Week
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Dates
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Lecture Notes
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Homeworks
Due on Thursdays at 12p
in Assignment Box
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1
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Jan. 9--13
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Jan. 9: Introduction
Jan. 11: Product and Sum Rules
Jan. 13: Permutations and Combinations
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Homework 1 (Due Jan. 19)
Solutions
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2
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Jan. 16--20
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Jan. 16: Integer Solutions; (Mistake corrected Jan. 18)
Jan. 18: Integer Solutions;
Jan. 20: Occupancy Problem I
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Homework 2 (Due Jan. 26)
Solutions
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3
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Jan. 23--27
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Jan. 23: Occupancy Problem II;
Jan. 25: Occupancy Problem III:
Jan. 27: Coloring Problem.
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Homework 3 (Due Feb. 9)
Solutions
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4
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Jan. 30--Feb. 3
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Jan. 30: Review I;
Feb. 1: Review II;
Feb. 3: Midterm 1 (Solutions)
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Midterm 1: Average 22.5, Median 24
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5
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Feb. 6--Feb. 10
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Feb. 6: Review of Midterm; Generating functions: Introduction
Feb. 8: Generating functions: Power series, partial fractions
Feb. 10: Generating functions I
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Homework 4 (Due Feb. 16)
Solutions
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6
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Feb. 13--Feb. 17
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Feb. 13: Generating functions II
Feb. 15: Recurrence relations I
Feb. 17: Recurrence relations II
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Homework 5 (Due Mar. 2)
Solutions
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Reading
week
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7
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Feb. 27--Mar. 3
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Feb. 27: Coloring with symmetry: examples
Mar. 1: Groups; Group actions; Burnside's Lemma
Mar. 3: Counting through Burnside's Lemma
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Homework 6 (Due Mar. 9)
Solutions
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8
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Mar. 6--10
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Mar. 6: The permutation group; Polya's theory
Mar. 8: Polya counting
Mar. 10: Review and more examples (Mistake corrected Mar. 10)
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Homework 7 (Due Mar. 23)
Solutions
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9
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Mar. 13--17
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Mar. 13: Review: Generating functions and recurrence relations
Mar. 15: Review: Polya counting
Mar. 17: Midterm 2 (Solutions)
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10
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Mar. 20--24
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Mar. 20: Review of Midterm 2; Introduction to graph theory
Mar. 22: Basics of graphs
Mar. 24: Coloring of graphs
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Homework 8 (Due Mar. 30)
Solutions
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11
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Mar. 27--31
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Mar. 27: Chromatic polynomials
Mar. 29: The 5-color theorem
Mar. 31: Review of Graph Theory and More examples
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Homework 9 (Due Apr. 6)
Solutions
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12
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Apr. 3--7
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Apr. 3: Block Design
Apr. 5: Latin Squares
Apr. 7: Review of the Semester
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13
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Apr. 10--12
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Apr. 10: Final Review I
Apr. 12: Final Review II
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