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Course Outline
TA: Georgios Tzanakis.
Topics covered in the class
Jan. 6: Introduction & Addition principle, Pigeonhole principle.
Jan. 8: Generalized pigeonhole principle, counting pairs, multiplication rule.
Jan. 13: Euler's Theorem, ordered selections with repetition, ordered selections without repetitions,
Jan. 15: permutations, binomial numbers, properties of binomial numbers.
Jan 20: unordered selection with repetition, binomial theorem.
Jan 22: binomial theorem, sieve principle.
Jan. 27: compute Euler function, designs.
Jan. 29: t-designs
Feb. 3: Partition of a set,
Feb. 5: distributions, multinomial coefficients.
Feb. 10: Multinomial thoerem, partition of integers, power series
Feb. 12: Partial fractions.
Feb. 18-22: reading week.
Feb. 24: Binomial Theorem for negative exponent. generating functions and linear recursion.
Feb. 26: Midterm
Mar. 3: Homogenous linear recursiion.
Mar. 5: Nonhomogenous linear recursion;
Mar. 10: partitions of integers and conjugate partitions
Mar. 12: generating function of partitions of a positive integer.
Mar. 17: restricted partitions.
Mar. 19: graphs, degree sequences, Halmitonian cycles and Eulerian walks.
Mar. 24: Eulerian walks, trees, vertex coloring, planar graphs.
Mar. 26:
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