Syllabus
Gradescope
Class Notes
LaTeX Homework Template
Google Drive (has all in-class activities and homework)
Office hours: Wednesday 10-11am, or by appointment, in MATH 223. You are also welcome to drop by on Mondays and Wednesdays between 4:30 and 6; I have office hours for MATH 2510, so I have to prioritize students in that class, but as long as it's not too busy I can help you too.
Monday, February 23
Today in class we worked with Cartesian products and disjoint unions.
Homework #14 is due at 2pm on Monday on Gradescope. Your solutions must be typed in LaTeX. When you submit your solutions on Gradescope, make sure to select pages for each question.
Before class on Wednesday, please read section 1.2 of Book of Proof.
Revisions 2/16-2/22, Revisions 2/23-3/1, and Assessment 4 have been graded. Please view the comments I left on your assessment in Gradescope. Reflect on the aspects of your responses that need improvement, and let me know if there's anything that you don't fully understand. For each homework problem, if I indicated that your solution did not meet expectations, you should revise and resubmit it.
Revisions are due on Sunday (March 8) for any problems you turned in to the "Revisions 2/16-2/22" assignment that need another round of revision. Please carefully read the instructions for submitting revised homework and turn them in to the Revisions 3/2-3/8 assignment on Gradescope.
Friday, February 27
Today in class we discussed cardinality, union, intersection, and difference of sets.
Homework #13 is due at 2pm on Monday on Gradescope. Your solutions must be typed in LaTeX. When you submit your solutions on Gradescope, make sure to select pages for each question.
Before class on Monday, please read sections 1.5-1.7 of Book of Proof.
Wednesday, February 25
Today in class we practiced describing sets by listing their elements or with set-builder notation.
Before class on Friday, please read section 1.1 of Book of Proof.
As a reminder, we will have an in-class assessment on Friday at the end of class. This will be the second assessment on Unit 2.
Monday, February 23
Today in class we practiced (dis)proving statements involving quantifiers or biconditional statements.
Before class on Wednesday, please read section 7.1 of Book of Proof.
We will have an in-class assessment on Wednesday at the end of class. It will cover the topics listed on the Unit 3 page of the class notes.
We will have an in-class assessment on Friday at the end of class. This will be the second assessment on Unit 2.
Homework 11 and Revisions 2/9-2/15 have been graded. Please view the comments I left on your assessment in Gradescope. Reflect on the aspects of your responses that need improvement, and let me know if there's anything that you don't fully understand. If I indicated that your solution did not meet expectations, you should revise and resubmit it.
Revisions are due on Sunday (March 1) for Homework 10, Homework 11, and any problems you turned in to the "Revisions 2/9-2/15" assignment that need another round of revision. Please carefully read the instructions for submitting revised homework and turn them in to the Revisions 2/23-3/1 assignment on Gradescope.
Friday, February 20
Today in class we talked about how to disprove (false) mathematical statements.
Homework #12 is due at 2pm on Monday on Gradescope. Your solutions must be typed in LaTeX. When you submit your solutions on Gradescope, make sure to select pages for each question.
Before class on Monday, please read section 2.10, section 7.3, and chapter 9 of Book of Proof. In section 7.3, you can stop before Proposition 7.1. Sections 2.9, 2.11, and 2.12 are also recommended but not required.
As a reminder, homework revisions are due on Sunday night. See Monday's entry for details.
Wednesday, February 18
Today in class we discussed how to prove statements with "for all" or "there exists", and we looked at a particular example of proving that a function is differentiable.
Before class on Friday, please read section 2.7 and 2.8 of Book of Proof.
There is no new homework assignment; instead, please review the proof we wrote in class today and do your best to understand the logical structure of the proof.
Homework 10 and Assessment 3 have been graded. Please view the comments I left on your assessment in Gradescope. Reflect on the aspects of your responses that need improvement, and let me know if there's anything that you don't fully understand. For each homework problem, if I indicated that your solution did not meet expectations, you should revise and resubmit it.
Monday, February 16
Today in class we used truth tables to explore logically equivalent statements.
Homework #11 is due at 2pm on Wednesday on Gradescope. Your solutions must be typed in LaTeX. When you submit your solutions on Gradescope, make sure to select pages for each question.
Before class on Wednesday, please read section 2.6 of Book of Proof.
Homework 4 has (finally!) been graded. Please view the comments I left on your assessment in Gradescope. Reflect on the aspects of your responses that need improvement, and let me know if there's anything that you don't fully understand. If I indicated that your solution did not meet expectations, you should revise and resubmit it.
Revisions are due on Sunday (February 22) for Homework 4, Homework 6, Homework 7, and any problems you turned in to the "Revisions 2/2-2/8" assignment that need another round of revision. Please carefully read the instructions for submitting revised homework and turn them in to the Revisions 2/16-2/22 assignment on Gradescope.
Friday, February 13
Today in class we started working with truth tables, and we took an assessment on Unit 2.
Homework #10 is due at 2pm on Monday on Gradescope. Your solutions must be typed in LaTeX. When you submit your solutions on Gradescope, make sure to select pages for each question. Here is some LaTeX code that you can use as a template for a truth table.
