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 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 15)
• Daily Homework 2: Read the Preface and Introduction. In addition, complete 2.3-2.9 in Chapter 2: Mathematics and Logic. (Due Wednesday, January 15)
• Daily Homework 3: Answer the following questions. (Due Friday, January 17)
1. What are some words you would use to describe mathematics?
2. What words would you use to describe a typical mathematician?
3. What do you think it means to be “good at mathematics”?
4. What does the phrase “doing mathematics” mean to you?
5. What do you do when you are struggling with a mathematical problem?
6. When has most of the mathematics we know been developed?
7. Who are some famous mathematicians? Can you name some contemporary mathematicians? I.e. mathematicians from the 20th or 21st century?
9. What do you think are the goals for this course?
10. What concerns, if any, do you have about taking this course?
• Daily Homework 4: Complete 2.11-2.19 in Chapter 2: Mathematics and Logic. (Due Friday, January 17)
• Daily Homework 5: Quickly skim Appendix A: Elements of Style for Proofs, Appendix B: Fancy Mathematical Terms, and Appendix C: Definitions in Mathematics. In addition, complete 2.20-2.23 in Chapter 2: Mathematics and Logic. (Due Wednesday, January 22)
• Daily Homework 6: Complete 2.25, 2.27 in Chapter 2: Mathematics and Logic. (Due Friday, January 24)
• Daily Homework 7: Complete 2.29, 2.30, 2.33, 2.34, 2.36-2.38 in Chapter 2: Mathematics and Logic. (Due Monday, January 27)
• Daily Homework 8: Complete 2.40, 2.42, 2.44, 2.45 in Chapter 2: Mathematics and Logic. (Due Wednesday, January 29)
• Daily Homework 9: Complete 2.46, 2.48-2.51 in Chapter 2: Mathematics and Logic. (Due Friday, January 31)
• Daily Homework 10: Complete 2.52-2.55, 2.57, 2.58 in Chapter 2: Mathematics and Logic. (Due Monday, February 3)
• Daily Homework 11: Complete 2.61-2.64, 2.66-2.69 in Chapter 2: Mathematics and Logic. (Due Wednesday, February 5)
• Daily Homework 12: Complete 2.71-2.75 in Chapter 2: Mathematics and Logic. (Due Friday, February 7)
• Daily Homework 13: Complete 2.77-2.80 in Chapter 2: Mathematics and Logic. (Due Monday, February 10)
• Daily Homework 14: Complete 2.85, 2.86, 3.3, 3.4, 3.6-3.9 in Chapter 2: Mathematics and Logic and Chapter 3: Set Theory and Topology. (Due Wednesday, February 12)
• Daily Homework 15: Complete 3.14-3.16 in Chapter 3: Set Theory and Topology. (Due Friday, February 14)
• Daily Homework 16: Complete 3.18 and 3.19 in Chapter 3: Set Theory and Topology. (Due Monday, February 17)
• Daily Homework 17: Complete 3.20, 3.22-3.24 in Chapter 3: Set Theory and Topology. (Due Wednesday, February 19)
• Daily Homework 18: Complete 3.26-3.31 in Chapter 3: Set Theory and Topology. (Due Wednesday, February 26)
• Daily Homework 19: Complete 3.33-3.37, 3.39-3.42 in Chapter 3: Set Theory and Topology. (Due Friday, February 28)
• Daily Homework 20: If needed, revisit 3.41 and 3.42. Also, complete 4.2 and 4.4 in Chapter 4: Induction. (Due Monday, March 2)
• Daily Homework 21: Complete 4.5 in Chapter 4: Induction. (Due Wednesday, March 4)
• Daily Homework 22: Complete 4.6-4.8, 4.11 in Chapter 4: Induction. (Due Friday, March 6)
• Daily Homework 23: Submit a two-page PDF of any written work to the corresponding assignment on BbLearn. See BbLearn for details. (Due by noon on Tuesday, March 24)
• Daily Homework 24: Complete 5.16-5.18, 5.21, 5.22 in Chapter 5: Three Famous Theorems. Submit a digital copy (PDF) of your work in BbLearn. (Due by noon on Wednesday, March 25)
• Daily Homework 25: Complete 6.5-6.13, 6.18, 6.19, 6.21 in Chapter 6: Relations. In addition, write a reflection on the student work for 5.17, 5.21, and 5.22 that is posted under “Student Work” in BbLearn. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Friday, March 27)
• Daily Homework 26: Complete 6.24-6.26, 6.28-6.31, 6.33, 6.34 in Chapter 6: Relations. In addition, write a reflection on all of the student work for 6.8, 6.9. 6.13, 6.19, 6.21 that is posted under “Student Work” in BbLearn. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Monday, March 30)
• Daily Homework 27: Complete 6.35-6.39, 6.42, 6.43 in Chapter 6: Relations. In addition, write a reflection on all of the student work for 6.24, 6.26, 6.29, 6.33, 6.34 that is posted under “Student Work” in BbLearn. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Wednesday, April 1)
• Daily Homework 28: Complete 6.47-6.51, 6.53, 6.54 in Chapter 6: Relations. In addition, write a reflection on all of the student work for 6.38, 6.39(a), 6.39(b), 6.42 that is posted under “Student Work” in BbLearn. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Friday, April 3)
• Daily Homework 29: Complete 6.59 in Chapter 6: Relations and 7.3, 7.5-7.9, 7.13, 7.14 in Chapter 7: Functions. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Monday, April 13)
• Daily Homework 30: Complete 7.15, 7.16, 7.18, 7.19, 7.22-7.25 in Chapter 7: Functions. Submit a digital copy (PDF) of your work in BbLearn. (Due by midnight on Wednesday, April 15)
• Daily Homework 31: Complete 7.26, 7.28-7.32 in Chapter 7: Functions. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Friday, April 17)
• Daily Homework 32: Complete 7.33-7.38, 7.40, 7.41 in Chapter 7: Functions. Submit a digital copy (PDF) of your work in BbLearn. (Due by 11:59pm on Monday, April 20)
• Daily Homework 33: Complete 7.42-7.44 in Chapter 7: Functions. In addition, take a look at Patrick’s work for Problem 7.32(b) and figure out what’s wrong with it (we know something must be wrong since we have a counterexample to the statement). Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Wednesday, April 22)
• Daily Homework 34: Complete 8.2-8.4, 8.7, 8.8, 8.20 in Chapter 8: Cardinality. I’m not going to assign any problems from Section 8.2, but you should read this section and digest the material. From this moment on, you can use any of the results in Section 8.2. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Wednesday, April 29)
• Daily Homework 35: Complete 8.21, 8.22, 8.24, 8.25, 8.26, 8.28, 8.31 in Chapter 8: Cardinality. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Friday, May 1)

