Core 101       Mind-Bending Math: Paradoxes & Puzzles        Fall 2016


Professor:      Dave Kung

Office:            175 Schaefer Hall, x4433 or 240-895-4433


Peer Mentor: Jake Miller,

Library Liaison: Amanda VerMeulen (, x4268)

Resources:     Mind-Bending Math: Riddles & Paradoxes, Lectures from the Great Courses, The 5 Elements of Effective Thinking, by Starbird & Burger

Office Hours:           










Paradoxes force us to confront seemingly contradictory statements, ones that the world’s best minds have spent centuries grappling with. This course takes you inside their thinking and shows you how to resolve the apparent contradictions – or why you should accept the strange results! Statements that prove themselves true! A train that is both contained inside a tunnel – and longer than that tunnel! Creating two balls from one, just by cutting and rearranging the pieces! Explore the riddles that stumped humans, and see the ingenious, sometimes revolutionary solutions they discovered. You will not only learn how complex and nuanced the world is, you’ll train your mind to better deal with life’s everyday conundrums.

By the end of this course, you will be a better thinker, writer and speaker. In particular, at the completion of this course, you will be able to…

Š      evaluate textual arguments for their usefulness, cohesiveness and logic.

Š      identify and access relevant information sources.

Š      use effective oral expression strategies in making a formal presentation.

Š      demonstrate effective written communication with use of revision.

Š      participate responsibly and respectfully in informal group discussions.



This course will take a wandering journey through many different topics, all related to mathematics, and all filled with mind-bending curiosities.

Š      basic logic & an introduction to strange loops

Š      simple” numbers, probability & statistics

Š      infinity

Š      set theory and the foundations of mathematics (including Gödel’s Theorems)

Š      politics

Š      game theory

Š      physics

Š      topology

Š      measure theory


If we have time, we’ll build to the strangest of all math theorems: the Banach-Tarski Paradox. This astounding, unbelievable result shows that you can take a solid ball, split it into a small number of pieces, and reassemble them to make two complete balls, the same size as the original. Now that’s mind-bending.


Throughout all of these topics, we’ll focus on honing our thinking skills, becoming more thorough, careful, creative and deliberate thinkers.


Four Core Skills:

As you know from reading the SMCM catalog (right?) your First Year Seminar is designed to introduce four fundamental skills:

Š      Critical Thinking

Š      Written Expression

Š      Oral Expression

Š      Information Literacy

These skills will be introduced early in the course and practiced throughout the semester, with the goal of preparing you to use these skills (and further build them) in later courses.


Writing & Presentation Assignments: 

There will be a variety of writing assignments and oral presentations this semester. All written assignments are to be turned in via Google Docs (see below for more on this). More information on these assignments will be provided at a later date. In all written work, the use of sources must be documented with a citation in the text and a corresponding entry in the list of references at the end. Any style (e.g. MLA is common in the humanities, APA in the social sciences, etc.) is fine, as long as the reader could reasonably find the reference. Any direct quote should include a page number. (Some professors are very exacting about citation styles in their classes; I am not one of them.)


Mathematical Autobiography: (draft due Wed., Aug. 30th, final copy due Wed, Sept. 7th, 1 full page single-spaced, to be handed in via Google Docs) Tell us about your history with mathematics.


Flat Earth Assignment: (draft due Wed., Sept. 21st, final copy due Fri. Sept. 30th,  2-3p. single spaced) There was a time when most people on earth believed the earth was flat. As a species, we’ve largely got that one down now – but there are still many topics many people are wrong about. Find one. Investigate the history of the issue – who first studied the issue, what breakthroughs occurred, where misconceptions originated, why many people are still wrong. Delve into the key question: why are so many people still wrong – why don’t they change their minds?


One Puzzle, Explained: (draft due Fri., Oct. 21st, final copy due Wed., Nov. 2nd, 2-3p. single spaced, oral presentations following) Choose a puzzle, conundrum, or paradox not covered in this course (you may want to check with Dave), and write about it. Dig into the history, the different versions, the different solutions/resolutions. What deeper ideas are involved? What are the underlying mathematical concepts? Are there related problems that are harder – maybe even unsolved? Think of this as writing a Martin Gardner-type column.


Changing Your Mind, (due Monday, Dec. 5th, 2-3p. single spaced, oral presentations that week) All humans – even the brilliant ones – are wrong about many things. That includes you. Find something that’s important to you that you’re wrong about, and change your mind. Write about the process you went through to change your mind. It cannot be trivial (e.g. “I though walking through the woods to get to Kent was faster, but it’s not.”).


One note about length – if you find yourself changing margins to make page requirements, stop. Turn around. Go back. Write more (and not filler). I have finely honed BS detection skills – and don’t appreciate having to use them.


Online Tools:

We will make extensive use of two digital tools:

Blackboard: You should have access via your SMCM login:

Google Docs: If you haven’t played around, you should. Cloud-based editing (and commenting) tools are fantastic.


Exams:  On Oct. 9th in-class, we will hold a midterm exam. On Dec. 16th from 2-4:15pm we will hold a final exam. (And yes, the final is comprehensive.)


Attendance & Participation: You are expected to come to class everyday (with two excused absences during the semester), participate in class discussions and activities, complete reading assignments, and …


Homework: Homework assignments will come in different shapes and sizes, including posts on the class Discussion Board, thought questions to ponder (and bring your ideas to class), and actual “hand it in on paper” homework. You will always have at least a day and a half to complete these assignments.


Fifth Hour: The SMCM community offers a stunning array of interesting things to do and events to attend. Like all students in First Year Seminars, you are required to partake in at least five of these (though I hope you do more). For our seminar, the five must come from the following categories:

§  a math- or science-related talk in the NSM Colloquium Series (usually Wednesdays at 4:40pm) or a department-sponsored talk.

§  an exploration of a near-by natural area (Historic St. Mary’s City, North Field trails, Fishers Creek a.k.a. ‘Nam, kayaking on the river, Point Lookout, etc.)

§  a meeting of a student club

§  a fine arts-related event (play, concert, exhibit opening)

§  an event where you are an outsider, where you feel like you don’t belong. Not sure what this means? Ask.

Please make sure to start in on these five activities early in the semester – and complete them all before Thanksgiving. At each, take a selfie and post it in the appropriate Google Sheet. For one of them, you will write up a one-page reflection on the experience (probably the last one?) and submit it to receive credit for the “Fifth Hour”.


Your course grade will be determined as follows:


Attendance & Participation


Midterm Exam




Fifth Hour


Oral Presentations




Final Exam




Late Assignments: Late assignments will only be accepted under the following circumstances: an arrangement is agreed on before the due date, or a documented emergency situation. Generally late work (when allowed) will be subject to at least a 10% deduction (with greater deductions for extremely late work, at Dave’s discretion).


Student Conduct:  Violations of Student Code of Conduct, such as copying, plagiarizing, handing in others’ work, and lying about a death in the family will not be tolerated. The rules are clear, and the consequences stiff and range from receiving a zero for the assignment to a failing grade for the course, to being expelled from the college.


Documented Learning Issues: Anyone with a documented learning disability should contact me via email and set up a time to meet within the first two weeks of the semester.