Math 220: Mathematical Reasoning and Proof (Spring 2020)

This course serves as an introduction to mathematical reasoning and pays particular attention to helping students learn how to write proofs. The topics covered may include logic, elementary set theory, functions, relations and equivalence relations, mathematical induction, sequences, and quantifiers.

Remote learning

Following the transition to remote learning after Spring break, the structure of the course will be changed as follows.

  • We will have synchronous class meetings via Zoom at 9am on Mondays and Fridays. See the Zoom link on the course moodle page for access.
  • Several pre-recorded videos will be posted on Tuesdays and Wednesdays. You may access these from the Dropbox link sent out by email (also linked from the Moodle page).
  • Office hours: during my scheduled office hours (below), I will be actively monitoring the class’s Slack channel, answering questions, and opening Zoom discussions as needed. Please set a message to the channel or to me privately if you would like to start a Zoom meeting.
  • The remaining exams will be open-book take-home exams (see below for details).
  • We will almost certainly cover less material this semester than was originally planned on the syllabus, due to the extraordinary circumstances. My primary concern as the instructor right now is to prioritize the main learning goals of Math 220: giving you practice and challenges to develop your proof-writing and problem solving skills so that you are prepared for future courses.

Help hours

  • My office hours in SMUD 401 on Slack and Zoom:
    • Visit Slack to ask questions, either as private messages to me or on the group channel.
    • Just ask if you want to start a Zoom meeting to discuss anything.
    • I will check Slack periodically throughout the day, but am guaranteed to be actively monitoring, and available to meet on Zoom, at the times below.
      • Monday 1:00-2:00
      • Tuesday 1:45-3:15
      • Wednesday 1:45-3:15
      • Friday 1:00-2:00
  • Allison Randy-Cofie’s Q Fellow help hours:
  • Jonah Botvinick-Greenhouse’s Math Fellow help hours:
    • Access from this Zoom link
    • Monday 7-9pm in SMUD 007 on Zoom
    • Wednesday 7-9pm in SMUD 007 on Zoom

Handouts and other items

LaTeX resources

  • Allison Tanguay’s LaTeX resource page
  • Overleaf LaTeX tutorials: some tutorial videos and other links about learning LaTeX. These focus on using Overleaf, an online platform to write LaTeX documents online without installing any software.
  • Overleaf Primer by Kristin Heysse (Macalester). Another tutorial on writing in LaTeX on Overleaf.
  • Detexify: this is an absurdly useful tool that allows you to sketch a symbol and quickly learn the LaTeX command for it.

Homework

Problem sets will be posted here. All problem sets are due at 10pm, via Gradescope.

Exams

  • Midterm 1: Monday 3/9, in class.

    • Remember to make a one-page note-sheet (front and back)!

    • The exam covers all material up to Monday 3/2, including anything on PSets 1 through 5.<li>Some sample exams from From 2019: Sample 1, Sample 2</li>

      • Solutions
      • Note: the format and difficulty of these is similar to what our exam will be like, but the topic emphasis may be slightly different.
    • Study items list (only items from PSets 1 to 5 are relevant for this exam).
    • Exam / Solutions

  • Midterm 2: Monday 4/27, in class distributed Monday 4/27 10pm, due Wednesday 4/29 10pm (Eastern time).

    • The exam will be untimed, open-book and open-notes. You will be expected not to discuss problems with any other students, or to look for solutions online.
    • You will have 48 hours to complete the exam.
    • The exam will be similar in length to a 50-minute in-class exam.

    • Some practice materials from Spring 2019:

      • Note: in Spring 2019, there were three midterms. I’ve provided samples from midterms 2 and 3 from that semester, which cover similar material to what is on our midterm 2, but also cover some material that was on our midterm 1.
      • Samples exams: Sample 1 Sample 2 Sample 3 Sample 4
      • (Solutions to sample exams will be posted in the next several days)
      • Practice problems: Batch 1 Batch 2
    • Study items list (only items from PSets 6 and after are relevant for this exam).<li>Exam / Solutions</li>

  • Final Exam: distributed Monday 5/11 at 5pm, due Thursday 5/14 at 5pm (Eastern time).

    • The exam will be untimed, open-book and open-notes. You will be expected not to discuss problems with any other students, or to look for solutions online.
    • You will have 72 hours to complete the exam.
    • The exam will be similar in length to a regular three-hour final exam.

    • Some exams and practice problems from prior years. I’ve redacted parts of these to remove topics we didn’t cover this year; note that the other parts may still have difference emphasis than our course. Note in particular that sequences/convergence were not covered in these prior years.