Autumn 2021
Math 300H: Honors Foundations of Mathematics Section 970.

MATH 300H Writing Assignment
Fall 2021

For Paper: University Writing Center
Submit paper to turnitin.com, using Class ID: 32682088 and Enrollment key 314159265.
Also turn in hard copy on the last day of class, 8 December. Sample Rubric. This is to help you think about the different aspects of your paper.

This is to be an expository paper, on a topic involving mathematics or mathematics education, written for a reader with a similar mathematical background as your fellow students. I have a list at the end of this page of some suggestions; feel free to come up with your own, and also feel free to talk to me about that. The paper need not contain proofs, but should have significant mathematical content, but for some topics, you will need to give some proofs, or a sketch, and for some you will need graphics to illustrate the main ideas. Any mathematics should be explained clearly enough that your classmates would understand it. You must use and cite two or more sources (e.g. books, journals, or newspaper articles), not including Wikipedia, but you should look at on-line sources as well. Numberphile may be a source for inspiration.
You should typeset it in LaTeX. This will create page numbers, and you should have your name on each page (we need to figure out how to do that, maybe google "running Heads"). The length guidelines are to prevent students from writing too little, and therefore not giving themselves enough space to develop their topics.
Due dates and further details are below.
Here are a few points that you need to keep in mind:

Your paper needs a title.
Please use 1 inch margins.
It is "mathematics" and not "math", or even "maths". (Do not use slang in formal writing).
Remember: 'number' for discrete things 'amount' for indiscrete things, e.g. less flour, fewer beans.
Use language, particularly mathematical language, properly.
Do not start a sentence with a mathematical symbol.
Please, no contractions.
Omit useless words, such as the filler phrases "In order [to]" or "the face that".
Do not use words for mere variety, make every word count, and be correct. E.g. verbs are not always interchangeable, and be careful with the overuse of adverbs and sloppy metaphors.
Pay attention to paragraph and sentence structure, and avoid being repetitious.

Friday 17 September	Proposal due at or before the start of class. This should be one or two sentences describing the chosen topic.
Monday 1 October	Outline of paper due at or before the start of class. It should contain most or all of the ideas that will appear in the final paper. Include references. Any reasonable style is OK. Latex automatically creates a bibliography, if you set it up properly (look up BiBTeX).
Friday 5 November	Nearly complete draft of paper due at or before the start of class. This should be in 12 point `\documentclass[12pt]{article}` and include the line `\renewcommand{\baselinestretch}{1.5}`
Monday 22 November	Peer Review. In class, with a participation grade.
Monday 8 December	Final paper due at or before the start of class. This must be a minimum of 3000 words, typeset in Latex with 12 point type. The length requirement is to help you have enough space to properly tell the story you intend. The grade will be based on mechanics, presentation, and content.

Here are some topics to get you thinking

Any topic covered in an article that won the Mathematical Association of America's Chauvenet Prize.
Same thing for the Mathematical Association of America's Paul R. Halmos – Lester R. Ford Award.
The Five Color Theorem. (This should include history and a proof).
The Four Color Theorem (Mostly history and an idea of the proof).
Any Fields medalist (including the most recent ones).
Any mathematician for which one can write 5–10 pages.
Any of the Millennium Prize problems.
Crystal structures and symmetry.
Euler-Poincaré Characteristic.
Gödel's Incompleteness Theorem.
Cantor's theory of infinite sets.
Continuum hypothesis.
The Cantor set and fractals.
Error-correcting codes, especially linear or matrix codes.
public key cryptography.
elliptic curve cryptography.
Prime number theorem.
Sphere packing problem (Kepler's conjecture).
Platonic solids in all dimensions.
Transcendental Numbers.
Big theorems or problems such as Fermat's Last Theorem, The Poincaré Conjecture, or the Riemann Hypothesis.
Other important applications of Mathematics.
Shapley's Stable Marriage Thoerem.
P vs. NP.
Democratic elections and Arrow theorem.
Proofs of impossibility (e.g. classical Greek constructions).
Collatz Conjecture.
The numbers 17, 257, and 65537.
Do not write on the Golden Ratio

Topics already chosen

Non-cooperative Game Theory abd thre Nash Equilibrium
Public Key Cryptography
Fermat's Last Theorem
Prime Number Theorem
Crystals and Symmetry
Four Color Theorem
Shapley's Stable Marriage Theorem
Symmetric Key Encryption
Grigori Perelman
The Mathematics of Rubik's Cubes
Riemann Hypothesi
Carl Friedrich Gauß
The Inscribed Square Problem
Elliptic Curve Cryptography
P vs NP
Applying PageRank to soccer
Parallel Postulate
Prouhet-Thue-Morse Sequence

Last modified: Tue Dec 21 07:57:08 CST 2021 by sottile

Autumn 2021 Math 300H: Honors Foundations of Mathematics Section 970.

MATH 300H Writing Assignment Fall 2021

Here are some topics to get you thinking

Topics already chosen

Autumn 2021
Math 300H: Honors Foundations of Mathematics Section 970.

MATH 300H Writing Assignment
Fall 2021