# Explorations in Modern Mathematics

Syllabus version 1.0 (Updated: January 7, 2021)

## Course Information

• Institution: Dordt University
• Course: Math 149-01 (3 cr.)
• Term: Spring 2021
• Instructor: Dr. Mike Janssen, Associate Professor of Mathematics
• Classroom: CL 2241
• Class time: 1:00-1:50pm MWF
• Office: SB 1612
• Student Hours: Make an appointment or drop by
• Course notes: https://prof.mkjanssen.org/emm/notes/ | PreTeXt source
• Course website: https://prof.mkjanssen.org/emm/
• Catalog Course Description: This course is focused on exploring college-level mathematics relevant for all students, regardless of discipline. We will investigate modern mathematical topics including number theory, modeling, fractals, infinity, probability, making meaning from data, and decision-making. Mathematical thinking, reasoning, and pattern discovery will be particularly emphasized. A guided discovery approach will be utilized, and we will discuss how a Reformed perspective impacts our view of the quantitative world. Prerequisite: an ACT mathematics score of 22 or higher or satisfactory completion of one course from Mathematics 100, 108, 115.

### Learning Objectives

In this course, students will

• be communicators by working together in groups on mathematical puzzles and sharing their thinking with the class. (CD)
• be explorers by playing with God’s mathematical creation, explicitly with the Rubik’s cube, and implicitly with other puzzles and problems. (CS)
• be connectors by exploring the power and limitations of mathematics for modeling the physical creation, and applying mathematical thinking to articulate a vision for a more just society. Students will also explore the notion of mathematical truth, and assess its place in understanding God’s creation. (RO, CS, CR)
• be ambassadors by identifying, analyzing, and presenting on an aspect of beauty in mathematics. (RO, CS)

### Assignments

The best way to learn mathematics is to do mathematics, and so we will regularly engage in the following items of work to strengthen our mathematical muscles.

#### In-Class Explorations

The heart of this course is the in-class work. Our class meetings will typically start with a short (5-10 minutes) introduction to the main questions under consideration. You’ll then work in assigned groups of approximately 3 to explore the activities posted to the course notes for the day. We’ll wrap up with discussions of whatever you found the most interesting, as well as some big-picture takeaways.

This mode of instruction is highly interactive; it is therefore essential that you participate in class each day (see also Flexible Course Design below for COVID contingency plans). Group participation will be monitored, and groups will regularly share their thinking with the class.

#### Weekly Checkpoints

On most Fridays on which we do not have a thematic checkpoint, we’ll end class with a short weekly checkpoint (approximately 5 points). The purpose of the weekly checkpoint is to get a sense of how well you’re understanding the material we discussed that week. They also have space for you to ask questions about the class; points will be awarded for both questions asked and answered.

#### Thematic Checkpoints

At the conclusion of each theme (e.g., Play, Truth, etc), we’ll have a larger thematic checkpoint. The standard format will be as a 50-point “exam”, but there are exceptions to this (such as the Play checkpoint, which will be a solve of the Rubik’s cube, or the Power checkpoint, which will be a presentation of the results of our graph-theoretic analysis of human trafficking networks). The thematic checkpoints will be held on:

• Play: February 5 (though you will have until February 26 to complete your Rubik’s cube solve)
• Truth: February 22
• Justice: March 15
• Power: April 23

Along the way, we’ll read Francis Su’s Mathematics for Human Flourishing, and consider the ways in which the practice of mathematics can help us lead lives of shalom. After reading a set of chapters, you’ll write a short (less than 3 pages) response to the ideas therein. A few days later, we’ll have an in-class discussion in small groups. Due dates are:

• Chapters 1-5: reflection due February 1, class discussion on February 3
• Chapters 6-7: reflection due February 19, class discussion on February 24
• Chapters 8-11: reflection due March 22, class discussion on March 24
• Chapters 12-13, Epilogue: reflection due April 21, class discussion on April 26

#### Final Project

The final project will highlight some aspect of beauty in mathematics. You may choose to work with others. There are several steps to completing the project:

