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 A of the course notes as a reference.

The following assignments are to be turned in at the end of the indicated class period. I reserve the right to modify the assignment if the need arises. These exercises will form the basis of the student-led sharing of solutions/proofs each day. Daily assignments will be graded on a $\checkmark$-system. During class, **you are only allowed 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 Friday, January 20)**Daily Homework 2:**Read and sign the Student Contract. (Due Friday, January 20)**Daily Homework 3:**Stop by my office (AMB 176) and say hello. If I’m not there, just slide a note under my door saying you stopped by. (Due by 4PM on Friday, January 20)**Daily Homework 4:**Read all of Chapter 1: Introduction of the course notes. In addition, complete 2.3-2.6 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Friday, January 20)**Daily Homework 5:**Skim through Appendix A: Elements of Style of Proof of the course. In addition, complete 2.7-2.9, 2.11-2.17 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Monday, January 23)**Daily Homework 6:**Skim through Appendix B: Fancy Mathematical Terms of the course notes. In addition, complete 2.18-2.20 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Wednesday, January 25)**Daily Homework 7:**Skim through Appendix C: Definitions in Mathematics of the course notes. In addition, complete 2.21-2.23 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Friday, January 27)**Daily Homework 8:**Complete 2.25, 2.27, 2.28, 2.31, 2.32, 2.34 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Monday, January 30)**Daily Homework 9:**Complete 2.35, 2.36, 2.38, 2.40-2.45 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Wednesday, February 1)**Daily Homework 10:**Complete 2.46-2.49, 2.51, 2.52 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Friday, February 3)**Daily Homework 11:**Complete 2.55, 2.56, 2.57, 2.58, 2.60-2.62 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Monday, February 6)**Daily Homework 12:**Complete 2.63, 2.65, 2.66 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Wednesday, February 8)**Daily Homework 13:**Complete 2.67-2.69, 2.71-2.74 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Friday, February 10)**Daily Homework 14:**Complete 2.79 and 2.80 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Monday, February 13)**Daily Homework 15:**Complete 3.20, 3.21, 3.23-3.28 in Chapter 3: Set Theory and Topology and digest the surrounding text along the way. (Due Wednesday, February 22)**Daily Homework 16:**Complete 3.29-3.33 in Chapter 3: Set Theory and Topology and digest the surrounding text along the way. (Due Friday, February 24)**Daily Homework 17:**Complete 3.35-3.39, 3.41-3.44 in Chapter 3: Set Theory and Topology and digest the surrounding text along the way. (Due Monday, February 27)**Daily Homework 18:**Complete 4.2-4.4, 4.6, 4.7, 4.9-4.12 in Chapter 4: Three Famous Theorems and digest the surrounding text along the way. (Due Friday, March 3)**Daily Homework 19:**Complete 4.14-4.17 in Chapter 4: Three Famous Theorems and digest the surrounding text along the way. (Due Wednesday, March 8)**Daily Homework 20:**Complete 4.19 and 4.20 in Chapter 4: Three Famous Theorems and 5.2 and 5.4 Chapter 5: Induction. (Due Friday, March 10)**Daily Homework 21:**Complete 5.5-5.8 in Chapter 5: Induction. (Due Monday, March 20)**Daily Homework 22:**Complete 5.11 and any three of 5.13-5.23 in Chapter 5: Induction. (Due Wednesday, March 22)**Daily Homework 23:**Complete 5.25 and any three of 5.27-5.31 in Chapter 5: Induction. (Due Friday, March 24)**Daily Homework 24:**Complete 6.5-6.13, 6.19, 6.20, 6.22 in Chapter 6: Relations. (Due Monday, March 27)**Daily Homework 25:**Complete 6.51, 6.52, 6.54-6.61 in Chapter 6: Relations. (Due Wednesday, April 5)**Daily Homework 26:**Complete 7.3, 7.5-7.9 in Chapter 7: Functions. (Due Friday, April 7)**Daily Homework 27:**Complete 7.13-7.15 in Chapter 7: Functions. (Due Monday, April 10)**Daily Homework 28:**Complete 7.16, 7.17, 7.19-7.22 in Chapter 7: Functions. (Due Wednesday, April 12)**Daily Homework 29:**Complete 7.23, 7.25-7.27 in Chapter 7: Functions. (Due Monday, April 17)**Daily Homework 30:**Complete 7.28-7.31 in Chapter 7: Functions. (Due Wednesday, April 19)**Daily Homework 31:**Complete 8.2-8.5 in Chapter 8: Cardinality. (Due Friday, April 21)**Daily Homework 32:**Complete 8.7 and 8.8 in Chapter 8: Cardinality. (Due Monday, April 24)**Daily Homework 33:**Complete 8.16, 8.17, 8.23, 8.24, 8.28, 8.29, 8.32, 8.33, 8.37 in Chapter 8: Cardinality. (Due Friday, May 5)

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:**Prove**two**of Problem 2.9, Theorem 2.14, Theorem 2.18, or Theorem 2.22 from Chapter 2: Mathematics and Logic. (Due Thursday, February 2 by 8PM)**Weekly Homework 2:**Prove**two**of Theorem 2.23, Theorem 2.43, Theorem 2.44, or Theorem 2.45 from Chapter 2: Mathematics and Logic. (Due Thursday, February 9 by 8PM)**Weekly Homework 3:**Prove**one**of Theorem 2.55 or Theorem 2.56 from Chapter 2: Mathematics and Logic. (Due Tuesday, February 14 by 8PM)**Weekly Homework 4:**Prove**two**of Theorem 3.20(a), Theorem 3.21(a), Theorem 3.25, Theorem 3.26, or Theorem 3.27 from Chapter 3: Set Theory and Topology. (Due Tuesday, February 28 by 8PM)**Weekly Homework 5:**Prove**one**of Theorem 3.43(a), Theorem 3.43(b), Theorem 3.44(a), and Theorem 3.44(b) from Chapter 3: Set Theory and Topology. (Due Tuesday, March 7 by 8PM)**Weekly Homework 6:**Prove**one**of Theorem 4.10, Theorem 4.12, Theorem 4.15, Theorem 4.20 from Chapter 4: Three Famous Theorems and**one**of Theorem 5.7, Theorem 5.8, Theorem 5.11, Theorems 5.13-5.23 in Chapter 5: Induction. (Due Tuesday, March 28 by 8PM)**Weekly Homework 7:**Prove**two**of Theorems 6.51, 6.56, 6.58 and 6.59 from Chapter 6: Relations. (Due Tuesday, April 11 by 8PM)**Weekly Homework 8:**Prove**one**of Theorems 7.20 and 7.21 from Chapter 7: Functions. (Due Tuesday, April 18 by 8PM)

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.

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.