Before class on Monday, please read sections 2.1-2.5 of Book of Proof.
Revisions for Homework 5 are due on Sunday night on Gradescope. Please carefully read these instructions before submitting revisions.
Wednesday, February 11
Today in class I gave you some time to finish Monday's activity, work on homework (or revisions), and prepare for Friday's assessment.
Homework #9 is due at 2pm on Friday on Gradescope. Your solutions must be typed in LaTeX. When you submit your solutions on Gradescope, make sure to select pages for each question.
We will have an in-class assessment on Friday at the end of class. It will cover the topics listed on the Unit 2 page of the class notes.
Homework 7 has been graded. Please view the comments I left on your assessment in GradescopeReflect on the aspects of your responses that need improvement, and let me know if there's anything that you don't fully understand. If I indicated that your solution did not meet expectations, you should revise and resubmit it. Revisions for Homework 5 are due this Sunday (February 15). Revisions for Homework 6 are and Homework 7 are due the following Sunday (February 22), but you're welcome to submit them with this week's revisions. Please carefully read the instructions for submitting revised homework before turning in your revisions on Gradescope.
Monday, February 9
Today in class we wrote our first proof by contradiction.
Homework #9 is due at 2pm on Friday (not Wednesday!) on Gradescope. Your solutions must be typed in LaTeX. When you submit your solutions on Gradescope, make sure to select pages for each question.
Before class on Wednesday, please read chapter 6 of Book of Proof, which discusses proof by contradiction.
Homework 6 has been graded. Please view the comments I left on your assessment in Gradescope (you'll need to click each question's number to view the comments). It is very important that you read all of the comments (even if I indicated that your response met expectations); this feedback is the primary way that you will improve your mathematical abilities in this class! Reflect on the aspects of your responses that need improvement, and let me know if there's anything that you don't fully understand. If I indicated that your solution did not meet expectations, you should revise and resubmit it. Revisions for Homework 5 are due this Sunday (February 15). Revisions for Homework 6 are due the following Sunday (February 22), but I strongly recommend completing them by this coming Sunday. Please carefully read the instructions for submitting revised homework before turning in your revisions on Gradescope.
Friday, February 6
Today in class we practiced writing the contrapositives and converses of mathematical statements, and we took the second assessment on Unit 1.
Homework #8 is due at 2pm on Monday on Gradescope. Your solutions must be typed in LaTeX. When you submit your solutions on Gradescope, make sure to select pages for each question.
Before class on Monday, please read section 5.2 and 5.3 of Book of Proof. Section 5.2 introduces congruence modulo n (also known as modular arithmetic); in addition to being an incredibly important and versatile mathematical concept, it will give us something to practice writing proofs about other than even and odd integers!
Now that you're getting homework assignments back with feedback, you can start revising your solutions which I indicated did not meet expectations. Each week there will be a Gradescope assignment where you can turn in homework revisions up until Sunday night (technically, any time before 8am on Monday). Whenever you get homework back with feedback, you can revise it up until the first Sunday night which is at least a week after you got it back. For example, you got Homework 5 back on Wednesday, and I aim to finish grading Homework 6 this weekend; that means that for both Homework 5 and 6 you have until Sunday, February 15 to submit revisions.
When you submit revisions on Gradescope, please clearly mark each problem with both the problem number and the number of the homework assignment that it came from. You also need to select pages for your solutions. I will list Questions 1 through 6 on each revision assignment; just select a different question number for each of your revised problems (it doesn't matter which numbers). If you ever need to submit more than six revised problems in a week, let me know.
Wednesday, February 4
Today in class we discussed contrapositives and converses.
Homework #7 is due at 2pm on Friday on Gradescope. Your solutions must be typed in LaTeX. When you submit your solutions on Gradescope, make sure to select pages for each question.
Before class on Friday, please read section 5.1 of Book of Proof.
Homework 5 has been graded. Please view the comments I left on your assessment in Gradescope (you'll need to click each question's number to view the comments). It is very important that you read all of the comments (even if I indicated that your response met expectations); this feedback is the primary way that you will improve your mathematical abilities in this class! Reflect on the aspects of your responses that need improvement, and let me know if there's anything that you don't fully understand. If I indicated that your solution did not meet expectations, you have one week to revise and resubmit it; instructions for resubmitting it will be provided soon.
We will have our second in-class assessment on Friday at the end of class. It will cover the topics listed on the Unit 1 page of the class notes.
Monday, February 2
Today in class we worked through a couple examples of direct proof using multiple cases.
Homework #6 is due at 2pm on Wednesday on Gradescope. Your solutions must be typed in LaTeX; you can use this template. When you submit your solutions on Gradescope, make sure to select pages for each question. I will be lenient about this for the first few assignments, but after that I will not accept submissions which don't have pages marked. As a hint, both questions will require you to use cases, and for the second question you'll need to use some of the facts on the Foundations page in the class notes.
Before class on Wednesday, please reread sections 4.4 and 4.5 of Book of Proof.
