# Make it simple. Make it cool.

Science4All is a website of *Quality Popular Science*.

I believe that the greatest challenge in education is to make science and math appealing.

This is why I aim at bringing enthusiasm and excitement to the readers’ learning experience.

The Secretary/Toilet Problem and Online Optimization The Secretary/Toilet Problem and Online Optimization

By Lê Nguyên Hoang | **Updated:**2015-04 | **Views**: 1343

A large chunk of applied mathematics has focused on optimizing something with respect to all relevant data. However, in practice, especially in the online world, the data is not available to us, and, yet, we’re still expected to make nearly optimal decisions. This problem is exemplified by the famous secretary problem, where a manager needs to decide to hire candidates right after interviews, even though he has not yet met all the candidates. In this article, we review this classic as well as many very recent developments., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Harmonious Mathematics of Music The Harmonious Mathematics of Music

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1590

It was when hearing the sounds of hammers that Pythagoras realized the ubiquity of numbers in mathematical harmony. He would go on laying down the mathematical foundations of music, based on octaves, perfect fifths and major thirds. This mathematics of music would then become the favourite playground of all musicians, from Beethoven to Gangnam Style., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Limitless Vertigo of Cantor’s Infinite The Limitless Vertigo of Cantor’s Infinite

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1384

No one believed him. Not even fellow mathematicians. They thought he was wrong. They thought he was crazy. Even he ended up doubting himself and went crazy. And yet, he had mathematically proved it all. Georg Cantor had figured out how to manipulate the infinite. Even more remarkable, he showed that there were actually several infinities; and some are bigger than others!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Beauty, the Driving Force of our Quest for Truth Beauty, the Driving Force of our Quest for Truth

By Lê Nguyên Hoang | **Updated:**2013-12 | **Views**: 932

According to Matthew Colless, the most important aspect of science is beauty. Not only is it what inspires scientists and their quests, I’d even claim that it’s also the compass that guide them in their quests, in a deeper and more surprising way that one can imagine!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Essence of Quantum Mechanics The Essence of Quantum Mechanics

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 6382

Quantum mechanics is the most accurate and tested scientific theory, Its applications to real life are countless, as all new technologies are based on its principles. Yet, it’s also probably the most misunderstood theory, because it constantly contradicts common sense. This article presents the most important features of the theory., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Glaciers: Retreat, Moraines, Valleys, Fjörds Glaciers: Retreat, Moraines, Valleys, Fjörds

By Lê Nguyên Hoang | **Updated:**2014-04 | **Views**: 763

Glaciers are spectacular phenomenons of nature. The physics they are based on is surprising, while the geological role they have is essential. In this article, we discuss these facts, as well as their retreats and their dangers., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Non-Euclidean Geometry and Map-Making Non-Euclidean Geometry and Map-Making

By Scott McKinney | **Updated:**2013-01 | **Views**: 2221

Geometry literally means “the measurement of the Earth”, and more generally means the study of measurements of different kinds of space. Geometry on a flat surface, and geometry on the surface of a sphere, for example, are fundamentally different. A consequence of this disparity is the fact that it is impossible to create a perfectly accurate (flat) map of the Earth’s (spherical) surface. Every map of the Earth necessarily has distortions. In this post we look at a few different methods of map-making and evaluate their distortions as well as their respective advantages., by Scott McKinney Scott McKinney

Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.

The forces of Nature: from Newton to String Theory The forces of Nature: from Newton to String Theory

By Thibault_Lehouillier | **Updated:**2012-10 | **Views**: 1230

, by Thibault_Lehouillier Thibault_Lehouillier

PhD candidate at Ecole Polytechnique of Montréal (Canada)

Engineer of the ENSIMAG (France)

Duality in Linear Programming Duality in Linear Programming

By Lê Nguyên Hoang | **Updated:**2014-05 | **Prerequisites: **Optimization by Linear Programming, Linear Algebra and Higher Dimensions | **Views**: 9162

Duality in linear programming yields plenty of amazing results that help understand and improve algorithms of resolution. This article shows the construction of the dual and its interpretation, as well as major results. In particular, matching of primal and dual bases will be dealt, before presenting the issue of degeneracy and its dual interpretation., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Linear Algebra and Higher Dimensions Linear Algebra and Higher Dimensions

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2685

Linear algebra is a one of the most useful pieces of mathematics and the gateway to higher dimensions. Using Barney Stinson’s crazy-hot scale, we introduce its key concepts., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Limitless Vertigo of Cantor’s Infinite The Limitless Vertigo of Cantor’s Infinite

