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 consult the Elements of Style for Proofs.

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

For most of the assignments below, you will be required to submit 2-3 formally written proofs. You are required to type your submission using LaTeX (see below). 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: Read The Secret to Raising Smart Kids by Carol Dweck and 7 Things Growth Mindset is Not. Write a one-page summary/reflection about the article. 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, September 5 by 8PM)
  • Weekly Homework 2: Prove two of Theorems 2.29, 2.37, 2.39, 2.41, 2.42. 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 Friday, September 13 by 8PM)
  • Weekly Homework 3: Prove two of Theorems 2.44, 2.45, 2.48(a), 2.48(b). You must type up your proofs using LaTeX. (Due Thursday, September 19 by 8PM)
  • Weekly Homework 4: Prove two of Theorems 2.75, 2.76, 2.78, 3.19, 3.21. You must type up your proofs using LaTeX. (Due Thursday, October 10 by 8PM)
  • Weekly Homework 5: Suppose $\phi:G_1\to G_2$ is a function between two groups that satisfies the homomorphic property (but may or may not be 1-1 or onto). Prove that the set $\ker(\phi):=\{g\in G_1\mid\phi(g)=e_2\}$, (where $e_1$ and $e_2$ are the identities of $G_1$ and $G_2$, respectively) is a subgroup of $G_1$. You must type up your proofs using LaTeX. (Due Thursday, October 17 by 8PM)
  • Weekly Homework 6: Prove two of Theorems 3.51, 3.52, 3.53, 3.54, 3.60, 3.64. You must type up your proofs using LaTeX. (Due Thursday, October 24 by 8PM)
  • Weekly Homework 7: Prove one of Theorems 4.24, 4.28, 4.32, 4.42. You must type up your proofs using LaTeX. (Due Thursday, October 31 by 8PM)

Using LaTeX for Weekly Homework

You are required to use LaTeX to type up your Weekly Homework assignments. 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 homework template, so to get started, all you need to do is click the link below and then click on “Open as Template”. Be sure to update your name and the course title.

Start your homework in Overleaf

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 411: Abstract Algebra
  MAT 690: Genome Combinatorics

About This Site

  This website was created using GitHub Pages and Jekyll together with Twitter Bootstrap.

  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 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.