# math

### Repository of files related to the NYT COVID-19 dataset

I’ve created a GitHub repository based on the New York Times’ COVID-19 database. The New York Times has been compiling COVID-19 data from various state health departments. They have published the data as a GitHub repository. There are two files of interest in their repository: us-states.csv and us-counties.csv. In these CSV files, each row represents the number of (confirmed) cases and deaths in a particular geographical area as of a particular date.

### Plotting with TikZ, Part III: Plotting a function defined by a formula, and plotting functions that go through certain points

In the last post, I described how I use TikZ to create a graph that might otherwise be created freehand: In this post, I will describe one method for using TikZ to to plot a function defined by a formula, such as $$y = \left(2x^2 - x - 1\right)e^{-x}.$$ Then I will show two ways to make a function go through a certain point. Plotting from a formula Simple example There are a number of ways to achieve this, and PGF actually includes the functionality to perform calculations in TeX.

### Plotting with TikZ, Part II: Functions without formulæ

In the last post, I explained why TikZ is awesome for making plots. One good use case for handmade TikZ plots is to typeset a question like this: (2 points each) A plot of the graph of the function $f$ is below: For each of the following expressions, either evaluate the expression or state that it is undefined: a. $\lim_{x \rightarrow 2^{-}} f(x)$ b. $\lim_{x \rightarrow 2^{+}} f(x)$

### Plotting with TikZ, Part I: Why?

This is the first part of a three-part series of posts on generating plots of graphs with TikZ. Last year, I left my position as a mathematics professor, after teaching mathematics at the college level for 15 years (nine years as a faculty member, and six years as a graduate teaching fellow). In that time, I picked up a lot of tricks using LaTeX to produce teaching materials (handouts and slides).

The other day, I was writing some lecture notes for my linear algebra class, and wanted to create the following diagram (to illustrate the concept of a Markov chain): I had a very limited time in which to finish these notes. Fortunately, I found the tkz-graph package, which made this a snap: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 \documentclass{standalone} \usepackage{tikz} \usepackage{fouriernc} \usepackage{tkz-graph} \begin{document} \begin{tikzpicture} \SetGraphUnit{5} \Vertex[x=0, y=10]{0 points}; \Vertex[x=0, y=5]{1 point}; \Vertex[x=0, y=0]{Win}; \Vertex[x=5, y=5]{Lose}; \Edge[style ={->}, label={$1/3$}]({0 points})({1 point}); \Edge[style ={->}, label={$1/3$}]({1 point})({Win}); \Edge[style ={->}, label={$1/6$}]({0 points})({Lose}); \Edge[style ={->}, label={$1/6$}]({1 point})({Lose}); \Loop[style ={->}, label={$1/2$}, labelstyle={fill=white}]({0 points}); \Loop[style ={->}, label={$1/2$}, labelstyle={fill=white}]({1 point}); \Loop[style ={->}, label={$1$}, dir=EA, labelstyle={fill=white}]({Lose}); \Loop[style ={->}, label={$1$}, labelstyle={fill=white}]({Win}); \end{tikzpicture} \end{document} You don’t even have to specify the locations of the vertices; you can throw caution to the wind and have LaTeX decide where to place them!

### Book recommendation: How Not to Be Wrong

Today, I finished reading How Not to Be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg. This is a very enjoyable, very well-written, general-audience book about mathematics, which I recommend whole-heartedly. Ellenberg, a math professor at the University of Wisconsin, does a great job weaving together a plethora of mathematical topics, including non-Euclidean geometry, probability, statistics, and mathematical analysis of voting systems. He writes in a way that someone who only vaguely remembers—or never really understood—high school algebra would be able to follow and enjoy.

### Sum question!

The American Mathematical Society made the following amusing post to their Facebook page today: It’s National Punctuation Day (at least in the U,S,)! To honor the occasion, for positive integers n, let n? = 1 + 2 + … + n. What is 3???? (Hint: < 1000) You can calculate 3???? = 26796, which of course is greater than 1000. The joke is that they aren’t asking you to calculate 3?

### This joke is awesome and deserves more than just a retweet

This joke is awesome and deserves more than just a retweet: I'd wager that right now, Eric Cantor’s sorrows are… (•_•) ( •_•)⌐■-■ (⌐■_■) uncountable. — “patrick” (@importantshock) June 11, 2014 (Georg Cantor’s diagonal argument shows that the real numbers are uncountable.)

### Brains over calculators, part 2.

MathJax.Hub.Config({ tex2jax: { inlineMath: [['$','$'], ['\$$','\$$']], displayMath: [['$$','$$'], ['\$','\$']], processEscapes: true, processEnvironments: true, skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'], TeX: { equationNumbers: { autoNumber: "AMS" }, extensions: ["AMSmath.js", "AMSsymbols.js"] } } }); I recently found another calculation that I would consider reasonable for my students to perform that their calculators cannot. On my Calc II students’ final exam, I asked them to evaluate the infinite series $\displaystyle \sum_{n = 1}^\infty \frac{4}{(n + 3)(n+5)}$.

### Brains over calculators!

I enjoy finding calculations that I would consider reasonable for my students to perform that their calculators cannot. MathJax.Hub.Config({ tex2jax: { inlineMath: [['$','$'], ['\$$','\$$']], displayMath: [['$$','$$'], ['\$','\$']], processEscapes: true, processEnvironments: true, skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'], TeX: { equationNumbers: { autoNumber: "AMS" }, extensions: ["AMSmath.js", "AMSsymbols.js"] } } }); Using a double-angle identity and the pythagorean identity, it’s pretty straightforward to show that $\sin\left(2\sin^{-1}\left(-\frac{4}{5}\right)\right) = -\frac{24}{25}.$ However, my TI-89 returns an unhelpful $-\sin(2\sin^{-1}(4/5))$ instead.