JLISZKA.GITHUB.IO

A Gentleman and a Scala

A Gentleman and a Scala. A Gentleman and a Scala. Understanding math through code. My name is Jason Liszka, and I’m a software engineer at Foursquare in New York. This blog chronicles my attempt to understand math better through code. I’ve always been interested in abstract math, but computation has always been more intuitive to me. Realizing abstract structures in code makes them more concrete and makes it easier for me to wrap my puny human brain around them. You should follow me on twitter. Raquo; A f...

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A Gentleman and a Scala. A Gentleman and a Scala. Understanding math through code. My name is Jason Liszka, and I’m a software engineer at Foursquare in New York. This blog chronicles my attempt to understand math better through code. I’ve always been interested in abstract math, but computation has always been more intuitive to me. Realizing abstract structures in code makes them more concrete and makes it easier for me to wrap my puny human brain around them. You should follow me on twitter. Raquo; A f...

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A Gentleman and a Scala | jliszka.github.io Reviews

https://jliszka.github.io

A Gentleman and a Scala. A Gentleman and a Scala. Understanding math through code. My name is Jason Liszka, and I’m a software engineer at Foursquare in New York. This blog chronicles my attempt to understand math better through code. I’ve always been interested in abstract math, but computation has always been more intuitive to me. Realizing abstract structures in code makes them more concrete and makes it easier for me to wrap my puny human brain around them. You should follow me on twitter. Raquo; A f...

INTERNAL PAGES

jliszka.github.io

1

Fun with Bayesian Priors

http://jliszka.github.io/2013/09/03/fun-with-bayesian-priors.html

A Gentleman and a Scala. Fun with Bayesian Priors. Say you have a biased coin, but you don’t know what the true bias is. You flip the coin 10 times and observe 8 heads. What can you say now about the true bias? It’s easy to say that the most likely bias is 0.8. That’s accurate, but maybe you also want to know what other biases are likely. How likely is it that you have a fair coin? Can you rule out having a bias as low as 0.4? That I’ve been working on as an exercise in trying to better understand some.

2

The Foursquare Theorem

http://jliszka.github.io/2013/11/14/the-foursquare-theorem.html

A Gentleman and a Scala. This has nothing to do with the playground game. Or the mobile/social/local city guide. That helps you make the most of where you are. (Disclosure: I work at Foursquare.). This is about Lagrange’s four-square theorem. Which states that every natural number can be expressed as the sum of four squares. For example,. The proof given on the Wikipedia page is only an existence proof, but I was able to find a mostly constructive proof. Main foursquare 123456789 (-2142,8673,6264,-2100).

3

Insertion sort is dual to bubble sort

http://jliszka.github.io/2013/09/18/insertion-sort-is-dual-to-bubble-sort.html

A Gentleman and a Scala. Insertion sort is dual to bubble sort. I noticed recently that insertion sort. Backwards. Or inside out. Or something. Both algorithms can be expressed as a main function that calls a recursive helper. Let’s take a look at the main functions first. Sorts a list by inserting the head of the list into the recursively sorted tail, in such a way that it remains sorted. Sorts a list by bubbling the smallest element to the front of the list and recursively sorting the tail. The data fl...

4

How traffic actually works

http://jliszka.github.io/2013/10/01/how-traffic-actually-works.html

A Gentleman and a Scala. How traffic actually works. Every so often this article. Makes the rounds and it annoys me. That isn’t how traffic works and the proposed solutions won’t fix anything. Maybe you can eliminate the annoying stop-and-go, but no one gets home any faster. In fact you can prove that you and everyone behind you get home strictly later than if you had just gone along with the stop-and-go traffic. Here’s how traffic works. First, we know from empirical studies. If anyone tries to tell you.

5

A frequentist approach to probability

http://jliszka.github.io/2013/08/12/a-frequentist-approach-to-probability.html

A Gentleman and a Scala. A frequentist approach to probability. One thing that always confused me in my intro stats classes was the concept of a random variable. A random variable is not a variable like I’m used to thinking about, like a thing that has one value at a time. A random variable is instead an object that you can sample values from, and the values you get will be distributed according to some underlying probability distribution. The idea is that. Returns a different value (of type. Over the un...

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A Gentleman and a Scala

A Gentleman and a Scala. A Gentleman and a Scala. Understanding math through code. My name is Jason Liszka, and I’m a software engineer at Foursquare in New York. This blog chronicles my attempt to understand math better through code. I’ve always been interested in abstract math, but computation has always been more intuitive to me. Realizing abstract structures in code makes them more concrete and makes it easier for me to wrap my puny human brain around them. You should follow me on twitter. Raquo; A f...

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