Chris Natoli

Introduction to Mathematical Proof Workshop

Hunter College, spring 2019, section 01

Resources

Exam stuff

  1. Exam 1 will be in class on March 27. It will cover sets, symbolic logic, direct proofs, induction proofs, and proofs by contrapositive and contradiction. No calculators, notes, or cheat sheets will be allowed. You can find review problems here.
  2. Exam 2 is a take-home exam and is due on May 1. (Solutions.)
  3. The final exam will be on Wednesday, May 22, 11:00–1:00, in the usual room, 204 HW. No calculators, notes, or cheat sheets will be allowed. It will focus on the following topics: proving “if and only if” statements, proofs involving sets, relations, functions, and cardinality of a set. However, it is cumulative in the sense that proof techniques we covered in the first part of the course might be on the final. You can find review problems here.

Workshops

  1. Diagnostic, due February 6
  2. Sets (§§ 1.1–1.8), due February 13
  3. Symbolic logic (§§ 2.1–2.10), due February 20
  4. Direct proof (§ 4), due February 27
  5. Induction (§§ 10.1–10.2, § 10.5), due March 6
  6. Proofs by contrapositive and contradiction (§§ 5.1–5.1, §6.1–6.2), due March 13
  7. Proving equivalences (§ 7.1), proofs involving sets (§ 8), existence and uniqueness, due March 20 (only do the first four problems)
  8. Relations (§§ 11.1–11.4), due April 10
  9. Functions (§ 12), due April 17 (revised version)
  10. Cardinality of a set (§ 14), due May 8

Extra credit

Each extra credit assignment is worth 10% to one of your exam grades (and will roll over to your workshop grade if you have perfect scores on your exams). They are both due by 11:59pm on May 24. I encourage you do to do both!

  1. Look up Russell’s paradox in the textbook, Wikipedia, YouTube, or wherever. Email me one paragraph (no more!) explaining the paradox. Your explanation should include the following sentences:
    • Let $S$ be the set of all sets such that …
    • If $S\in S$, then …
    • If $S\notin S$, then …
    Fill in the blanks. If you're having trouble writing symbols like $\in$, you can just write “is an element of”.
  2. cuny faculty are fighting for $7,000 per three-credit course for adjuncts. In this assignment, you’ll learn about the context of this struggle, who adjuncts are, and why we’re fighting. The assignment itself is just a Google Form with a few questions and a little research. It should take about 30–45 minutes, including a 14 minute introductory video.