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.

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**.

**Daily Homework 1:**Read the syllabus and write down 5 important items.*Note:*All of the exam dates only count as a single item. Turn in on your own paper at the beginning of class. (Due Wednesday, August 28)**Daily Homework 2:**Read and sign the Student Contract. (Due Wednesday, August 28)**Daily Homework 3:**Stop by my office (AMB 176) and say hello. If I’m not there, just slide note under my door saying you stopped by. (Due by 5PM on Friday, August 30)**Daily Homework 4:**Read all of the Preface and Chapter 1: Introduction of the course notes. In addition, complete 2.1-2.11 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Wednesday, August 28)**Daily Homework 5:**Skim through Appendix A: Elements of Style of Proof of the textbook. In addition, complete 2.12-2.14 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Friday, August 30)**Daily Homework 6:**Skim through Appendix B: Fancy Mathematical Terms of the textbook. In addition, complete 2.17-2.21 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Wednesday, September 4)**Daily Homework 7:**Skim through Appendix C: Definitions in Mathematics of the textbook. Also, complete 2.22-2.24, 2.26-2.29, 2.31, 2.32 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Friday, September 6)**Daily Homework 8:**Complete 2.34-2.39 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Monday, September 9)**Daily Homework 9:**Complete 2.40-2.45 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Wednesday, September 11)**Daily Homework 10:**Complete 2.48, 2.49 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Friday, September 13)**Daily Homework 11:**Complete 2.51, 2.54-2.56 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Monday, September 16)**Daily Homework 12:**Complete 2.57-2.59 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Wednesday, September 18)**Daily Homework 13:**Complete 2.60-2.68 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Friday, September 20)**Daily Homework 14:**Complete 2.70-2.72 in Chapter 2: An Introduction to Groups and digest the surrounding text along the way. (Due Monday, September 23)**Daily Homework 15:**Complete 3.15, 3.16, 3.20, 3.22, 3.25 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Friday, October 4)**Daily Homework 16:**Complete 3.26-3.30 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Monday, October 7)**Daily Homework 17:**Complete 3.32, 3.33, 3.35-3.40 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Wednesday, October 9)**Daily Homework 18:**Complete 3.41-3.45, 3.47-3.49 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Friday, October 11)**Daily Homework 19:**Complete 3.50-3.57 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Monday, October 14)**Daily Homework 20:**Complete 3.58-3.63 in Chapter 3: Subgroups and Isomorphisms and digest the surrounding text along the way. (Due Wednesday, October 16)**Daily Homework 21:**Complete 3.64-3.66 and 4.1, 4.3, 4.4, 4.7, 4.12, 4.13 in Chapter 3: Subgroups and Isomorphisms and Chapter 4: Families of Groups. Be sure to skim the problems in Chapter 4 that I did not assign. (Due Friday, October 18)**Daily Homework 22:**Complete 4.20, 4.21, 4.23-4.29 in Chapter 4: Families of Groups. Also, be sure to read and digest 4.15-4.19 (some of which appeared on the take-home portion of Exam 1). (Due Monday, October 21)**Daily Homework 23:**Complete 4.32, 4.33, 4.36-4.39 in Chapter 4: Families of Groups. Also, be sure to read and digest 4.34 and 4.35. (Due Wednesday, October 23)**Daily Homework 24:**Complete 4.40-4.47 in Chapter 4: Families of Groups. (Due Friday, October 25)**Daily Homework 25:**Complete 4.49-4.53 in Chapter 4: Families of Groups. (Due Monday, October 28)**Daily Homework 26:**Read/skim 4.54, 4.55-4.57, 4.60-4.66 and then complete 4.68, 4.69, 4.71-4.77 in Chapter 4: Families of Groups. (Due Wednesday, October 30)**Daily Homework 27:**Complete 4.78-4.84 in Chapter 4: Families of Groups. (Due Friday, November 1)**Daily Homework 28:**Complete 4.85-4.96 in Chapter 4: Families of Groups. (Due Monday, November 4)**Daily Homework 29:**Read/skim 6.1, 6.3-6.8 and complete 6.2, 6.9-6.14 in Chapter 6: Products and Quotients of Groups. (Due Wednesday, November 20)**Daily Homework 30:**Read/skim 6.16, 6.17, 6.19, 6.20, 6.24 and complete 6.15, 6.18, 6.21, 6.22, 6.23, 6.25, 6.26 in Chapter 6: Products and Quotients of Groups. (Due Friday, November 22)**Daily Homework 31:**Read/skim 6.30, 6.31, 6.32, 6.37, 6.38 and complete 6.27, 6.28, 6.29, 6.33, 6.34, 6.35, 6.36, 6.39, 6.40 in Chapter 6: Products and Quotients of Groups. (Due Monday, November 25)**Daily Homework 32:**Read/skim 7.1, 7.3-7.8, 7.11, 7.12, 7.14 and complete 7.2, 7.9, 7.10, 7.13, 7.14, 7.16, 7.19 in Chapter 7: Homomorphisms and the Isomorphism Theorems. (Due Wednesday, November 27)**Daily Homework 33:**Complete 8.9, 8.11, 8.15-8.17 in Chapter 8: An Introduction to Rings. (Due Wednesday, December 4)**Daily Homework 34:**Complete 8.33, 8.36(a)(b), 8.38, 8.39 in Chapter 8: An Introduction to Rings. (Due Friday, December 6)

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)

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.

Mathematics & Teaching

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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.