Math/CS 299/399 Colloquium in Mathematics & Computer Science I & II Fall 2020

# Introductory Essay

## Video Overview

I've created a Video Overview. For some reason, the audio drops out and returns late in the video.

## Goals

The goals of this assignment are for you to reflect on your previous mathematical experiences. It also serves as a exercise in learning LaTeX (299) or recalling how to use LaTeX (399). Use a simple article style for your latex document. Contact me if you have questions on the use of LaTeX.

## Assignment

#### 299 and 399: Stylized name

(5 points) Express your name creatively using the special and mathematical symbols available to you in LaTeX. For example, here is one way to express my name:

Which is created in LaTeX using the following code:

$\mathcal{D}\alpha\vec{\rm v}$\i $\partial$
$\Lambda$.~$\mathbb{R}e^i$\raisebox{-.3ex}{\footnotesize\Scorpio}\textcircled{a}n$^2$


You can simplify some things in LaTeX by using macros. Here is an example that creates a macro called \myName that contains my name in special symbols and then uses it in a ecntered line.

\newcommand{\myName}{%
$\mathcal{D}\alpha\vec{\rm v}$\i $\partial$
$\Lambda$.~$\mathbb{R}e^i$\raisebox{-.3ex}{\footnotesize\Scorpio}\textcircled{a}n$^2$}
\begin{center}
\myName
\end{center}


Have fun and be creative!

#### Math/CS 299: Memorable mathematics or computer science experience

(10 points) Write a brief essay (100-250 words) using LaTeX on one of your most memorable experiences learning mathematics or computer science. What math or CS did you learn? Why was this memorable? This could be from a college course, a high school or grade school course, or an extracurricular activity. Include some mathematical symbols, code blocks, or other LaTeX features in the body of your essay (not just an add-on at the end).

#### Math/CS 399: Favorite theorem or Algorithm

(10 points) Restate a favorite mathematical theorem or computational algorithm and include a proof. Explain why you choose this theorem or algorithm.

If you are writing about a favorite theorem, two components are required for this component of the assignment:

1. Restate a favorite mathematical theorem. Clearly define any variables.
2. Give a proof.
3. Use LaTeX's theorem environment as follows:
\begin{theorem}[NameOfTheorem]
State theorem here.
\end{theorem}
\begin{proof}
Give proof here.
\end{proof}

4. Write a paragraph why this theorem interests you.
5. See Overleaf's Theorems and proofs page for additional information on the Theorem environment.

If you are writing about a favorite computational algorithm, two components are required for this component of the assignment:

1. Restate computational algorithm. Clearly define any variables. This could be expressed using pseudocode or a specific programming language.
2. Give a brief description why it works.
3. It is OK to copy from a book as long as you cite the source using BibTeX. Use one of LaTeX's environments. See Overleaf's Algorithms page for additional information on options for typesetting algorithms.
4. Write a paragraph why this algorithm interests you.

Kevin Knudson and Evelyn Lamb have a podcast series where they have interviewed contemporary mathematicians about their favoritive theorems called My Favorite Theorem. They have completed roughly 50 interviews so far; all are available as audio and have been transcribed. At least two of these episodes feature speakers who have given colloquium talks at Albion!

## Deliverables

Email your instructor a pdf of your paper that contains your stylized name followed by the other component.

Use 1 inch margins. You can do this by placing the following code in the preamble (above \begin{document}).

\usepackage[letterpaper, portrait, margin=1in]{geometry}