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1384

No one believed him. Not even fellow mathematicians. They thought he was wrong. They thought he was crazy. Even he ended up doubting himself and went crazy. And yet, he had mathematically proved it all. Georg Cantor had figured out how to manipulate the infinite. Even more remarkable, he showed that there were actually several infinities; and some are bigger than others!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Entropy and the Second Law of Thermodynamics Entropy and the Second Law of Thermodynamics

By Lê Nguyên Hoang | **Updated:**2014-11 | **Views**: 18238

The second law of thermodynamics is my favorite law in physics, mainly because of the troubling puzzles it raises! Indeed, what your professors may have forgotten to tell you is that this law connects today’s world to its first instant, the Big Bang! Find out why!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Topology: from the Basics to Connectedness Topology: from the Basics to Connectedness

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 3004

Topology was my favorite course in pure maths. I love it because it’s a powerful abstract theory to describe intuitive and visual ideas about space. This article gives you an introduction to this amazing field. We’ll introduce graph topology, metric spaces, continuity and connectedness., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

P versus NP: A Crucial Open Problem P versus NP: A Crucial Open Problem

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 4736

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Most Beautiful Equation of Math: Euler’s Identity The Most Beautiful Equation of Math: Euler’s Identity

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 22894

In 1988, Euler’s identity was elected most beautiful theorem of mathematics. It has been widely taught worldwide. But have you ever stopped to really sense the meaning of this incredible formula? This article does., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Dynamics, Chaos, Fractals (pt 2) Dynamics, Chaos, Fractals (pt 2)

By Scott McKinney | **Updated:**2013-04 | **Views**: 971

Dynamical systems such as a system of 3 planetary bodies can exhibit surprisingly complicated behavior. If the initial state of the system is slightly varied, the resulting system behaves in a radically different manner. This “sensitivity to initial conditions” is a key element of what’s become (perhaps disproportionately) well-known as chaos. Using the mathematical notion of iterative systems, we can model such systems and understand how chaos arises out of deceptively simple foundations., by Scott McKinney Scott McKinney

Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.

Dynamics of the Wave Function: Heisenberg, Schrödinger, Collapse Dynamics of the Wave Function: Heisenberg, Schrödinger, Collapse

By Lê Nguyên Hoang | **Updated:**2014-02 | **Prerequisites: **The Essence of Quantum Mechanics, Imaginary and Complex Numbers, Linear Algebra and Higher Dimensions | **Views**: 3685

On one hand, the dynamics of the wave function can follow Schrödinger equation and satisfy simple properties like Heisenberg uncertainty principle. But on the other hand, it can be probabilistic. This doesn’t mean that it’s totally unpredictable, since the unpredictability is amazingly predictable. Find out how these two dynamics work!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Differential Calculus and the Geometry of Derivatives Differential Calculus and the Geometry of Derivatives

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 3322

Differential calculus is one of the most important concept of mathematics for science and engineering. This article focuses on its fundamental meaning., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Evolutionary Game Theory Evolutionary Game Theory

By Lê Nguyên Hoang | **Updated:**2014-02 | **Views**: 2377

Evolutionary Game Theory is a relatively recent branch of game theory which studies the dynamics of games. Originally used to describe populations of species in biology, and more particularly, the consequences of their interactions to the evolution of their populations, this field now produces interesting results for economic and environmental modelings., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Geological Wonders of Iceland Geological Wonders of Iceland

By Lê Nguyên Hoang | **Updated:**2013-06 | **Views**: 1077

Iceland is at an amazingly active volcanic location, yielding extreme geological phenomenons. Iceland is therefore a giant laboratory for geologists. It’s also an awesome place for visitors, especially hikers. This article introduces some of Iceland’s wonders., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Column Generation and Dantzig-Wolfe Decomposition Column Generation and Dantzig-Wolfe Decomposition

By Lê Nguyên Hoang | **Updated:**2014-05 | **Prerequisites: **Linear Algebra and Higher Dimensions, Optimization by Linear Programming | **Views**: 3046

Column generation and the Dantzig-Wolfe decomposition are powerful tricks which have revolutionized optimization addressed to industrial problems, and generated millions and millions of dollars. My PhD supervisor effectively took great advantage of these tricks and founded companies with it. This article explains the tricks., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Type Theory: A Modern Computable Paradigm for Math Type Theory: A Modern Computable Paradigm for Math

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 6540

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!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Cryptography and Quantum Physics Cryptography and Quantum Physics

By Scott McKinney | **Updated:**2012-12 | **Views**: 1506

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., by Scott McKinney Scott McKinney

Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.

