You are allowed and encouraged to work together on homework. Yet, each student is expected to turn in their own work. Unless you are explicitly told otherwise, 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. **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.

In order to pass the course, you must complete each of the Required Assignments to a satisfactory level. If your work is deemed unsatisfactory, you will have one chance to resubmit your work. We will negotiate a due date for any resubmissions. In general, late Required Assignments will *not* be accepted. However, you are allowed to turn in up to **two late Required Assignments** with no questions asked. I reserve the right to modify an assignment if the need arises.

**Homework 1:**Create a free Discord account, accept the invite to our Discord server (see Welcome Message, which was sent to your NAU email), and post something about yourself in the #introductions channel. (Due Wednesday, August 31 by 9pm)**Homework 2:**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 Monday, September 12)**Homework 3:**Read the syllabus and write down 5 items that you think are important. (Due Monday, September 12 by classtime)**Homework 4:**Complete at least one Flexible Assignment from the list below. (Due Monday, September 12)**Homework 5:**Let’s call this your “Math Autobiography” assignment. Address the following prompts. (Due Monday, September 19 by classtime)- Story: Please write the story of your mathematical past. Through this story, you should communicate your reasons for being a mathematics/mathematics education/data science major (or major X) and your current feelings about mathematics as well as the events and experiences in your past that brought you here. You might consider including examples of positive and negative episodes from past math courses, moments in which math came up in other situations, and plans for the future.
- Expertise: What skills do you bring with you to your mathematics courses? This response could include your skills with computational tools, like algebra, but it should go beyond mathematics. What other areas of academic expertise do you bring to class discussions? What co-academic skills and topics do you have at your finger-tips? In what areas are you currently building skills that you can connect with mathematics?
- Support: Is there anything that you’d like me to know about you or your context that might make it harder for you to succeed and excel in this course and/or your other mathematics courses?

**Homework 6:**Use software (your choice!) to create a flow chart that illustrates the prerequisite structure of all of the undergraduate mathematics courses (both MAT and STA) offered by NAU with course numbers greater than or equal to 123 and less than 500. For each course, also include the following information: Course number (e.g., MAT 320), Title (e.g., Foundations of Mathematics), number of credits, and when a course is offered (e.g., every semester, fall only, springs of even years, etc.). Note: You do not need to include Honors courses nor MAT 199, MAT 299, MAT 399, MAT 499. (Due Monday, September 26 by classtime)**Homework 7:**Create your individual degree progression plan for the mathematics, mathematics education, or data science degree. Assume that you take cources every semester and graduate in 4 years (include this semester). Your plan should more or less be a list of 8 semeters, where each semester lists the courses that you would take during a given semester. Creating a table would be fine. You only need to include required courses or courses you opt to take when there are choices. You do not need to include your Liberal Studies courses. You should utilize your flow chart for prerequisites to help. Do not just blindly copy the degree progression plans that are posted on NAU’s webpage as these make assumptions that may not hold true for you. (Due Monday, October 3 by classtime)**Homework 8:**Address the following prompts. Feel free to use the Internet to answer these questions (but mention your sources). (Due Monday, October 10 by classtime)- What is data science?
- What is a data scientist and how does one become a data scientist?
- What sorts of places employ data scientists?
- What’s an average or typical starting salary for a data scientist?

**Homework 9:**Answer the following questions by scouring the Internet. (Due Monday, October 17 by classtime)- What are the duties of a university Provost?
- Who is NAU’s Provost?
- How many colleges does NAU have? List them.
- Who is the Dean of the College of of the Environment, Forestry, and Natural Sciences (CEFNS)?
- Who is the chair of the Department of Mathematics and Statistics?
- How many of each of the following does the Department of Mathematics and Statistics have? (a) Instructor, (b) Lecturer or Senior Lecturer, (c) Assistant Teaching Professor, (d) Associate Teaching Professor, (e) (Full) Teaching Professor, (f) Assistant Professor, (g) Associate Professor, (h) (Full) Professor.
- Which faculty members in the Department of Mathematics and Statistics are active in research and what are their research interests? Also, list their title (e.g., Full Teaching Professor, Associate Professor, etc.). You will likely stumble on an outdated list while researching this. Here are some updates: Blows and Burch have retired, Yildiz has resigned, and we’ve recently hired Samuel Harris, Michele Torielli, Benjamin Lucas, and Jaechoul Lee. See if you can find the research interests of our new faculty members.

- There is no required homework assignment due on Monday, October 24. Instead, you should focus on obtaining at least 150 points worth of Flexible Assignments by
**by Friday, October 21**. **Homework 10:**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 at least a 1-page typed reflection. 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. At least a page! Typed! Don’t be a goofball with font size and margins. (Due Monday, October 31 by classtime)**Homework 11:**Generate a (rough) draft resume for the future you. Assume you are about to graduate and apply for your first job. Tailor your resume to the type of job you think you might apply for. You’ll need to make some assumptions about the types of experiences and qualifications you will have in a few years. Be hopeful and creative! You’ll get a chance to revise in a couple weeks. (Due Monday, November 7 by classtime)**Homework 12:**Type at least one page that generally addresses the question “Is mathematics invented or discovered?” You should address the following items in your write up. If you end up looking anything up on the Internet about this question, please cite your sources. (Due Monday, November 14 by classtime)- What do you mean by the words “invented” vs “discovered”?
- What do you mean by “mathematics”? Or at least what are you considering to be “mathematics” for the purposes of this discussion?
- Argue your point of view concerning whether mathematics in invented vs discovered.

