Tag Archives: Computer Science

Mathematical Physics, Determinism, Game of Life (Hiking in Modern Math 6/7)

March 03, 2016More Hiking in Modern Math World798 vuesEdit

Chaos Theory, Meteorology, Navier-Stokes, Wolfram (Hiking in Modern Math 5/7)

February 21, 2016More Hiking in Modern Math World879 vuesEdit

Complexity Theory, P versus NP, RSA Cryptography (Hiking in Modern Math 2/7)

February 13, 2016More Hiking in Modern Math World1273 vuesEdit

Theory of Computation, Turing Machine (Hiking in Modern Math 1/7)

February 09, 2016More Hiking in Modern Math World2054 vuesEdit

Shannon’s Information Theory (Trek through Math 5/8)

February 03, 2016A Trek through 20th Century Mathematics901 vuesEdit

Univalent Foundations of Mathematics

April 21, 2014Article2366 vuesEdit
In an effort to make mathematics more computable, a consortium of today's greatest mathematicians have laid out new foundations. Amazingly, they all lie upon one single axiom, called univalence. The goal of this axiom is to make formal mathematics more similar to informal mathematics. With univalence, our Arabic numbers aren't just like natural numbers; They are natural numbers. Univalence also has unforeseen and mesmerizing consequences.

Homotopy Type Theory and Higher Inductive Types

April 06, 2014Article2057 vuesEdit
In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) circle and sphere.

Type Theory: A Modern Computable Paradigm for Math

March 20, 2014Article8359 vuesEdit
In 2013, three dozens of today's brightest minds have just laid out new foundation of mathematics after a year of collective effort. This new paradigm better fits both informal and computationally-checkable mathematics. There is little doubt that it will fundamentally change our perspective on rigorous knowledge, and it could be that, in a few decades, the book they published turns out to be the bedrock of all mathematics, and, by extension, all human knowledge! Have a primer of this upcoming revolution, with this article on type theory, the theory that the book builds upon!

The Tortuous Geometry of the Flat Torus

March 09, 2014Article10619 vuesEdit
Take a square sheet of paper. Can you glue opposite sides without ever folding the paper? This is a conundrum that many of the greatest modern mathematicians, like Gauss, Riemann, and Mandelbrot, couldn't figure out. While John Nash did answer yes, he couldn't say how. After 160 years of research, Vincent Borrelli and his collaborators have finally provided a revolutionary and breathtaking example of a bending of a square sheet of paper! And it is spectacularly beautiful!

The New Big Fish Called Mean-Field Game Theory

February 05, 2014Article8490 vuesEdit
In recent years, at the interface of game theory, control theory and statistical mechanics, a new baby of applied mathematics was given birth. Now named mean-field game theory, this new model represents a new active field of research with a huge range of applications! This is mathematics in the making!

Numbers and Constructibility

November 05, 2013Article4907 vuesEdit
Last summer, I got to discover Morellet's artwork on inclined grids. Amazingly, this artwork is a display of the irrationality of $\sqrt{2}$! It's also a strong argument for the existence of this number. In this article, after discussing that, I take readers further by discussing what numbers can be constructed geometrically, algebraically, analytically or set theoretically using the power of mathematics!

Shannon’s Information Theory

March 17, 2013Article23763 vuesEdit
Claude Shannon may be considered one of the most influential person of the 20th Century, as he laid out the foundation of the revolutionary information theory. Yet, unfortunately, he is virtually unknown to the public. This article is a tribute to him. And the best way I've found is to explain some of the brilliant ideas he had.

Cryptography and Quantum Physics

December 28, 2012Article1779 vuesEdit
Recent discoveries in the branch of physics known as quantum mechanics have powerful applications in the field of network security - they have the potential to break forms of internet security based on mathematics such as the RSA algorithm, and also present new ways to safely send information. In this article we’ll see how a physics-based method can be used to secure online information.

Bayesian Games: Math Models for Poker

November 12, 2012Article5031 vuesEdit
How to better understand Poker and card games in general? Bayesian games provide the right mathematical model just for that! These correspond to games with incomplete information and include probabilistic reasonings.

Probabilistic Algorithms, Probably Better

August 31, 2012Article1319 vuesEdit
Probabilities have been proven to be a great tool to understand some features of the world, such as what can happen in a dice game. Applied to programming, it has enabled plenty of amazing algorithms. In this article, we discuss its application to the primality test as well as to face detection. We'll also deal with quantum computers, as well as fundamental computer science open problems P=BPP and NP=BQP.

Web Programming: From HTML to AJAX

July 16, 2012Article3051 vuesEdit
The Internet is an unavoidable component of today's life, and will only become more and more important in the future. In this article, we"ll have an overview of its development in terms of coding languages. This article explains how webpages actually work. In particular, we'll discuss HTML, CSS, PHP, WordPress, MySQL, Javascript, XML and JSON, as well as their competitors.

P versus NP: A Crucial Open Problem

June 28, 2012Article5572 vuesEdit
P=NP is probably today's most crucial open problem. Not only is it a very theoretical question in computer science and mathematics, but it also has major implications to real world. Its resolution could revolutionize the world. This article gives the definition and major results of P=NP.

From Divide and Conquer to Parallelization

June 26, 2012Article1422 vuesEdit
Divide and conquer is a extremely powerful concept that is being used a lot in computer science, and that can also be applied in real life. We present its application to sorting algorithms. Then we'll talk about a major fundamental open mathematical problem, called P=NC.