The Amazing Physics of Water in Trees The Amazing Physics of Water in Trees

By Lê Nguyên Hoang | **Updated:**2014-03 | **Views**: 13225

As explained by Derek Muller on Veritasium, the flow of water in trees involves complex physical phenomena including pressure, osmosis, negative pressure, capillarity and evapotranspiration. What seems simple will blow your mind!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Spacetime of General Relativity Spacetime of General Relativity

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 8436

Most popular science explanations of the theory of general relativity are very nice-looking. But they are also deeply misleading. This article presents you a more accurate picture of the spacetime envisioned by Albert Einstein., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

From Divide and Conquer to Parallelization From Divide and Conquer to Parallelization

By Lê Nguyên Hoang | **Updated:**2013-04 | **Views**: 1274

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Revolutionary Galois Theory The Revolutionary Galois Theory

By Lê Nguyên Hoang | **Updated:**2014-12 | **Prerequisites: **Linear Algebra and Higher Dimensions, Imaginary and Complex Numbers, Symmetries and Group Theory | **Views**: 10124

In 1832, Évariste Galois died. He was 20. The night before his death, he wrote a legendary letter to his friend, in which he claims to have found a mathematical treasure! Sadly, this treasure had long been buried in total indifference! It took nearly a century to rediscover it! Since then, Galois’ legacy has become some of the finest pure mathematics, which represents a hugely active field of research today with crucial applications to cryptography. Galois’ work is now known as Galois theory. In essence, it unveils the hidden symmetries of numbers!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Beauty of Ellipses, Parabolas and Hyperbolas The Beauty of Ellipses, Parabolas and Hyperbolas

By Lê Nguyên Hoang | **Updated:**2013-10 | **Views**: 15954

The conic sections, that is, ellipses, parabolas and hyperbolas, are too often presented analytically. Yet, their amazing beauty is actually their spectacular geometry, as well as their omnipresence! This article presents plenty of illustrative descriptions of their uncountable applications!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Proof by Mathematical Induction Proof by Mathematical Induction

By Lê Nguyên Hoang | **Updated:**2014-04 | **Views**: 4387

This article explores the potency of proofs by induction with 4 different stunning puzzles, from a lock puzzle and a lion issue, to the monk problem and the pencil conundrum!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Numbers and Constructibility Numbers and Constructibility

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 3550

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!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

From Britain’s coast to Julia set: an introduction to fractals From Britain’s coast to Julia set: an introduction to fractals

By Thomas C | **Updated:**2013-05 | **Views**: 1997

, by Thomas C Thomas C

I studied applied mathematics at Ecole Polytechnique and I am currently working as a consultant in information and communications technologies.

Colours and Dimensions Colours and Dimensions

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 1289

You’ve probably learned early on that there are three primary colours. But why three? And why these three? Surprisingly, the answer lies in the beautiful mathematics of linear algebra and (high) dimension spaces!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Computing Hunger worldwide: the Global Hunger Index (GHI) Computing Hunger worldwide: the Global Hunger Index (GHI)

By Estève Giraud | **Updated:**2014-04 | **Views**: 398

The Global Hunger Index was first published in 2006 by the International Food Policy Research Institute and the NGO Welthungerhilfe. In 2007, Concern worldwide joined them. Since then, the Index reports every year the evolution of the hunger situation worldwide and focus on a given topic. How is it calculated? And what is hunger? How are we connected ? What can be done? To learn more, read the article below. , by Estève Giraud Estève Giraud

I hold a MSc in Management from Toulouse Business School (France). I currently work as a MRes/PhD student in University Pompeu Fabra (Barcelona, Spain) and research on ethical mindsets in business.

Does God play dice? Does God play dice?

By Arthur Marronnier | **Updated:**2013-05 | **Views**: 824

For Albert Einstein, the answer is no. But what did he mean? Has the greatest theoretical physicist of all time really missed the bandwagon of quantum physics? What are the real issues of the controversy that has opposed him to the Copenhagen School (Bohr, Heisenberg …)? Back to the physics of the early twentieth century, its history, philosophy and ideas., by Arthur Marronnier Arthur Marronnier

Research intern in Spintronics in Spintec Lab (Grenoble, France)

Education:

2013-2014: Stanford University (Master of Science in Material Science & Engineering)

2010-2013: Engineer degree in École polytechnique (Paris), Solid state physics, X2010

2008-2010: Intensive Preparatory Classes in Mathematics&Physics (undergrad)