- There is no required homework assignment due on Monday, November 21. Instead, you should focus on getting close to at least 300 points worth of Flexible Assignments.
**Homework 13:**Complete at least two course evaluations and submit documentation that you completed the evaluation. When you complete each evaluation, you’ll have the option to save a certificate (or possibly send to me directly). (Due Monday, November 28 by class time)

These assignments are a sort of “choose your own adventure”. Each Flexible Assignment has a designated point value. Over the course of the semester, you must complete enough Flexible Assignments to **achieve at least 150 points by Friday, October 21** and a **total of at least 300 points by the end of semester** (by 5pm on Thursday, December 15). Unless stated otherwise, you can only get credit for each item one time. Feel free to suggest more items for the list.

- Attend the Department of Mathematics & Statistics picnic on Saturday, September 10 at Thorpe Park. To get credit for this, you need to submit a picture of yourself at the picnic. (50 points)
- Attend FAMUS (Friday Afternoon Mathematics Undergraduate Seminar). FAMUS takes place most Friday afternoons at 4-5pm in Adel 164. For more info, see the FAMUS schedule. To get credit for this, you must attend FAMUS for the full hour and submit a selfie with Jeff Rushall, the host of FAMUS. You may get credit for this multiple times. (25 points each)
- Attend our department colloquium. The colloquium meets most Tuesday at 4-5pm in Adel 164. These talks are generally pitched at a high level. For more info, see the colloquium schedule. To get credit for this, you must attend for the full hour and submit a selfie with the speaker for that day. You may get credit for this multiple times. (25 points each)
- Submit a solution to the Problem of the Week that scores at least 2 points. You may get credit for this multiple times. (25 points each)
- Post a meaningful question in Discord. (50 points)
- Post a meaningful response to a questions in Discord. (50 points)
- Hike to the top of Mount Elden. To get credit for this, you need to submit a picture of yourself at the summit. (25 points)
- Watch N is a Number: A Portrait of Paul Erdos (54 mins) and then write a 1-2 page typed reflection. In your reflection, consider addressing the following questions. (100 points)
- Who is Paul Erdos?
- Why is he well known?
- What aspect of his life did you find interesting and/or suprising?

- 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. (100 points)- Did you identify with the author of the story? If so, in what way?
- How does the author’s experience differ from your own?
- What surprised you about the author’s story?
- Did this story make you think differently about mathematics? I’m expecting more than “yes/no”.
- What about the story inspires and/or bothers you?

- Join any club on campus and attend at least one of the club’s meetings. To get credit for this, find a way to verify your attendance at the meeting. (50 points)
- Visit one of your other professor’s office hours. To get credit for this, have the professor write a short note or email indicating that you were there. Include the course and the day/time that you visited their office. (50 points)
- Read The State of Being Stuck by Ben Orlin (of Math with Bad Drawings fame) and write a 1-2 page typed reflection. While this article makes some comments about the state of education and math students currently, I want you to focus and reflect on Andrew Wiles’ idea of what makes a good mathematician. Use the following questions/prompts below to guide you. (100 points)
- Pick 1-2 statements from this article that stuck out to you and briefly describe why they had an impact on you.
- How does Wiles define a good mathematician? Is this how you previously would have described a good mathematician?
- Have you ever felt stuck in math before? How did you react?
- How can we practice accepting this state of being stuck?
- How can we disconnect the idea of being stuck with failure?
- How is being stuck part of the process of doing mathematics?
- How does mathematics and being stuck incorporate both the intellectual and the emotional?
- I sometimes describe math research as “How to deal with disappointment every day of your life.” How does this compare with Wiles’ ideas about math research?

- Interview a mathematics, statistics, or mathematics education professor about their research. Write a 1-2 page typed summary of your conversation. Consider addressing the following questions in your interview. (100 points)
- What is your research area? And what does this mean?
- What does it mean to do research in your area?
- How did you choose to pursue this research area?
- What do you love about your research?
- What contribution to your research area are you most proud of?

- Interview a current mathematics or statistics graduate student in our department. Write a 1-2 page typed summary of your conversation. Consider addressing the following questions in your interview. (50 points)
- Why did you choose to go to graduate school?
- How much does it cost to go to graduate school?
- What’s your favorite part of graduate school?
- What is the most challenging aspect of graduate school?

- Listen to any episode labeled “Audiobook” on the Learner Lab Podcast and write a 1-2 page typed summary/reflection. You may get credit for this multiple times by listening to multiple episodes. (75 points each)
- Read Mathematics for Human Flourishing by Francis Su and write a 1-2 page typed summary/reflection. I have a copy of the book if you want to borrow it for a couple weeks. (100 points)
- Attend an athletic event on campus. To get credit for this, you need to submit a picture of yourself at the event. The picture needs to make it clear what the event is. (25 points)
- Use the Internet to learn about the Millennium Prize Problems. Which problems have been solved? What are the remaining unsolved problems? Pick one of the unsolved problems and attempt to write a 1-2 page typed summary. (75 points)
- Use the Internet to learn about the Fields Medal. What is a Fields Medal? How does one get selected for a Fields Medal? Is there anyone that has ever refused to receive their Fields Medal after being selected? Choose 1-2 recent Fields Medal recipients and write a 1-2 page typed summary of their life and work. (75 points)
- Attend the Math Achievement Program (“MAP room”) for help with MAT 121, MAT 136, MAT 137, MAT 238, or STA 270. (50 points)
- Attend one of the Math Achievement Program’s (MAP) review sessions for MAT 121, MAT 136, or MAT 137. (50 points)
- Attend either a supplemental instruction session or drop-in tutoring at one of the Academic Success Centers (ASC). (50 points)
- Take a picture of yourself in the aspens and post to Discord. (25 points)
- Send me a screenshot indicating that you have completed all of our course evaluations. (25 points)

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MAT 226: Discrete Math

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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.