Math 235: Mathematical Problem Solving, Fall 2020
Professor: Darij Grinberg


Organization

Classes:
Videos: up late Monday on this site (see Course Calendar below).
Recitations: Tue 3:00--3:40 PM (repeated Wed 3:30--4:10 PM) on https://drexel.zoom.us/j/2350700617.
Office hours:
Fri 1:00--2:00 PM and Sun 1:00--2:00 PM on https://drexel.zoom.us/j/2350700617. Also by appointment.
Notes:
Notes on mathematical problem solving.
Gradescope:
https://www.gradescope.com/courses/193396.
Piazza:
https://piazza.com/drexel/fall2020/235.
Instructor email:
darij.grinberg@drexel.edu

Course description

An introduction to mathematical problem solving. We will learn techniques and tools for solving problems of the kind that appear in mathematical competitions and journals. These techniques (like induction, the Pigeonhole Principle, modular arithmetic or the Cauchy-Schwarz inequality) have uses all over mathematics; we will explore these uses through hands-on problem solving.

Each week will have approx. 50 minutes of video lectures (see the "Course materials" below for the links) and 40 minutes of recitations (i.e., collaborative problem-solving sessions over Zoom). Weekly homework sets will reinforce the training.

Prerequisites: Math 200.

Course materials

Required:
Recommended:
Contests:

Course calendar

Week 1:
Week 2:
Week 3:
Week 4:
Week 5:
Week 6:
Week 7:
Week 8:
Week 9:
  • Video lectures (corresponding to Sections 7.5--7.8 of the notes).
  • Homework set 8 is not to be handed in. The problems are in the notes (Section 8.3).
Week 10:

Grading and policies

Grading matrix:
  • 100%: homework sets. (Homework set #0 is worth 20 points; homework set #8 is worth 0 points; each remaining homework set is worth 50 points.)
Grade scale:
These numbers are tentative and subject to change:
  • A: (50%, 100%].
  • B: (40%, 50%].
  • C: (20%, 45%].
  • D: [0%, 20%].
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 235 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.
  • Solutions have to be submitted electronically via Gradescope 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. If there are problems with submission, send your work to me by email for good measure.
Expected outcomes:
Students should have obtained some hands-on experience solving competition-type mathematical problems. They should be aware of standard problem solving techniques in mathematics (such as the pigeonhole and extremal principles) and be familiar with examples of their application.

Other resources

Homework help:
  • Math Resource Center (Zoom registration link; use your Drexel email), open Mon-Thu: 10:00 am - 7:00 pm and Fri: 10:00 am - 4:00 pm. Starts September 23rd.
University policies:
Disability resources:
Writing center: