Math 221: Discrete Mathematics, Winter 2023
Professor: Darij Grinberg
Organization
Course description
This course introduces a range of topics in Discrete Mathematics, including set theory, counting, number theory,
graphs, and cryptography.
Level: undergraduate.
Prerequisites: Math 220 (Introduction to Proofs) or CS 270 (Mathematical Foundations of Computer Science) or ECE 200 (Digital Logic Design).
Course materials
Course calendar
- Note:
- The notes below have evolved into my Introduction to Discrete
Mathematics text (which includes all the material covered in the notes as well as some additions). While the notes below occasionally see corrections, all new development happens only in the just-mentioned text.
- All weeks:
- ZIP archive containing all the lecture notes and assignments listed below.
- Week 0:
- Week 1:
- Week 2:
- Week 3:
- Week 4:
- Week 5:
- Week 6:
- Week 7:
- Week 8:
- Week 9:
- Week 10:
- Lecture 19 (graphs introduction, dominant and independent sets, Hamiltonian paths and cycles).
- Lecture 20 (paths, cycles, trees, coloring).
- For the material of these last two lectures, see my Math 530 notes, which does it all in more detail and with proofs. You are also welcome to attend my Math 530 class this spring!
- No Copyright:
- The above lecture notes and assignments have been released under the CC0 license, i.e., are dedicated to the public domain. They can be copied, modified and distributed without permission. See the license for details.
Grading and policies
- Grading matrix:
- 40%: homework sets. (Your lowest homework score will be dropped.)
- 20%: midterm 1.
- 20%: midterm 2.
- 20%: midterm 3 (due in finals week).
- Grade scale:
- These numbers are tentative and subject to change:
- A+, A, A-: (80%, 100%].
- B+, B, B-: (60%, 80%].
- C+, C, C-: (40%, 60%].
- D+, D, D-: (20%, 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 221 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 submitted electronically via Gradescope. Make sure that what you submit is readable (e.g., your text is not cut off). If there are problems with submission, send your work to me by email for good measure.
- Midterm policy:
- Late midterms will not be accepted unless agreed in advance and with serious justification.
- Collaboration is not allowed on midterms.
- Everything else is the same as for homework (yes, midterms are take-home).
- Expected outcomes:
- The students should have gained experience and familiarity with the mainstays of discrete mathematics: the language of sets and maps; proofs by induction; basic principles of enumeration; graphs and their major features; integers and their divisibility properties; prime numbers and possibly their use in cryptography.
Other resources
- Homework help:
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- University policies:
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- Disability resources:
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