On each homework assignment, please write (i) your name, (ii) name of course, and (iii) homework number. You are allowed and encouraged to work together on homework. Yet, each student is expected to turn in their own work. In general, late homework will not be accepted. However, you are allowed to turn in up to three late homework assignments with no questions asked. Unless you have made arrangements in advance with me, homework turned in after class will be considered late. When doing your homework, I encourage you to use the Elements of Style for Proofs (see Appendix B of the course notes as a reference.

Daily Homework

The following assignments are due at the beginning of the indicated class meeting. However, most assignments will be collected at the end of the class meeting. I reserve the right to modify the assignment if the need arises. These exercises will form the basis of the student-led presentations. Daily assignments will be graded on a $\checkmark$-system. During class, you are only allowed and encouraged to annotate your homework using the colored marker pens that I provide.

Weekly Homework

In addition to the Daily Homework, we will also have Weekly Homework assignments. For most of these assignments, you will be required to submit 2-3 formally written proofs. Typically, two of the problems will come directly from the Daily Homework from the previous week. Any additional problems will likely be new. You will be required to type your submission using LaTeX (see below for more on this). You can either submit a hardcopy of your assignment or email me the PDF of your completed work. If you email me the PDF, please name your file as WeeklyX-Lastname.pdf, where X is the number of the assignment and Lastname is your last name. Notice there are no spaces in the filename.

  • Weekly Homework 1: On the Course Materials page there is a list of videos about growth mindset and productive failure under “Miscellaneous Materials”. Watch “Grit: the power of passion and perseverance” and any other 4 from the list and then write a reflection that is at least 10 sentences long. You should comment on each of the videos you watched, but rather than reflecting on each video separately, try to reflect on growth mindset, productive failure, and grit, in general. You are required to type your reflection in LaTeX. For this assignment, I suggest you use the template on Overleaf found here instead of using the “Start your homework in Overleaf” link below. (Due Thursday, January 25 by 8PM)
  • Weekly Homework 2: Prove two of Theorems 2.29, 2.37, 2.39. You must type up your proofs using LaTeX. I suggest you use my Overleaf template, which you can access by clicking the “Start your homework in Overleaf” link below. (Due Thursday, February 1 by 8PM)
  • Weekly Homework 3: Prove two of Corollary 2.41, Theorem 2.42, Theorem 2.44, Theorem 2.45, Theorem 2.47(a), Theorem 2.47(b), Theorem 2.50, Theorem 2.63. You must type up your proofs using LaTeX. (Due Thursday, February 8 by 8PM)
  • Weekly Homework 4: Complete each of the following tasks. (Due Thursday, February 22 by 8PM)
    • Prove one of Theorems 3.19 and 3.21.
    • Determine whether each of the following statements is true or false. If a statement is true, write a short proof. If a statement is false, justify your reasoning. In each case, the context should make it clear what each letter represents. In particular, in Items 1, 3, and 5, $r$ represents rotation of a square by a quarter turn clockwise. But in Item 4, $r$ represents rotating a triangle by a third of a turn clockwise.
      1. $\{s, r, sr, rs\}\leq D_4$
      2. $\{1, -1, i, -i, j, -j\}\leq Q_8$
      3. $\{e, sr, rs, r^2\}\leq D_4$
      4. $\{e, r, r^2\} \leq D_3$
      5. $\{e, r, r^2\} \leq D_4$
  • Weekly Homework 5: Prove two of Theorem 3.23, Theorem 3.24, Theorem 3.51, Theorem 3.52, Theorem 3.53, Theorem 3.54. (Due Thursday, March 8 by 8PM)
  • Weekly Homework 6: Prove two of Theorem 4.10, Theorem 4.17, Theorem 4.19, Theorem 4.27, Theorem 4.39. (Due Thursday, March 29 by 8PM)
  • Weekly Homework 7: Prove two of Theorem 4.41, Theorem 4.44, Theorem 4.45, Problem 4.51, Problem 4.52. (Due Thursday, April 5 by 8PM)

Using LaTeX for Weekly Homework

You are required to use LaTeX to type up your Weekly Homework assignments. To do this, I suggest that you use my LaTeX Homework Template. The easiest way to get started with LaTeX is to use an online editor. I recommend using Overleaf, but there are other options. The good folks over at Overleaf have preloaded my template, so to get started, all you need to do is click the link below.

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 226: Discrete Math
  MAT 690: CGT

About This Site

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  Unless stated otherwise, content on this site is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

  The views expressed on this site are my own and are not necessarily shared by my employer Northern Arizona University.

  The source code is on GitHub.

Land Acknowledgement

  Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.