Math 184 - Enumerative Combinatorics (Winter 2022)


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Notes for course


Lectures will be recorded, see Canvas for the videos.
Jan 4 Sample of problems to be studied in course
Bijections (Section 1.1, 1.2 of notes)
12-fold way (Section 1.3 of notes)
Review of weak induction (Sections 1.4 of notes)
pdf from lecture
Jan 6 Review of strong induction (Section 1.5 of notes)
Permutations (Bona 3.1, notes 2.1)
Words (Bona 3.2, notes 2.2)
pdf from lecture
Jan 11Choice problems (Bona 3.3, notes 2.3)
pdf from lecture
Jan 13Compositions (Bona 5.1, notes 3.1)
Set partitions (Bona 5.2, notes 3.2)
pdf from lecture
Jan 18Integer partitions (Bona 5.3, notes 3.3)
pdf from lecture
Jan 20Binomial theorem (Bona 4.1, notes 4.1)
Multinomial theorem (Bona 4.2, notes 4.2)
pdf from lecture
Jan 25Quiz 1
Jan 27Formal power series (notes 5.1)
pdf from lecture
Feb 1General binomial theorem (notes 5.2)
Linear recurrence relations (Bona 8.1.1, notes 6.1)
pdf from lecture
Feb 3Combinatorial interpretations for OGF (Bona 8.1.2, notes 6.2)
Partition generating functions (notes 6.3)
pdf from lecture
Feb 8Catalan numbers (Bona, Section 6.4 of notes)
pdf from lecture
Feb 10Exponential generating functions (Bona 8.2.1, Section 7.1 of notes)
Products of EGFs (Bona 8.2.2, Section 7.2 of notes)
pdf from lecture
Feb 15Quiz 2
Feb 17Compositions of EGFs (Bona 8.2.3, Section 7.3 of notes)
pdf from lecture
Feb 22Cayley's enumeration of labeled trees (Section 7.4 of notes)
Lagrange inversion formula (Section 7.5 of notes)
pdf from lecture
Feb 24Inclusion-exclusion (Bona 7, Section 8.1 of notes)
pdf from lecture
Mar 1Möbius inversion (Section 8.2 of notes)
pdf from lecture
Mar 3Recreational math problems related to counting
pdf from lecture
Mar 8Quiz 3
Mar 10Review for final
Mar 15Final exam: 11:30AM-2:29PM