Math 184 - Enumerative Combinatorics (Fall 2023)

Notes for course

Homework

Submit homework through Gradescope.
Each homework is due Wednesday night by 11:59PM.
Assignments are always posted at least 7 days before due date. Computational problems will have answers for special cases on the last page along with hints when available.
If you do not get the right answer, I highly recommend figuring how what you did wrong before turning in your assignment.
Solutions will be posted on Canvas on Saturdays. Look under "Files".

Exam materials

Schedule

The schedule is based on past experience teaching the course.
I've changed a few topics so the pacing might change a little, and I will update this as we go.
Not everything fits neatly into a single lecture, so interpret a listed topic to mean that we plan to start discussing it that day.

Podcasts of the lectures are posted to Canvas. See "media gallery".
Sep 29Sample of problems to be studied in course
Bijections (Section 1.1, 1.2 of notes)
Week 1
Oct 2 12-fold way (Section 1.3 of notes)
Review of induction (Bona 2.1, notes 1.4)
Permutations (Bona 3.1, notes 2.1)
Oct 4 Words (Bona 3.2, notes 2.2)
Oct 6 Choice problems (Bona 3.3, notes 2.3)
Week 2
Oct 9Compositions (Bona 5.1, notes 2.4)
Oct 11 12-fold way, summary so far
Set partitions (Bona 5.2, notes 3.1)
HW1 due
Oct 13 Falling factorials (Section 3.2 of notes)
Week 3
Oct 16Cycles in permutations (Section 3.3 of notes)
Oct 18 Binomial theorem (Bona 4.1, notes 4.1)
Multinomial theorem (Bona 4.2, notes 4.2)
HW2 due
Oct 20Formal power series (notes 5.1)
Week 4
Oct 23General binomial theorem (notes 5.2)
Linear recurrence relations (Bona 8.1.1, notes 6.1)
Oct 25Midterm 1
Oct 27Linear recurrence relations continued
Week 5
Oct 30Partition generating functions (Bona 5.3, notes 6.2)
Nov 1Partition generating functions continued
HW3 due
Nov 3Catalan numbers (Bona 8.1.2.1, Section 6.3 of notes)
Week 6
Nov 6continue
Nov 8 Products of exponential generating functions (Bona 8.2.1, 8.2.2, Section 7.1 of notes)
HW4 due
Nov 10 Holiday - no class
Week 7
Nov 13Compositions of EGFs (Bona 8.2.3, Section 7.2 of notes)
Nov 15continue
HW5 due
Nov 17 Review
Week 8
Nov 20Midterm 2
Nov 22Cayley's enumeration of labeled trees (Section 7.3 of notes)
Nov 24 Holiday - no class
Week 9
Nov 27 Lagrange inversion formula (Section 7.4 of notes)
Nov 29 Inclusion-exclusion (Bona 7, Section 8.1 of notes)
Dec 1Continue
Week 10
Dec 4Möbius inversion (Section 8.2 of notes)
Dec 6Catchup
HW6 due
Dec 8Review
Finals week
Dec 13Final exam: 3-6PM Pepper Canyon Hall 109
Note: this is not the usual lecture location!