#### ALGORITHM

### The faster-than-fast Fourier transform

The Fourier transform is one of the most fundamental concepts in the information sciences. It’s a method for representing an irregular signal — such as the voltage fluctuations in the wire that connects an MP3 player to a loudspeaker — as a combination of pure frequencies. It’s universal in signal processing, but it can also be used to compress image and audio files, solve differential equations and price stock options, among other things.The reason the Fourier transform is so pre...

1,313 0 0 FFT FAST FOURIER TRANSFORM MIT COMPRESSION

### Will We Need Teachers Or Algorithms?

Editor’s note: This is Part III of a guest post written by legendary Silicon Valley investor Vinod Khosla, the founder of Khosla Ventures. In Part I, he laid the groundwork by describing how artificial intelligence is a combination of human and computer capabilities In Part II, he discussed how software and mobile technologies can augment and even replace doctors. Now, in Part III, he talks about how technology will sweep through education. In my last post, I argue...

985 0 0 ALGORITHM DEVELOPMENT TEACHER

### Why Data Structures Matter

Our experience on Day 0 of JPR11 yielded a nice example of the need to choose an appropriate implementation of an abstract concept. As I mentioned in the previous post, we experimented with Michael Barker’s Scala implementation of Guy Steele’s parallelizable word-splitting algorithm (slides 51-67). Here’s the core of the issue. Given a type-compatible associative operator and sequence of values, we can fold the operator over the sequence to obtain a single accumulated value. For exam...

1,138 0 0 IMPORTANCE DATA STRUCTURE JPR

### What the Heck are Algebraic Data Types? ( for Programmers )

This post is meant to be a gentle introduction to Algebraic Data Types. Some of you may be asking why you should learn Algebraic Data Types and how will they change your world? I am not going to answer that, but suffice it to say that Algebraic Data Types are the underpinning of the type systems to the ML derived languages, Haskell and OCaml included, and their construction and properties allow for the power (and inference) that accompanies these type systems. They are cropping...

1,572 0 0 PROGRAMMER ALGEBRAIC DATA TYPE SET OPERATOR

### Build your own internet search engine - Part 2

After having started to build my own internet search engine as described in a previous blog post, I now have read some papers and books about web search engine architecture and information retrieval to complete my hobby project. Here is a list of papers and books that I highly recommend to anybody who is interested in this topic: 1. Google: data structures and algorithms by Petteri Huuhka 2. The Anatomy of a Large-Scale Hypertextual Web Search Engine by the Google founde...

2,046 0 0 DATABASE SEARCH ENGINE PAPER DATA STRUCTURE

### How Integers Should Work (In Systems Programming Languages)

My last post outlined some of the possibilities for integer semantics in programming languages, and asked which option was correct. This post contains my answers. Just to be clear: I want practical solutions, but I’m not very interested by historical issues or backwards compatibility with any existing language, and particularly not with C and C++. We’ll start with: Premise 1: Operations on default integer types return the mathematically correct result or else trap. This is the same pre...

1,121 0 0 ALGORITHM NUMBER SYSTEM EMBEDDED SYSTEM

### Eleven Equations True Computer Science Geeks Should (at Least Pretend to) Know

This idea is a complete rip off an article that appeared in Wired a little while ago and it got me thinking what would my list for Computer Science look like? Plus I thought it might be a fun post and unlike the Wired list this one goes to eleven. So here they are in no particular order: Binomial Coefficient The Binomial Coefficient equation generates Pascal’s Triangle and gives you the coefficients for the Binomial Theorem these ideas are often attributed to Pascal ...

1,413 0 0 ALGORITHMS COMPUTER SCIENCE EULER FORMULA FERMAT

### Surprising applications of math

The comments in the previous post touched on surprising applications of math, so I thought I’d expand this theme into it’s own post. Below I’ll give a couple general examples of surprising applications and then I’ll give a couple more personal applications I found surprising.Number theory has traditionally been the purest of pure mathematics. People study number theory for the joy of doing so, not to make money. At least that was largely true until the advent of public key...

1,086 0 0 MATH ALGORITHMS NUMBER THEORY DIFFERENTIAL EUQATION