## 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 his or her 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.

• 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, January 16)
• Daily Homework 2: If you haven’t already, read Chapter 1: Introduction (6 pages) in Topology Through Inquiry. In addition, complete 2.2-2.8 in Chapter 2 and digest the surrounding text along the way. These problems should be review. (Due Wednesday, January 16)
• Daily Homework 3: Complete 2.9-2.12 in Chapter 2 and digest the surrounding text along the way. Again, these problems should be review. (Due Friday, January 18)
• Daily Homework 4: Complete 2.13 in Chapter 2 and digest the surrounding text along the way. (Due Wednesday, January 23)
• Daily Homework 5: Complete 2.14, 2.16-2.20 in Chapter 2 and digest the surrounding text along the way. (Due Friday, January 25)
• Daily Homework 6: Complete 2.21, 2.22, 3.1, 3.2 and digest the surrounding text along the way. In addition, carefully read (but don’t worry about proving the theorems, unless you want to) Section 2.4 (focusing on Theorems 2.25 and 2.26) and skim Section 2.5. (Due Monday, January 28)
• Daily Homework 7: Complete 3.3-3.7 in Chapter 3 and digest the surrounding text along the way. If you haven’t already, be sure to carefully read Section 3.1. (Due Wednesday, January 30)
• Daily Homework 8: Complete 3.8-3.12 in Chapter 3 and digest the surrounding text along the way. (Due Friday, February 1)
• Daily Homework 9: Complete 3.13-3.17 in Chapter 3 and digest the surrounding text along the way. (Due Monday, February 4)
• Daily Homework 10: Complete 3.18-3.20. (Due Wednesday, February 6)
• Daily Homework 11: Complete 3.21-3.25. (Due Friday, February 8)
• Daily Homework 12: Complete 3.26-3.30. (Due Monday, February 11)
• Daily Homework 13: Complete 4.1 and 4.2. (Due Wednesday, February 13)
• Daily Homework 14: Complete 4.3-4.5. (Due Friday, February 15)
• Daily Homework 15: Complete 4.10 and 4.25. (Due Monday, February 18)
• Daily Homework 16: Complete 4.26-4.28. (Due Wednesday, February 20)
• Daily Homework 17: Read the rest of Chapter 4 and then complete 5.1-5.6. (Due Monday, March 4)
• Daily Homework 18: Complete 5.7-5.8. (Due Wednesday, March 6)
• Daily Homework 19: Complete 5.9, 5.12-5.14. (Due Friday, March 8)
• Daily Homework 20: Complete 5.16-5.18. (Due Monday, March 11)
• Daily Homework 21: Complete 5.19. (Due Wednesday, March 13)
• Daily Homework 22: Complete 5.20, 5.23, 6.1, 6.2. (Due Friday, March 15)

## 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 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 Tuesday, January 22 by 8PM)
• Weekly Homework 2: Prove two of Theorems 2.10, 2.11, 2.12, 2.14, 2.16. 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 Tuesday, January 29 by 8PM)
• Weekly Homework 3: Prove two of Theorems 2.20, 2.21, 2.22. You must type up your proofs using LaTeX. (Due Tuesday, February 5 by 8PM)
• Weekly Homework 4: Prove two of Theorems 3.3, 3.13, 3.15, 3.20. You must type up your proofs using LaTeX. (Due Tuesday, February 12 by 8PM)
• Weekly Homework 5: Prove one of Theorems 3.22(1), 3.22(2), 3.28. You must type up your proofs using LaTeX. (Due Tuesday, February 19 by 8PM)
• Weekly Homework 6: Either prove two of Theorem 5.1, Exercise 5.6(4), Theorem 5.8, Theorem 5.9, or complete the last part of Exercise 4.10. You must type up your proofs using LaTeX. (Due Tuesday, March 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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