The assessment from last Friday has been graded. Please view the comments I left on your assessment in Gradescope (you'll need to click each question's number to view the comments). It is very important that you read all of the comments (even if I indicated that your response met expectations); this feedback is the primary way that you will improve your mathematical abilities in this class! Reflect on the aspects of your responses that need improvement, and let me know if there's anything that you don't fully understand.
We will have our second in-class assessment on Friday at the end of class. It will cover the topics listed on the Unit 1 page of the class notes.
Friday, January 30
Today in class, we had our first assessment. I will upload the assessments to Gradescope, and you'll get an email notification once I've graded them.
Wednesday, January 28
Today in class, we continued working on the activity from Monday.
There is no new homework assignment. Use your time to prepare for Friday's assessment.
We will have our first in-class assessment on Friday at the end of class. It will cover the topics listed on the Unit 1 page of the class notes, except for writing a proof by analyzing multiple cases. Among other things, the assessment will ask you to state definitions of some of the terms listed on the Unit 1 page. You don't need to memorize the definitions word for word, but you do need to produce definitions that are mathematically precise, complete, and correct.
Monday, January 26
Today in class, we worked on writing direct proofs.
Homework #5 is due at 2pm on Wednesday on Gradescope. Your solutions must be typed in LaTeX; you can use this template. When you submit your solutions on Gradescope, make sure to select pages for each question. I will be lenient about this for the first few assignments, but after that I will not accept submissions which don't have pages marked.
Before class on Wednesday, read sections 4.4 and 4.5 of Book of Proof.
We will have our first in-class assessment on Friday at the end of class. It will cover the topics listed on the Unit 1 page of the class notes.
Friday, January 23
Today in class we discussed the homework that was due today, the course website (there are some new links at the top of the page!), the syllabus and the structure of the course, and one example of a direct proof.
Homework #4 is due at 2pm on Monday on Gradescope. Your solutions must be typed in LaTeX; you can use this template. When you submit your solutions on Gradescope, make sure to select pages for each question. I will be lenient about this for the first few assignments, but after that I will not accept submissions which don't have pages marked.
Look over the Foundations page in the class notes, which provides a fairly thorough list of the basic mathematical facts which we will use throughout this course. This is meant to serve as a reference, not something you need to memorize (but you will need to use many of these facts throughout the semester when you write proofs).
Look over the Unit 1 page of the class notes, which outlines the topics that we will cover in the first portion of the course, over the next week or so.
Before class on Monday, read sections 4.1-4.3 of Book of Proof. (I will ask you to read sections 4.4 and 4.5 before class on Wednesday, so you may wish to read ahead if you have time over the weekend.) Don't worry too much about the discussion of the truth table for P ⇒ Q on p. 118 (we will return to this when we cover Chapter 2) or the proof that lcm(ca, cb) = c * lcm(a, b) on p. 122 (this is a difficult proof).
We will have our first in-class assessment next Friday at the end of class. It will cover the topics listed on the Unit 1 page of the class notes.
If you haven't yet, please do read the syllabus, or at least the first three pages (the remainder is general university policies). If you have any questions about the structure of course, please let me know.
Wednesday, January 21
Today in class we proved that the sum of two even integers is even. The proofs you wrote during class can be found here. The most important takeaway is that proving something is much easier when you work with precise definitions of all relevant terms (in this case, even).
Please read the syllabus, or at least the first three pages (the remainder is general university policies). If you have any questions about the structure of course, please let me know.
The polynomial f(n) = n^2 + n + 41 generates prime numbers when n is a non-negative integer. For example, the first few outputs are 41, 43, 47, 53, 61, 71, 83, ... . Try to work out an argument that f(n) is prime for all non-negative integers n. If you don't come up with a complete proof of this fact, write up a thorough description of everything that you tried, whether or not it seemed to make progress. Turn this in on Gradescope by 2pm on Friday.
As discussed in the syllabus, you may work with your classmates, but you may not search the internet or use AI, even just to look for a hint. If you're spinning your wheels for more than an hour, reach out to me for a hint.
Friday, January 16
Today in class we worked in groups to write a proof that the number of tilings from Monday's activity is indeed given by the Fibonacci numbers. Here are the proofs from class.
There is no homework today.
Wednesday, January 14
Today we did this activity in class, introducing the mathematical typesetting software LaTeX. If you don't finish the activity in class, please work through the rest of it outside of class (you can skip #8). Either way, turn in the resulting PDF file (which you can download from Overleaf) on Gradescope by 11:59pm on Friday.
See Monday's entry for the assignment due at 2pm on Friday.
Monday, January 12
We did this activity in class today. We saw that the numbers of tilings are given by Fibonacci numbers, and we briefly discussed why that is the case. Write a mathematical argument demonstrating that this is correct (for all values of n), and submit it on Gradescope by 2pm on Friday. This should probably take you a paragraph or two. Don't stress about the formatting or notation; focus on communicating the ideas clearly, and aim to make it easily readable to your peers. Please also bring a copy, either printed or digital, to class on Friday; we will work in small groups and as a class to refine our writing into a rigorous mathematical proof.
Please bring a laptop to class on Wednesday, since you will be learning how to use LaTeX.
Friday, January 9
We met on Zoom today and discussed the goals of the course.