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 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 Friday, January 24 by 3PM)
• Weekly Homework 2: Prove one of 2.3, 2.4, 2.8, 2.14, 2.18, 2.22, 2.23. 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 Thursday, January 30 by 8PM)
• Weekly Homework 3: Prove one of 2.49-2.51. You must type up your proofs using LaTeX. In addition, read the Foreword, Preface, and any two stories (they aren’t too long) from Living Proof, and then type up responses to the following questions for each story. Be sure to indicate which stories you read. Once again, use the “Start your homework in Overleaf” link below. You’ll need to delete one of the theorem/proof pairs to write your responses to the reflection questions. (Due Thursday, February 6 by 8PM)
1. Did you identify with the author of the story? If so, in what way?
2. How does the author’s experience differ from your own?
3. What surprised you about the author’s story?
4. Did this story make you think differently about mathematics? I’m expecting more than “yes/no”.
5. What about the story inspires and/or bothers you?
• Weekly Homework 4: Prove two of 2.49, 2.50, 2.61 (only need to prove in one way, your choice), 2.86. 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 Thursday, February 13 by 8PM)
• Weekly Homework 5: Prove two of 3.9, 3.18, 3.19(a), 3.19(b), 3.20(a), 3.20(b). 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 Sunday, February 23 by 8PM)
• Weekly Homework 6: Prove two of 3.26, 3.41(a), 3.41(b), 3.42(a), 3.42(b). 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 Thursday, March 5 by 8PM)

In light of our move to remote instruction for the remainder of the Spring 2020 semester, the format and purpose of the Weekly Homework has changed. Every few days, I will post solutions (PDFs of my handwritten work or video) to a subset of the problems that were recently due. Your task will be to reflect on the work you previously did for the corresponding problems and to take notes on my proposed solutions. As with the Daily Homework, you will submit your work as a PDF to BbLearn. Each Weekly Homework assignment will be worth 4 points and your score will be based on the quality of the work that you submit.

• Weekly Homework 7: Using the solutions that I posted on BbLearn and the samples of student work that you’ve seen, reflect on the work you did for Daily Homeworks 24 and 25. To accomplish this, I suggest you do some combination of annotating your work and taking notes on my solutions. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Tuesday, March 31)
• Weekly Homework 8: Write a reflection on all of the student work for 6.50, 6.53, 6.54 that is posted under “Student Work” in BbLearn. In addition, using the solutions that I posted on BbLearn and the samples of student work that you’ve seen, reflect on the work you did for Daily Homeworks 26-28. To accomplish this, I suggest you do some combination of annotating your work and taking notes on my solutions. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Monday, April 6)
• Weekly Homework 9: Using the solutions that I posted on BbLearn, reflect on the work you did for Daily Homeworks 29-31. To accomplish this, I suggest you do some combination of annotating your work and taking notes on my solutions. Submit a digital copy (PDF) of your work in BbLearn. (Due by 5pm on Tuesday, April 21)

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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Land Acknowledgement

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.