Math 220P

Course Materials

Uploaded 1/17/20

Uploaded 1/17/20

Uploaded 1/17/20

Uploaded 1/17/20

Transition to Distance Learning

[Monday, March 16]

(1) We are going to use Google Classroom for submitting daily assignments and for distributing grades. The code for our Google Classroom is qjdehep. Please sign up as soon as possible.

If you have not used Google classroom previously, you can find instructions on how to claim your Google Apps for Education account at After claiming your account, you should then be able to sign on to Google Classroom under the username of the form “”. You can then join our Google Classroom using the code qjdehep.

You cannot use your personal Google account, you must use your CAMS account to sign in.

(2) For virtual meetings, both during class time and one-on-one, I will be using Zoom. It is a free application available on pretty much any device you want to use. Again, you do not need to pay for Zoom. Please download this software.

[Wednesday, March 18] I have posted the materials for Monday's lecture on Google Classroom. This includes an activity sheet, just like we always have, at your convenience. Along with the activity sheet is posted a video with me going over the worksheet as well as a PDF of the my completed sheet.

During the live video session on Monday, we can discuss the worksheet, exercises, or anything you like.

[Friday, March 20] For several reasons, I've decided I am going to keep updating this website on top of using Google Classroom, so you should be able to find all relevant information for the course in both places (but, daily prep assignments should be submitted on Google Classroom.)

I am going to post materials as I prepare them, so you will be able to find several days worth of lectures, activities, and daily preps. You should feel free to go as far into the future material as you like, but our live video discussions will only focus on that day's given content (or prior content) so that everyone is on the same page.

[Tuesday, March 24] Below is information regarding our second exam. Here is the plan:

  • Exam 2 will be a “take-home” exam.
  • Exam 2 will cover Sections 3.5, 4.1–4.3, and 5.1–5.3.
  • I will post the exam on Google Classroom (and the course website) Wednesday, April 15 around 9am. You will either print the exam or complete it digitally (for instance, if you have a tablet), complete the exam, scan it (either using a scanner or using a scanning app on a smartphone), and submit it on Google Classroom (or email it to me) by the beginning of class Monday, April 20.
  • As far as resources go, you may use the textbook and any course notes/materials. You may not discuss the test with anyone nor use the internet.
  • I reserve the right to request a one-on-one meeting with any student and ask that student to explain their work. If they cannot explain their work (or refuse to do so), they will not receive credit.
  • We will have a regular day on Monday, April 13; meaning, there will be a Daily Prep and a live video session.
  • There will be no live video session and no daily prep or proof draft due on Wednesday, April 15 (you should think of this as a test day).
  • Remember that the exam questions will be exercises from the book, so you should be working on these exercises. You can feel free to ask questions about exercises during the live video sessions if you like.

Our third and final exam will follow similar guidelines.

[Sunday, May 3] Information for Exam 3: first, let me you remind you that the third exam is not cumulative. It will cover sections 5.4, 6.1–6.5, and 7.1–7.3. Exam 3 will be distributed during the afternoon of Friday, May 15 (by 5pm) and it will be due Tuesday, May 19 at 11:59pm. This time frame encompasses the time slot for the course's final exam given by the college—which would have been on Monday, May 18. The exam taking process will be identical to that of the second exam.

Course Log

Week 1: 1/27–1/31

[Monday, Jan. 27] Notes

Welcome to the Math 220P Webpage! In today's class we will go over some of the basics for the class and jump right into our first activity, which will go over material from Section 1.1 in the textbook.

For next class, complete the Daily Prep listed immediately adjacent to Wednesday's date.

Also, take the time time to carefully read the Syllabus and Daily Prep Guidelines and then sign and turn in the signature page handed to you in class declaring that you have read and understood these documents (if you have questions, make sure I answer them). Another copy of the signature page can be found here. Please turn in this page by Wednesday, February 5.

[Wednesday, Jan. 29] Daily Prep, Notes

Remember to do the Daily Prep for Monday's class: you can find it below under Week 2 next to Monday's date. On Monday, I will handout the first collection of problems for the Proof Portfolio and discuss this project in more detail. In the meantime, head over to and create an account. You will use OverLeaf as an interface for LaTeX in which you will write mathematics.

Regarding CS 220: I have looked up some past syllabi from CS 220 online and they all seem to focus on some of the upper chapters in Rosen's text Discrete Mathematics and Its Applications. Looking at the table of contents, I do believe that our class should provide a solid enough background for CS 220 (in particular, we will have significant overlap with parts of Chapters 1, 2, 4, 5, and 6).

