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 prerecorded 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 openbook takehome 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 proofwriting and problem solving skills so that you are prepared for future courses.
Help hours
 My office hours
in SMUD 401on 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 1:002:00
 Tuesday 1:453:15
 Wednesday 1:453:15
 Friday 1:002:00
 Allison RandyCofie’s Q Fellow help hours:
 Access from this Zoom link
 MondayThursday 1:304:30
in SMUD 007on Zoom  Friday 10:0012:00
in SMUD 007on Zoom  Or schedule an appointment
 Jonah BotvinickGreenhouse’s Math Fellow help hours:
 Access from this Zoom link
 Monday 79pm
in SMUD 007on Zoom  Wednesday 79pm
in SMUD 007on Zoom
Handouts and other items
 Syllabus
 2/5: Worksheet: logical symbols / Solutions
 2/17: Worksheet: Induction leadin / Solutions
 2/24: Worksheet: Pigeonhole / Solutions
 Prove It, a chapter from the book The Art of Problem Solving (a concise summary of the proof techniques we discuss in this course, with a number of nice problems)
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.
 Course survey and Gradescope instructions (due 1/31)
 Problem Set 1 (due 2/5)
 Problem Set 2 (due 2/12)
 Problem Set 3 (due 2/19)
 Problem Set 4 (due 2/26)
 Problem Set 5 (due 3/4)

Problem Set 6 (due
3/253/30) Proof Portfolio Entry 1 Template (see last page of PSet 6 for more detailed instructions)
 Problem Set 7 (due 4/3)
 Problem Set 8 (due 4/8)
 Problem Set 9 (due 4/15)
 Problem Set 10 (due 4/22)
 Not to hand in: Problem Set 11 (for review and practice only) / Solutions
Exams

Midterm 1: Monday 3/9, in class.
 Remember to make a onepage notesheet (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 classdistributed Monday 4/27 10pm, due Wednesday 4/29 10pm (Eastern time). The exam will be untimed, openbook and opennotes. 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 50minute inclass 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, openbook and opennotes. 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 threehour 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.