On each homework assignment, please write (i) your name, (ii) name of course, and (iii) homework number. In general, late homework will not be accepted. However, you are allowed to turn in **up to three late homework assignments**. 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 I encourage you to consult the “Elements of Style for Proofs” appendix in the textbook.

Reviewing material from previous courses and looking up definitions and theorems you may have forgotten is fair game. Since mathematical reasoning, problem solving, and critical thinking skills are part of the learning outcomes of this course, all assignments should be prepared by the student. Developing strong competencies in this area will prepare you to be a lifelong learner and give you an edge in a competitive workplace. When it comes to completing assignments for this course, unless explicitly told otherwise, you should *not* look to resources outside the context of this course for help. That is, you should not be consulting the web (e.g., Chegg and Course Hero), generative artificial intelligence tools (e.g., ChatGPT), mathematics assistive technologies (e.g., Wolfram Alpha and Photomath), other texts, other faculty, or students outside of our course in an attempt to find solutions to the problems you are assigned. On the other hand, you may use each other, the textbook, me, and your own intuition. You are allowed and encouraged to work together on homework. Yet, each student is expected to turn in their own work. **If you feel you need additional resources or support, please come talk to me and we will come up with an appropriate plan of action.**

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 an assignment if the need arises. These exercises will form the basis of the student-led presentations. During class, you are encouraged to annotate your homework, but **you are required to use a different color than what you used to complete your homework**.

**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 at beginning of class or email me a copy of your write up prior to class. (Due Wednesday, August 30)**Daily Homework 2:**Read the*Preface*and*Chapter 1: Introduction*in the textbook. In addition, complete 2.2-2.4 in Section 2.1 of*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Wednesday, August 30)**Daily Homework 3:**Complete 2.6 and 2.7 in Section 2.1 of*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Friday, September 1)**Daily Homework 4:**Complete 2.8-2.11 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Wednesday, September 6)**Daily Homework 5:**Complete 2.12 and 2.13 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Friday, September 8)**Daily Homework 6:**Complete 2.14, 2.15, 2.17, 2.19, 2.22, 2.23 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Monday, September 11)**Daily Homework 7:**Complete 2.24-2.30 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Wednesday, September 13)**Daily Homework 8:**Complete 2.32, 2.34, 2.35, 2.37-2.40 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Friday, September 15)**Daily Homework 9:**Complete 2.41-2.43, 2.45, 2.46 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Monday, September 18)**Daily Homework 10:**Complete 2.47, 2.50-2.52, 2.55 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Wednesday, September 20)**Daily Homework 11:**Complete 2.56-2.59, 2.61-2.64 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Monday, September 25)**Daily Homework 12:**Complete 2.66-2.73 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Wednesday, September 27)**Daily Homework 13:**Complete 2.75-2.80 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. (Due Friday, September 29)**Daily Homework 14:**Complete 2.86-2.89 in*Chapter 2: Mathematics and Logic*and digest the surrounding text along the way. For 2.86, you can just worry about finding counterexamples. (Due Monday, October 2)**Daily Homework 15:**Complete 2.91, 3.2, 3.3, 3.5 in*Chapter 2: Mathematics and Logic*and*Chapter 3: Set Theory*and digest the surrounding text along the way. (Due Wednesday, October 4)**Daily Homework 16:**Complete 3.7-3.10, 3.12 in*Chapter 3: Set Theory*and digest the surrounding text along the way. (Due Friday, October 6)**Daily Homework 17:**Complete 3.48-3.53 in*Chapter 3: Set Theory*and digest the surrounding text along the way. (Due Wednesday, October 18)**Daily Homework 18:**Complete 3.59, 3.60 and any three from 3.61 in*Chapter 3: Set Theory*and digest the surrounding text along the way. (Due Friday, October 20)**Daily Homework 19:**Complete 4.2, 4.4-4.6 in*Chapter 4: Induction*and digest the surrounding text along the way. (Due Monday, October 23)**Daily Homework 20:**Complete 4.8 and any three of 4.11-4.23 in*Chapter 4: Induction*and digest the surrounding text along the way. (Due Wednesday, October 25)**Daily Homework 21:**Complete 4.27, 4.29, 4.30 or 4.31, and 4.32 in*Chapter 4: Induction*and digest the surrounding text along the way. (Due Friday, October 27)**Daily Homework 22:**Complete 4.34, 4.36 in*Chapter 4: Induction*and digest the surrounding text along the way. (Due Monday, October 30)**Daily Homework 23:**Complete 4.37, 4.38, 6.19 and read 4.39, 4.40 in*Chapter 4: Induction*and*Chapter 6: Three Famous Theorems*and digest the surrounding text along the way. (Due Wednesday, November 1)**Daily Homework 24:**Complete 7.10, 7.12, 7.13, 7.16, 7.19 in*Chapter 7: Relations and Partitions*and digest the surrounding text along the way. (Due Friday, November 3)**Daily Homework 25:**Complete 7.22-7.24, 7.27-7.30, 7.34 (for 7.34 don’t worry about proving your claims) in*Chapter 7: Relations and Partitions*and digest the surrounding text along the way. (Due Monday, November 6)**Daily Homework 26:**Complete 7.36-7.42 in*Chapter 7: Relations and Partitions*and digest the surrounding text along the way. (Due Wednesday, November 8)**Daily Homework 27:**Complete 7.43, 7.47-7.50 in*Chapter 7: Relations and Partitions*and digest the surrounding text along the way. (Due Monday, November 13)**Daily Homework 28:**Complete 8.54, 8.55, 8.57-8.60 in*Chapter 8: Functions*and digest the surrounding text along the way. (Due Wednesday, November 29)**Daily Homework 29:**Complete 8.61-8.63, 8.64 or 8.65, and 8.68, 8.69 in*Chapter 8: Functions*and digest the surrounding text along the way. (Due Friday, December 1)**Daily Homework 30:**Complete 8.71-8.75 in*Chapter 8: Functions*and digest the surrounding text along the way. (Due Monday, December 4)**Daily Homework 31:**Complete 8.76-8.79 in*Chapter 8: Functions*and digest the surrounding text along the way. (Due Wednesday, December 6)**Daily Homework 32:**Complete 8.81, 8.82, 8.84, 8.86, 8.87 in*Chapter 8: Functions*and digest the surrounding text along the way. (Due Friday, December 8)

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).

**Weekly Homework 1:**Prove**two**of 2.2, 2.3, 2.7. 2.11, 2.13, 2.15. You must type up your proofs using LaTeX. I recommend using my Overleaf template. (Due in Canvas by Thursday, September 21 by 8PM)**Weekly Homework 2:**Prove**two**of 2.51, 2.52, 2.56, 2.57. You must type up your proofs using LaTeX. I recommend using my Overleaf template. (Due in Canvas by Thursday, September 28 by 8PM)**Weekly Homework 3:**Prove**one**of the true statements from 3.61 and**one**of 4.2-4.6. You must type up your proofs using LaTeX. I recommend using my Overleaf template. (Due in Canvas by Thursday, October 27 by 8PM)**Weekly Homework 4:**Prove**one**of 4.11-4.23 and**one**of 4.27-4.31, 4.34. You must type up your proofs using LaTeX. I recommend using my Overleaf template. (Due in Canvas by Thursday, November 2 by 8PM)**Weekly Homework 5:**Prove**two**of 4.36, 4.38, 6.19 You must type up your proofs using LaTeX. I recommend using my Overleaf template. (Due in Canvas by Thursday, November 9 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 my 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 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.