Proof Portfolio

Over the course of the semester you will create a portfolio of mathematical writing. The portfolio will consist of 9 entries: 6 formal mathematical proofs and 3 other expository entries. Proofs will come from a list of portfolio problems (under revision). The other entries will be responses to reading an expository article on mathematics, an older mathematics article, and some modern matheamtics. Details are below.

The portfolio entries should be written using LaTeX. This is free, open source software, so you can download it onto your personal computers (which I can help you with). You can also make use of the computers in certain labs. Examples, links to software sources, and templates are posted below.

The class after a portfolio proof is due will be a peer-review day. You will read portfolio proofs and make suggestions for how they could be improved. This may mean correcting spelling or grammar, but the focus should be on the mathematical content. We may collectively develop a rubric to use when evaluating proofs. Comments and suggestions will be returned to the authors, who will then revise their proofs before turning in a final draft for grading. The final draft is due about 1 week later (see the schedule for deadlines).

I will be evaluating the final proofs using the same rubric, so your honest critiques should help your classmates earn better grades (don't go easy on each other). At the end of the semester you will compile the portfolio entries into one document (again using LaTeX). This gives you one last chance to revise your proofs and other portfolio entries before they get a final grade.

LaTeX resources:

• Getting started with LaTeX. A good place to start if you want to install LaTeX on your computer.
• TeXworks. A free (simple) LaTeX editor to install locally.
• Overleaf. An online LaTeX editor and compiler (use the free plan).
• LaTeX Base. Another online LaTeX editor and compiler (free).
• Short Math Guide with all the symbols you'll need.
• template.tex and template.pdf.
• Short video intro to math in LaTeX (and the file in the video).

First LaTeX assignment (the pre-portfolio entry):

Create a LaTeX document that compiles to make a pdf with your name, the date, and the LaTeX logo (\LaTeX). Due 1/21.

Expository entry 1:

Read and respond to an expository article on mathematics. Choose one of the following readings. Due 1/31.

Readings:

• Mathematicians Measure Infinities and Find They're Equal
• Mathematicians Identify Threshold at Which Shapes Give Way
• Graduate Student Solves Quantum Verification Problem
• Graduate Student Solves Decades-Old Conway Knot Problem
• Statistics Postdoc Tames Decades-Old Geometry Problem
• New Black Hole Math Closes Cosmic Blind Spot

Write (using LaTeX) a paragraph or two (about a half page total) in response to the reading. Questions to help guide your response (you do not have to answer all these questions):

• What was the reading about? Give a brief summary of the article.
• Was there any connection to what you've done in this class or other classes (not just math classes)?
• Did the author do a good job explaining the technical details? Did you understand? Do you think a non-mathematician would understand? Who do you think was the intended audience?
• Were there any figures or illustrations that helped? Should there have been figures?
• What could have made the article better? Or, what made it so good that you can't see room for improvements?

Expository entry 2:

Read and respond to a mathematician writing informally about mathematics. Choose one of the following readings. Due 2/14.

Readings:

• Mathematics and Thinking Mathematically by Lucy Cartwright
• The Mathematician by John von Neumann

Write (using LaTeX) a paragraph or two (about a half page total) in response to the reading. Answer the same questions as for expository entry 1 and compare with your first reading where applicable.

Expository entry 3:

Read and respond to a formal mathematics article. Read one of the following short articles from the The American Mathematical Monthy. Answer the same questions as for the first expository entry and compare and contrast with the article you read for portfolio entry 1. Due 4/20.

Readings:

• Ramanujan Primes and Bertrand's Postulate
• Another Continued Fraction for π
• A Note on Euler's Factoring Problem
• Superabundant Numbers and the Riemann Hypothesis
• Dynamical Systems and Irrational Angle Construction by Paper-Folding

Portfolio proofs:

Prove one statement from each section. This will give you 6 in total. Deadlines:

• Section A (also .tex) due 2/23.
• Section B (also .tex) due 3/16.
• Section C (also .tex) due 3/23.
• Section D (also .tex) due 4/1.
• Section E (also .tex) due 4/11.
• Section F (also .tex) due 4/27.

Final portfolio:

Revise your 9 portfolio entries and assemble them into one cohesive document. Use the template (tex) and (pdf) as a guide. Due by 4:00 PM on Thursday, May 5.

Links and class resources

• The Book of Proof
• Schedule
• Syllabus
• Math 301 Fall 2018
• Math 301 Spring 2015
• Math 301 Fall 2014
• WolframAlpha
• Geogebra
• Desmos
• Overleaf
• LaTeX Base

Office hours

In person in Herak 307A unless otherwise specified, or via Zoom by request.

• Monday 9-10 in the Math Learning Center and 2:30-3:30
• Wednesday 2:30-3:30
• Friday 9:30-10:30
• Or by appointment

Last updated 1/24/2022