients.
Feb. 9: Multinomial thoerem, partition of integers, power series
Feb. 11: Partial fractions.
Feb. 15-19: reading week.
Feb. 23: Binomial Theorem for negative exponent. generating functions and linear recursion.
Feb. 25: Midterm
Mar. 1: Homogenous linear recursiion.
Mar. 3: Nonhomogenous linear recursion, partitions of integers and conjugate partitions
Mar. 8: generating function of partitions of a positive integer.
Mar. 10: restricted partitions
Mar. 15: graphs, degree sequences, Halmitonian cycles and Eulerian walks.
Mar. 17: Eulerian walks, trees, vertex coloring,
Mar. 22: planar graphs
Mar. 27: planar graphs, introduction to coding theory.
Mar. 29: linear codes basics, a game.
Mar. 31: Hamming codes;
Apr. 5: Decoding 1 error; Cyclic codes.
Apr. 7: Reviews.
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