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Course Outline
TA: Georgios Tzanakis, Office hours: Wednesday 2-3pm.
Topics covered in the class
Jan. 8: Introduction & Addition principle, Pigeonhole principle.
Jan. 10: Generalized pigeonhole principle, counting pairs, multiplication rule.
Jan. 15: Euler's Theorem, ordered selections with repetition, ordered selections without repetitions,
Jan. 17: permutations, binomial numbers.
Jan 22: properties of binomial numbers, unordered selection with repetition.
Jan 24: binomial theorem, sieve principle.
Jan. 29: compute Euler function, designs.
Jan. 31: t-designs, partition of a set.
Feb. 5: Partition of a set, distributions, multinomial coefficients.
Feb. 7: Power series and partial fractions.
Feb. 12: Generating functions and linear recursion.
Feb. 14: Homogeneous and nonhomogenous linear recursion.
Feb. 18-22: reading week.
Feb. 26: Nonhomogenous linear recursion; Partitions of integers.
Feb. 28: Midterm
Mar. 5: conjugate partitions, generating function of partitions of a positive integer. (Assignment #2 is handed out).
Mar. 7: more examples of generating functions of partitions of a positive integer, restricted partitions.
Mar. 12: recursive formula for p(n), graphs.
Mar. 14: degree sequences, Halmiton cycles and Eulerian Walk
Mar. 19: trees and vertex coloring.
Mar. 21: planar graphs
Mar. 26: plnar graphsm, introduction to coding theory.
Mar. 28: linear codes basics.
Apr. 2: a game on linear codes and Hamming codes.
Apr. 4: correcting 1 error and cyclic codes.
Apr. 9: review.
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