1. Rank the topics (10% of project grade): You will be presented with a list of possible topics (including space to propose your own) and asked to rank them in order from most to least interesting. Your topic will be assigned based on your rankings in such a way that no one gets the same project topic. Due March 19.
2. Preliminary Report (20% of project grade): By April 2, you will submit a 1-2 page description of what you have learned about your topic, what questions you still have, and what artifact you are planning to create. Due April 2.
3. Artifact (50% of project grade): By April 30 (last day of class), you will create something that communicates or otherwise explores meaningful mathematics in your topic. That is, you should go deeper than just a surface-level understanding. You have freedom in what, exactly, you create. Here are some preapproved artifacts:
• A work of fine, visual, or literary art, with a 300-450 word interpretive guide. You can make or write something that explores the mathematical idea. Much of the work of your interpretive guide is in helping your audience understand the significant mathematics that is being explored so that we can better grasp your work.
• A research paper and slide deck. If you are not so keen to create a work of art, perhaps you’d rather write an 1800-2400 word research paper describing the mathematics you explored, as well as its history and why it is thought to be beautiful. You will cite at least five (5) reputable edited sources and format your paper using MLA guidelines. You should also prepare a short (3-5 minute) slide deck for the presentation (see below).
• A lesson plan and activity. If education is your thing, maybe you’d like to create a lesson plan using the full Dordt Education Department lesson plan template that introduces the students you hope to teach to your particular topic (e.g., if you are hoping to teach middle-level students, aim it at 6-8th graders). You should also create the activity that you would use to help these students explore the topic, as well as a short slide deck to help our class understand your topic and what you’ll ask the students to do.
• Other. In your topic rankings, you may propose to do something not on this list. You should carefully describe what you will do so that I have a clear sense that it will be roughly equivalent in depth and workload to the preapproved options. If I don’t think it is, I will either ask for clarification, suggest an alternative based on your idea, or assign you to one of the preapproved options.
4. Presentation (20% of your project grade): By the last day of class (April 30), you will submit plans for a short (less than 5 minutes) presentation. We will give our final presentations in person during our assigned final exam slot (TBA).

### Flexible Course Design

Assuming Dr. Janssen is not in quarantine/isolation, and less than 40% of the class is not in quarantine/isolation, class discussion will be recorded in screencast format and posted to the day’s notes homepage shortly after class. Students in quarantine or isolation will participate asynchronously. We will follow the day’s notes very closely to ease the burden of remote participation.

If Dr. Janssen is in quarantine/isolation and otherwise feels healthy, or more than 40% of the class is in quarantine/isolation, we will hold synchronous class meetings over Zoom, utilizing breakout rooms for groupwork.

If Dr. Janssen is ill, activities will be posted on the day’s homepage for independent/group work.

Your final percentage $G$ will be calculated according to the following weights.

Category Weight
Attendance and Participation 10%
Weekly Checkpoints 15%
Thematic Checkpoints 40%
Final Project 20%

Your final grade will then be assigned based on this scale:

A $92\% \le G \le 100\%$
A- $90\% \le G < 92\%$
B+ $87\% \le G < 90\%$
B $83\% \le G < 87\%$
B- $80\% \le G < 83\%$
C+ $77\% \le G < 80\%$
C $73\% \le G < 77\%$
C- $70\% \le G < 73\%$
D+ $67\% \le G < 70\%$
D $63\% \le G < 67\%$
D- $60\% \le G < 63\%$

### Other Polices and Advice

• I am generally fairly accepting of late work, with a built-in 24-hour grace period for any non-classroom activities. Additional time beyond the 24-hour grace period must be approved ahead of time.
• Student hours are your time to ask questions about all aspects of the class and college life. If you can’t find an appointment, send me an email! I will do my very best to accommodate your schedule.
• Email Policy: I check my email twice per school day: once in the morning, where I’ll deal with any emergencies, and once in the afternoon, when I’ll respond to other emails (including any that have come in since the morning). If you require a more immediate response, you’re welcome to come find me in my office.

