Math 222: Enumerative Combinatorics, Fall 2019
Professor: Darij Grinberg
Organization
- Classes:
- Classes are over!
- Office hours:
- Tuesday 14:00--16:00, Thursday 13:00--14:00 in Korman Center #263. Also by appointment.
- Blackboard:
- Blackboard site for Math 222.
- Instructor email:
- darij.grinberg@drexel.edu
- Mailbox:
- Mathematics Common Room (Korman Center, 2nd floor).
Course description
An introduction to enumerative combinatorics covering binomial coefficients, bijective proofs, the twelve-fold way, inclusion-exclusion, permutations, partitions and generating functions. Emphasis on proof writing.
Prerequisites: Math 220.
Course materials
- Required:
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- Recommended:
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- Remedial:
- [LeLeMe]: Eric Lehman, F. Thomson Leighton, Albert R. Meyer, Mathematics for Computer Science, 2018: a great introduction to rigorous mathematics. Chapters 1--5 cover the Math 220 basics we will need: proofs, sets, relations, in/sur/bijections. Later chapters go into topics, even covering a bit of what we will do in this course.
- [Newstead]: Clive Newstead, An Infinite Descent into Pure Mathematics: introduction to proofs and mathematical thinking. (Work in progress.)
- Richard Hammack, Book of Proof: introduction to proofs.
- A list of undergraduate-level texts and notes on proofs (freely accessible).
- Further:
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Course calendar
- Week 1:
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- Week 2:
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- Week 3:
- Material covered: Counting basics.
- Week 4:
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- Week 5:
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- Week 6:
- Material covered: More binomial coefficients, inclusion/exclusion.
- Week 7:
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- Week 8:
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- Week 9:
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- Week 10:
- Material covered: Permutations, odds and ends (only Monday).
- Week 11:
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Grading and policies
- Grading matrix:
- 40%: homework sets (the lowest score will be dropped if all homework sets are submitted).
- 20%: midterm 1.
- 20%: midterm 2.
- 20%: midterm 3.
There will be no final exam.
- Grade scale:
- These numbers are tentative and subject to change:
- A: (80%, 100%].
- B: (60%, 80%].
- C: (40%, 60%].
- D: [0%, 40%].
- Homework policy:
- Collaboration and reading is allowed, but you have to write solutions in your own words and acknowledge all sources that you used.
- Asking outsiders (anyone apart from Math 222 students and Drexel staff) for help with the problems is not allowed. (In particular, you cannot post homework as questions on math.stackexchange before the due date!)
- Late homework will not be accepted. (But keep in mind that the lowest homework score will be dropped.)
- Solutions have to be either handed in at the beginning of class, or submitted electronically (via Blackboard) in a format I can read (PDF, TeX or plain text if it works; no doc/docx!). If you submit a PDF, make sure that it is readable and does not go over the margins.
- This is a proof-based class. All claims have to be proven, unless they were proven in class or are sufficiently elementary to be taken for granted at this level (e.g., uniqueness of prime factorization). Even if the problem asks "find X satisfying A", you will have to prove that your X indeed satisfies A. Solutions will be graded based on both correctness and readability.
- Midterm policy:
- Late midterms will not be accepted unless agreed in advance and with serious justification.
- Everything else is the same as for homework (yes, midterms are take-home), but collaboration is not allowed on midterms.
- Expected outcomes:
- Students will understand and be able to reason about the staples of enumerative combinatorics such as binomial coefficients, permutations, and partitions. Students will have some familiarity with bijective, inductive and algebraic proofs of combinatorial identities, and will have seen various approaches to solving enumeration problems.
Back to Darij Grinberg's teaching page.