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If you’re a math genius — many of you are! — and you’ve blogged about equations you’ve worked on, you’ve probably used LaTeX before. If you’re just starting out (or simply curious to see how it all works), we’ve gathered a few examples of great math and computing blogs on WordPress.com that will inspire you.

In general, to display formulas and equations, you place LaTeX code in between $latex and $, like this:

$latex YOUR LATEX CODE HERE$

So for example, inserting this when you’re creating a post . . .

$latex i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>$

. . . will display this on your site:

i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>

Nifty, huh? Learning LaTeX is like learning a new language, and the bloggers below show just how much you can do. And if you’re not a math whiz, don’t worry! You’re not expected to understand the snippets below, but we hope they show what’s possible.

Gödel’s Lost Letter and P=NP

Suppose Alice gives Bob two boxes labelled respectively {X} and {Y}. Box {X} contains some positive integer {x}, and as you might guess, box {Y} contains some positive integer {y}. Bob cannot open either box to see what integer it holds. Bob can shake the boxes, or hold them up to a bright light, but there is no way he can discover what they contain.

This blog, on P=NP and other questions in the theory of computing, presents the work of Dick Lipton at Georgia Tech and Ken Regan at the University at Buffalo. One of their main goals is to pull back the curtain so readers can understand how research works and who is behind it.

From the recent post “Move the Cheese” to an older piece on “Navigating Cities and Understanding Proofs,” they present problems and sketch solutions, and publish thorough and thoughtful discussions that not only talk about interesting open problems, but offer context and history.

You can see LaTex in action in the example above, from the recent post “Euclid Strikes Back.”

Math ∩ Programming

Note that we will have another method to determine the necessary coefficients later, so we can effectively ignore how these coefficients change. Next, we note the following elementary identities from complex analysis:

\displaystyle \cos(2 \pi k t) = \frac{e^{2 \pi i k t} + e^{-2 \pi i k t}}{2}
\displaystyle \sin(2 \pi k t) = \frac{e^{2 \pi i k t} - e^{-2 \pi i k t}}{2i}

Jeremy Kun, a mathematics PhD student at the University of Illinois in Chicago, explores deeper mathematical ideas and interesting solutions to programming problems. Math ∩ Programming is both a blog and portfolio, and well-organized: you can use the left-side menu to navigate Jeremy’s sections, from Primers to the Proof Gallery. The site is also clean and well-presented — can you believe he uses the Confit theme, which was originally created for restaurant sites?

The snippet above illustrates more you can do with LaTeX, taken from “The Fourier Series — A Primer.”

Terence Tao

Definition 1 (Multiple dense divisibility) Let {y \geq 1}. For each natural number {k \geq 0}, we define a notion of {k}-tuply {y}-dense divisibility recursively as follows:

  • Every natural number {n} is {0}-tuply {y}-densely divisible.
  • If {k \geq 1} and {n} is a natural number, we say that {n} is {k}-tuply {y}-densely divisible if, whenever {i,j \geq 0} are natural numbers with {i+j=k-1}, and {1 \leq R \leq n}, one can find a factorisation {n = qr} with {y^{-1} R \leq r \leq R} such that {q} is {i}-tuply {y}-densely divisible and {r} is {j}-tuply {y}-densely divisible.

We let {{\mathcal D}^{(k)}_y} denote the set of {k}-tuply {y}-densely divisible numbers. We abbreviate “{1}-tuply densely divisible” as “densely divisible”, “{2}-tuply densely divisible” as “doubly densely divisible”, and so forth; we also abbreviate {{\mathcal D}^{(1)}_y} as {{\mathcal D}_y}.

Mathematician, UCLA faculty member, and Fields Medal recipient Terence Tao uses his WordPress.com site to present research updates and lecture notes, discuss open problems, and talk about math-related topics.

He uses the Tarski theme with a modified CSS (to do things such as boxed theorems). As stated on his About page, he uses Luca Trevisan’s LaTeX to WordPress converter to write his more mathematically intensive posts. Above, you’ll see an example of how he uses LaTeX on his blog, excerpted from the post “An improved Type I estimate.”

Terence also has a blog category for non-technical posts, aimed at a more general audience, and offers helpful advice on mathematical careers.

Using LaTeX

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