#### Dordt University Student’s Right to Accommodations Policy

Any student who needs access to accommodations based on the impact of a documented disability should contact the Coordinator of Services for Students with Disabilities (CSSD): Marliss Van Der Zwaag, Academic Enrichment Center, (712) 722-6490, marliss.vanderzwaag@dordt.edu.

#### COVID-19 Classroom Protocols

As we begin the Spring 2021 semester, Dordt is a mask-required environment. While on Dordt’s campus, you will need to wear a mask in all public places or common indoor spaces, which include: classrooms, hallways, laboratories, restrooms, the Hulst Library and all building lobbies.

If you are approved by Student Services for accommodations for virtual learning due to COVID-19, your instructor will be notified via the COVID-19 Dashboard, and you will receive information from your instructor about virtual learning during your isolation/quarantine period. Please be patient as there may be some delay between you being notified of quarantine/isolation, placed on the COVID dashboard, and contacted by your instructor about your status. Students not approved (or not awaiting approval) for virtual learning should follow normal class attendance policies.

Major assessments must be completed in-person on the scheduled date unless prior approval for online/remote (or delay) has been approved by Student Services due to isolation, quarantine, or other approved medical reasons.

### Tentative Schedule

I aim to build a dynamic classroom; as such, the schedule below may be changed as the semester progresses. Any changes will be reflected here and in the course notes.

Week Day Topic Work Due
1 15-Jan Course intro WCP 1
2 18-Jan All about cubies
2 20-Jan Challenge Day I
2 22-Jan Challenge Day II WCP 2
3 25-Jan Notation and Order
3 27-Jan Magic Cube Moves I
3 29-Jan Magic Cube Moves II WCP 3
4 1-Feb Magic Cube Moves III-IV M4HF Reflection: Chs. 1-5
4 3-Feb Reading discussion; Truth and Inductive Reasoning
4 5-Feb Thematic Checkpoint 1 Thematic Checkpoint 1
5 8-Feb Axioms
5 10-Feb Deductive Reasoning
5 12-Feb Formal Logic WCP 4
6 15-Feb No class
6 17-Feb The Foundational Crisis of Mathematics
6 19-Feb Infinity and Incompleteness WCP 5; M4HF Reflection: Chs. 6-7
7 22-Feb Thematic Checkpoint 2 Thematic Checkpoint 2
7 24-Feb Reading discussion; Apportionment I
7 26-Feb Apportionment II WCP 6; Final in-office attempt at Thematic Checkpoint 1
8 1-Mar Apportionment III
8 3-Mar Electoral College I
8 5-Mar Electoral College II WCP 7
9 8-Mar Electoral College III
9 10-Mar Electoral College IV
9 12-Mar Math and Democracy Conclusion WCP 8
10 15-Mar Thematic Checkpoint 3 Thematic Checkpoint 3
10 17-Mar Discrete Dynamical Systems I
10 19-Mar Discrete Dynamical Systems II WCP 9; Project ranking due
11 22-Mar Discrete Dynamical Systems III M4HF Reflection: Chs. 8-11
11 24-Mar Reading discussion; Discrete Dynamical Systems IV
11 26-Mar Discrete Dynamical Systems V WCP 10
12 29-Mar Discrete Dynamical Systems VI
12 31-Mar Graph Theory I
12 2-Apr Graph Theory II WCP 11; Preliminary Report due
13 5-Apr Graph Theory III
13 7-Apr No class
13 9-Apr Graph Theory IV WCP 12
14 12-Apr Graph Theory V
14 14-Apr Graph Theory VI
14 16-Apr HT Lab WCP 13
15 19-Apr HT Lab
15 21-Apr HT Lab M4HF Reflection: Chs. 12-13, Epilogue
15 23-Apr Thematic Checkpoint 4 Thematic Checkpoint 4
16 26-Apr Reading discussion; Fractal Geometry I
16 28-Apr Fractal Geometry II
16 30-Apr Fractal Geometry III WCP 14
Finals Mathematical beauty presentations