## Guidelines

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. 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.

Reviewing material from previous courses and looking up definitions and theorems you may have forgotten is fair game. However, when it comes to completing assignments for this course, you should not look to resources outside the context of this course for help. That is, you should not be consulting the web, other texts, other faculty, or students outside of our course in an attempt to find solutions to the problems you are assigned. This includes Chegg and Course Hero. On the other hand, you may use each other, the textbook, me, and your own intuition. If you feel you need additional resources, please come talk to me and we will come up with an appropriate plan of action. Please read NAU’s Academic Integrity Policy.

## 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. 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 on your own paper at the beginning of class or email me a copy of your write up prior to class. (Due Wednesday, August 25)
• Daily Homework 2: Create a free Discord account, accept the invite to our Discord server (see welcome message in email), and post something about yourself in the #introductions channel. (Due Wednesday, August 25 by 8PM)
• Daily Homework 3: Read the Preface and Introduction. In addition, complete 2.2-2.4 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Wednesday, August 25)
• Daily Homework 4: Complete 2.6 and 2.7 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Friday, August 27)
• Daily Homework 5: Complete 2.8-2.11 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Monday, August 30)
• Daily Homework 6: Complete 2.12 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Wednesday, September 1)
• Daily Homework 7: Complete 2.13-2.15, 2.17, 2.19 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Friday, September 3)
• Daily Homework 8: Complete 2.22 and 2.23 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Wednesday, September 8)
• Daily Homework 9: Complete 2.24-2.27 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Friday, September 10)
• Daily Homework 10: Complete 2.28-2.30, 2.32, 2.34, 2.35, 2.37-2.39 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Monday, September 13)
• Daily Homework 11: Complete 2.50-2.52, 2.55, 2.56 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Wednesday, September 15)
• Daily Homework 12: Complete 2.57-2.59, 2.61-2.64 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Friday, September 17)
• Daily Homework 13: Complete 2.66-2.72 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Monday, September 20)
• Daily Homework 14: Complete 2.73, 2.75-2.80 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Wednesday, September 22)
• Daily Homework 15: Complete 2.86-2.88 in Chapter 2: Mathematics and Logic and digest the surrounding text along the way. (Due Friday, September 24)
• Daily Homework 16: Complete 2.89 and 2.91 in Chapter 2: Mathematics and Logic and 3.2, 3.3 in Chapter 3: Set Theory and digest the surrounding text along the way. (Due Monday, September 27)
• Daily Homework 17: Complete 3.5, 3.7-3.10 in Chapter 3: Set Theory and digest the surrounding text along the way. (Due Wednesday, September 29)
• Daily Homework 18: Complete 3.12, 3.16-3.21 (do either (a) or (b) for 3.21) in Chapter 3: Set Theory and digest the surrounding text along the way. (Due Friday, October 1)
• Daily Homework 19: Complete 3.48-3.51 in Chapter 3: Set Theory and digest the surrounding text along the way. (Due Wednesday, October 13)
• Daily Homework 20: Complete 3.52-3.59 in Chapter 3: Set Theory and digest the surrounding text along the way. (Due Friday, October 15)
• Daily Homework 21: Complete 3.60-3.62 in Chapter 3: Set Theory and digest the surrounding text along the way. (Due Monday, October 18)
• Daily Homework 22: Complete 4.2, 4.4, 4.5 in Chapter 4: Induction and digest the surrounding text along the way. (Due Wednesday, October 20)
• Daily Homework 23: Complete 4.7, 4.8, 4.9, 4.11 in Chapter 4: Induction and digest the surrounding text along the way. (Due Friday, October 22)
• Daily Homework 24: Complete any three theorems from 4.13-4.23 in Chapter 4: Induction and digest the surrounding text along the way. (Due Monday, October 25)
• Daily Homework 25: Complete 4.24 in Chapter 4: Induction and digest the surrounding text along the way. (Due Wednesday, October 27)
• Daily Homework 26: Complete 4.25 and one of 4.27-4.31 in Chapter 4: Induction and digest the surrounding text along the way. (Due Friday, October 29)
• Daily Homework 27: Complete one of 4.32-4.33 and both of 4.34 and 4.36 in Chapter 4: Induction and digest the surrounding text along the way. (Due Monday, November 1)
• Daily Homework 28: Complete 4.37-4.39 in Chapter 4: Induction and digest the surrounding text along the way. (Due Wednesday, November 3)
• Daily Homework 29: Complete 7.10, 7.12, 7.13, 7.15, 7.16 in Chapter 7: Relations and Partitions and digest the surrounding text along the way. (Due Friday, November 5)
• Daily Homework 30: Complete 7.19-7.24, 7.27, 7.28 in Chapter 7: Relations and Partitions and digest the surrounding text along the way. (Due Monday, November 8)
• Daily Homework 31: Complete 7.29, 7.30, 7.34, 7.36-7.39 in Chapter 7: Relations and Partitions and digest the surrounding text along the way. (Due Wednesday, November 10)
• Daily Homework 32: Complete 7.40-7.43, 7.47, 7.48 in Chapter 7: Relations and Partitions and digest the surrounding text along the way. (Due Friday, November 12)
• Daily Homework 33: Complete 8.60, 8.64, one of 8.65 or 8.66, and both 8.67 and 8.68 in Chapter 8: Functions and digest the surrounding text along the way. (Due Wednesday, December 1)
• Daily Homework 34: Complete 8.69, 8.71-8.76 in Chapter 8: Functions and digest the surrounding text along the way. (Due Friday, December 3)