Week 2: 2/3–2/7

[Monday, Feb. 3] Daily Prep, Notes

Today we talked about topics from Sections 2.1 and 2.2. I also handed out Problem Group A for the proof portfolio. You are responsible for submitting one draft of one problem from group A on Monday, Feb. 10 following the guidelines in the Proof Portfolio Guidelines. I have used the provided LaTeX Template above to write a sample proof of a theorem from last Wednesday's class: Here it is. You can either copy and paste the text into your own file over at Overleaf or you can download the file (save it as .tex) and upload it to Overleaf. This should help you get off the ground with LaTex.

Next class we will finish Section 2.2 and move into Chapter 3. Make sure to look over the proof portfolio guideliens and problems so that I can answer any of questiosn in office hours or class on Wednesday.

Also, I forgot to hand back your first Daily Prep assignments from last week. Don't let me forget to do so on Wednesday!

[Wednesday, Feb. 5] Daily Prep, Notes

Remember that you have your first draft due on Monday (Feb. 10) for the proof portfolio.

I misspoke in class today regarding submission of your draft for your portfolio. As stated in the guidelines, you will email me a link to your Overleaf file (it needs to be the "Anyone with this link can edit this project" version). For instructions on how to share via a link, please go to Please see the guidelines for the appropriate subject for your email to me. Once you provide me this link, I will be able to leave comments directly in your document.

Week 3: 2/10–2/14

[Monday, Feb. 10] Daily Prep, Notes

I want to remind you that all questions on exams will be exercises from our textbook. If you have not already started, the upcoming break from class might be a good time to start working through various exercises and make sure you are staying up-to-date.

[Wednesday, Feb. 12] No Class (college closed for Lincoln's Birthday)

For those of you who submitted a draft for the Proof Portfolio, I put some comments into your files that you should address in the next draft. For reference, I gave you score imagining the draft was a final submission in your portfolio.

Week 4: 2/17–2/21

[Monday, Feb. 17] No Class (college closed for Presidents' Day)

[Wednesday, Feb. 19] Daily Prep, Notes

Just to clarify: you have a draft due today, just one draft. It can either be a first draft of your second problem or the second draft of your first problem. It is up to you.

Change in office hours today: I will have an office hour from 12–1pm (instead of 11am–12pm and 4:30–5:30pm).

Note: Our first exam is two weeks from today.

Week 5: 2/24–2/28

[Monday, Feb. 24] Daily Prep

I have left comments on all drafts I received last Wednesday.

[Wednesday, Feb. 26] Daily Prep, Notes

Exam 1 is a week from today on Wednesday, March 4. Remember all problems will come from the exercises in Sundstrom's text. The exam will cover Chapter 1, Chapter 2, and Chapter 3 up through §3.4.

On Monday, we will wrap up any loose ends and spend sometime preparing for the exam (we can work on, talk about or go over exercises from the text), so there will be no Daily Prep for Monday. You still have a draft due as usual.

Finally, as a friendly reminder, attendance is mandatory: unexcused absences will negatively affect your grade.

Week 6: 3/2–3/6

[Monday, March 2] No Daily Prep

Exam 1 on Wednesday. No draft due on Wednesday.

[Wednesday, March 4] Exam 1

Next draft due on Monday, March 9. At some point next week, you will most likely need to start considering problems from Problem Group B. Make sure to do the Daily Prep for next Monday, which covers both Section 3.5 and Section 4.1.

Week 7: 3/9–3/13

[Monday, March 9] Daily Prep, Notes

We will not discuss Section 3.5 in class even though it is part of the day's Daily Prep. We already discussed the main takeaway in this section in last Monday's class, so we will focus on Section 4.1, which discusses induction.

Office Hours: Starting today, my morning office hours on Monday and Wednesday will be moved to 12–1pm (from 11am–12pm) to better accomodate people's schedules. These office hours are now during free hour, so I may occasionally have mandatory meetings in which case I will announce a change in office hours for the day.

[Wednesday, March 11] Daily Prep, Notes

Week 8: 3/16–3/20

No classes.

In accordance with the most recent announcement for CUNY’s transition to online courses, we do not have any official meetings this week. Therefore, any assignments that would be normally due this Monday, March 16 will instead be due Monday, March 23. This includes a Daily Prep assignment and a Portfolio draft.

I will be in touch early next week with information regarding our transition to online only. This will not affect the portfolios, but we will switch to using some online platform (e.g. Blackboard, Google Classroom) to maintain grades and assignment submissions.

I’ll be in touch. Stay safe and have a good weekend.