Symmetries and Group Theory Symmetries and Group Theory

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 1552

Beauty is extremely hard to define. Yet, physicists and artists seem to agree on an important feature of beauty, created by mathematicians: Symmetries. This article aims at introducing the beauty and the concepts on symmetries, from the basic geometrical symmetries to the more abstract fundamental automorphisms., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Marriage Assignment Problem and Variants Marriage Assignment Problem and Variants

By Lê Nguyên Hoang | **Updated:**2014-01 | **Views**: 3331

Marriage problems consist in matching boys and girls. They are a very interesting class of problems that include assignment problems, which have a very large range of applications. Additional results have been found for variants which include the introduction of boys and girls’ preferences, and cases where people cannot be categorized into two groups., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Primal and Dual Simplex Methods Primal and Dual Simplex Methods

By Lê Nguyên Hoang | **Updated:**2014-05 | **Prerequisites: **Optimization by Linear Programming, Duality in Linear Programming | **Views**: 5295

The simplex method is one of the major algorithm of the 20th century, as it enables the resolution of linear problems with millions of variables. An intuitive approach is given. But that’s not all. We present an important variant called the dual simplex. Finally, we’ll explain its main default, that is, when facing degeneracy., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

High Dynamic Range and Tone Mapping High Dynamic Range and Tone Mapping

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 1148

Our eyes are amazing! Even today’s cameras are nowhere near competing with them. However, the recent development of high dynamic range (HDR) and tone mapping technologies creates new possibilities to get images nearly as awesome as what our eyes really see!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Unlikely Correctness of Newton’s Laws The Unlikely Correctness of Newton’s Laws

By Lê Nguyên Hoang | **Updated:**2014-05 | **Views**: 2106

Do moving objects exhaust? Does the Moon accelerate? How strong is the gravity pull of the Moon on the Earth compared to that of the Earth on the Moon? While we’ve all learned Newton’s laws of motion, many of us would get several answers of these questions wrong. That’s not so surprising, as Newton’s laws are deeply counter-intuitive. By stressing their weirdness with Veritasium videos, this article dives into a deep understanding of classical mechanics., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Bayesian Games: Math Models for Poker Bayesian Games: Math Models for Poker

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 3578

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Self-Reference, Math Foundations and Gödel’s Incompleteness Self-Reference, Math Foundations and Gödel’s Incompleteness

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2645

Although highly appreciated by artists, self-reference has been a nightmare for mathematicians. It took one of the greatest, Kurt Gödel, to provide a better understanding of it. This article deals with paradoxes, recursion, fractals and Gödel’s incompleteness theorems., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The coach’s dilemma. The coach’s dilemma.

By Herminio López | **Updated:**2012-06 | **Views**: 568

, by Herminio López Herminio López

Degree in Economics and Business. Bank worker. Maths fan.

Webmaster of www.matifutbol.com

Logarithms and Age Counting Logarithms and Age Counting

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1759

Amusingly, the age difference between a 45-year-old man and a 25-year-old woman doesn’t seem as big as the age difference between them 20 years earlier, when the woman was a little 5-year-old girl. This remark was the insight the late science popularizer Albert Jacquart liked to give to his readers to explain logarithms. This article pays tribute to the great scientist by introducing age difference as he liked to tell it., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Game Theory and the Nash Equilibrium Game Theory and the Nash Equilibrium

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 7669

In the movie “A Beautiful Mind”, the character is John Nash. He is one of the founders of a large and important field of applied mathematics called game theory. Game Theory is the study of human interactions. Its fallouts in economy, politics or biology are countless. This article gives you an introduction to the concepts of this amazing way of thinking., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Dynamics, Chaos, Fractals (pt 1) Dynamics, Chaos, Fractals (pt 1)

By Scott McKinney | **Updated:**2013-04 | **Views**: 2441

The study of dynamical systems, natural or abstract systems that evolve at each instance in time according to a specific rule, is an active and fruitful area of research in mathematics. Its study has yielded insights into the nature of social networks such as Facebook, the spread of diseases such as influenza, and the behavior of the financial markets. In this series of posts, we’ll look in depth at dynamical systems, as well as at the related subjects of chaos theory and fractals, all of which are both interesting and useful for understanding our world., by Scott McKinney Scott McKinney

Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.