## 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: Watch “Grit: the power of passion and perseverance” and any other 4 videos listed under Videos on Growth Mindset and Productive Failure on the Course Materials page and then write a reflection that is at least 15 sentences long. You should list the videos you watched. 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 using LaTeX. For this assignment, I suggest you use the template on Overleaf found here (after clicking link, click on “Open as Template”) instead of using the “Start your homework in Overleaf” link below. (Due Thursday, September 2 by 8PM)
• Weekly Homework 2: Prove one of 2.7, 2.11, 2.13. 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 10 by 8PM)
• Weekly Homework 3: Prove one of the ones you did not do for Weekly Homework 2 and then prove one of 2.14 or 2.15. You must type up your proofs using LaTeX. You can access an Overleaf template by clicking the “Start your homework in Overleaf” link below. (Due Friday, September 17 by 8PM)
• Weekly Homework 4: Prove Theorem 2.57 and one of Theorems 2.51, 2.52, 2.56. You must type up your proofs using LaTeX. You can access an Overleaf template by clicking the “Start your homework in Overleaf” link below. (Due Friday, September 24 by 8PM)
• Weekly Homework 5: Prove both of Problem 2.86(i) and Theorem 2.88. You must type up your proofs using LaTeX. You can access an Overleaf template by clicking the “Start your homework in Overleaf” link below. (Due Friday, October 1 by 8PM)
• Weekly Homework 6: Prove two of Theorem 3.56, Problem 3.61(a), Problem 3.61(c), Problem 3.61(e), or Problem 3.62. You must type up your proofs using LaTeX. You can access an Overleaf template by clicking the “Start your homework in Overleaf” link below. (Due Friday, October 22 by 8PM)
• Weekly Homework 7: Prove two of Theorems 4.2-4.8, Problem 4.8. You must type up your proofs using LaTeX. You can access an Overleaf template by clicking the “Start your homework in Overleaf” link below. (Due Friday, October 29 by 8PM)
• Weekly Homework 8: Prove one of Theorems 4.11-4.23 and one of Theorems 4.27-4.31. You must type up your proofs using LaTeX. You can access an Overleaf template by clicking the “Start your homework in Overleaf” link below. (Due Friday, November 5 by 8PM)
• Weekly Homework 9: Prove one of Problems 4.32-4.34. You must type up your proofs using LaTeX. You can access an Overleaf template by clicking the “Start your homework in Overleaf” link below. (Due Friday, November 12 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.

# Dana C. Ernst

Mathematics & Teaching

Northern Arizona University
Flagstaff, AZ
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