Week 9: 3/23–3/27

[Monday, March 23] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting

This is our first official day of class after our transition to distance learning.

You should proceed as follows: you should do the Activity sheet on your own and then you can watch the video lecture of me going through the sheet and/or view the sheet I completed in the video under the "Completed Activity Sheet" link. On Monday, during class time (starting at 3:10pm), we will have a live video session through Zoom. You can join the "meeting" by clicking the "Zoom Meeting" link above.

Unrelated, I have created a solution set to the first exam: Exam 1 Solutions.

[Wednesday, March 25] Daily Prep, Activity Sheet, Completed Activity Sheet, Zoom Meeting

The content for today, Section 5.1, is mostly a lot of definitions and notation. I decided not to make a video as I thought the completed activity sheet was enough in this case.

No classes next week, so your next proof draft is due on Monday, April 6.

Week 10: 4/6–4/10

[Monday, April 6] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes

Additionaly, you can see the following document containing formal proofs of two theorems from the worksheet: Sample Proofs. I wanted to give you an example of a formal proof with sets.

[Tuesday, April 7] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes, Zoom Recording

This Tuesday is following a Wednesday's schedule, so we do have class. There is a draft due as usual, but since we had class yesterday, if you need additional time, feel free to submit the draft by Thursday.

Week 11: 4/13–4/17

[Monday, April 13] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes, Zoom Recording

Remember, Exam 2 will be given out on Wednesday, April 15. Please check back here around 9am Wednesday for the exam (or find it on Google Classroom). There is not proof draft or daily prep for Wednesday's class. Also, there will be no live Zoom session on Wednesday as I am viewing that day as an exam day.

[Wednesday, April 15] Exam 2

Some notes about the exam:

  • Please read the instructions carefully, especially regarding what resources you are permitted and not permitted to use. You may use your notes and the materials found on our course website. You are not allowed to use any other internet resources or discuss the exam with anyone else.
  • Please also read the instructions regarding submission of your completed exam.
  • For creating a scan of your final exam, I have created a video of myself using Adobe Scan on my iPhone to create a scan of a document. You can watch the video here: Using Adobe Scan. Adobe Scan is free and available on multiple smartphone platforms and should work similarly on those platforms. You can find out more on the the Adobe Scan website.
  • The exam is due by class time on Monday, April 20.

Remember that we will not have a Zoom meeting today nor is there a draft due. The next portfolio draft is due on Monday, April 20, as well as a daily prep for that day.

Week 12: 4/20–4/24

[Monday, April 20] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes, Zoom Recording

We are now entering the last third of the class and so here is Problem Set C for proof portfolio. Due to a lost class, you now need to complete only nine proofs for the portfolio (as opposed to ten).

[Wednesday, April 22] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes, Zoom Recording

Week 13: 4/27–5/1

[Monda, April 27] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes, Zoom Recording

Here is a formal proof write up of the problem on page 3 of the Activity Sheet: Example Bijection Proof.

[Wednesday, April 29] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes, Zoom Recording

Week 14: 5/4–5/8

[Monday, May 4] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes, Zoom Recording

Your final proof porftolio draft is due on Wednesday, May 6.

[Wednesday, May 6] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes, Zoom Recording

Your proof portfolio is due one week from today on Wednesday, May 13, the last day of class. You should compile all the final drafts of your proofs into one LaTeX file. Each theorem/conjecture should be appropriately labeled. Each problem should start a new page, so after the proof of a theorem and before the beginning of the next theorem/conjecture statement should be the LaTeX command "\newpage".

You should then download the pdf compiled by LaTeX and submit it on Google Classroom, or email it to me if there is difficulty with Google Classroom.

Week 15: 5/11–5/15

[Monday, May 11] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes, Zoom Recording

Remember, the Proof Portfolio is due next class (Wednesday, May 13). Please make sure to carefully proof read your work. The rubric (see the Proof Portfolio Guidelines) is very strict: it assumes you have done two drafts of each proof and that you have carefully proofread.

[Wednesday, May 13] Daily Prep, Activity Sheet, Video Lecture, Completed Activity Sheet, Zoom Meeting, Zoom Notes, Zoom Recording

Last day of class! Exam 3 will be posted here in the afternoon of Friday, May 15.

[Friday, May 15] Exam 3


This course is designed around the course Math 250 taught by Anna Haensch at Duquesne University. Prof. Haensch shared her course materials with me and gave me permission to freely use, edit, and share these materials. I would also like to note that Prof. Haensch's materials were originally based on materials created by Matt Boelkins at Grand Valley State.