Optimization by Linear Programming Optimization by Linear Programming

By Lê Nguyên Hoang | **Updated:**2014-05 | **Views**: 3560

Operations Research deals with optimizing industrial systems. Those systems can be very complex and their modeling may require the use of hundreds, thousands or even millions of variables. Optimizing over millions of variables may seem impossible, but it can be done if the optimization problem has a linear structure. Learn more on this linear structure and optimization solutions!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Temperature Misconception: Heat is Not How it Feels Temperature Misconception: Heat is Not How it Feels

By Lê Nguyên Hoang | **Updated:**2014-10 | **Views**: 1142

In the last FIFA football world cup, many players complain about Manaus’ unbearable heat condition. Yet, the thermometer only went up to 30°C (86°F). Why is that? Well, as it turns out, how you feel is not really the outside temperature. This article unveils many of our deep misconceptions about heat., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

A Model of Football Games A Model of Football Games

By Lê Nguyên Hoang | **Updated:**2014-10 | **Views**: 3969

Back then, I simulated the outcome of the 2006 World Cup, based on a modelling of football games. This article explains this model and presents its results., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Web Programming: From HTML to AJAX Web Programming: From HTML to AJAX

By Lê Nguyên Hoang | **Updated:**2013-03 | **Views**: 1951

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Most Troubling Experiments on Human Behavior The Most Troubling Experiments on Human Behavior

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 1167

We all intuitively think of ourselves as independent creatures with strong free will. However, many disturbing experiments about fashion, conformity, obedience, environment, choice and opinions have been troubling this idea we make of ourselves. These ought to be lessons of humility for all of us., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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Fair division in Game Theory modelled using Friends. pretty awesome @helpatz http://t.co/yVCCS887

— Emma Alexander (@emmaaaaa8) November 27, 2012

Lê Nguyên Hoang (el promotor science4all) es uno de los jóvenes matemáticos más brillantes de la actualidad (y una gran persona)

— IMUVA (@IMUVA_) March 7, 2013

Really nice article with great visuals covering Stable Marriage algorithms and variants. http://t.co/rSHnDKCyxa #GraphNerds

— David W. Allen (@DataRiot) March 24, 2013

#Marriage Problem and Variants: http://t.co/XLMGMcIO98 #FF @science__4__all (he's a #genius)

— Berlanda Mauro (@mauroberlanda) April 12, 2013

This post almost makes me want to teach science again http://t.co/d6csaIRgra Almost.

— Fawn Nguyen (@fawnpnguyen) April 18, 2013

Great article on tree physics by @science__4__all: http://t.co/uiftTXyh3G

— Derek Muller (@veritasium) April 18, 2013

This really is a great article: Hypothesis Testing http://t.co/KVVKayG84K Well done @science__4__all (cc @DrTonyPadilla @numberphile)

— James Grime (@jamesgrime) May 17, 2013

AMAZING! Indeed I was talking about http://t.co/DqHJ4kkcxI articles. @science__4__all More scientists should contribute – @benstill !!!???

— Jennifer Crouch (@JenniferCrouch) May 30, 2013

why do I end up reading poincare conjecture? http://t.co/R2hdy1Xgh8 :).

— Avivah Yamani (@ivie97) June 5, 2013

So good. Love how Le takes the Euler formula (and utilities problem) and kicks it up a bunch of notches. http://t.co/KVoxCjvsQI

— Fawn Nguyen (@fawnpnguyen) June 20, 2013

Masterful exposition of topology made accessible: Euler's Formula and the Utilities Problem http://t.co/uL4Aw9VAnC HT @fawnpnguyen

— Joshua Bowman (@Thalesdisciple) June 21, 2013

Enjoy #math with @republicofmath @jamestanton @maanow @MrHonner @wilderlab @earlsamuelson @WWMGT @daveinstpaul @science__4__all #ff

— Alexander Bogomolny (@CutTheKnotMath) June 21, 2013

I would like to do a #ff for @science__4__all who are doing an excellent job with their maths articles http://t.co/R7G1EhMcg7

— James Grime (@jamesgrime) June 21, 2013

Just RIDICULOUS HOW GOOD this is, "The Beauty of Ellipses, Parabolas and Hyperbolas" by @science__4__all
http://t.co/eBCazmcxVi

— Fawn Nguyen (@fawnpnguyen) July 22, 2013

Bravo! Lê Nguyên Hoang Founder Science4All Your Papers are Brilliant!
http://t.co/AvCQPZcwPB What Does this Mean!

— David Valin (@gbdavid1) July 22, 2013

@science__4__all Your document it's all beauty! Thanks for sharing it!

— Margarita Parra (@BMPM1) September 9, 2013

Shannon's Information Theory: lucid, illustrated thorough introduction, keep it as a reference, share it as a gift! http://t.co/tqR8xKqDBA

— Arthur Doohan (@artied) September 29, 2013

#shannon <3<3<3 #enmettrepartout <3<3<3 #dansmaface “@MathUpdate: Shannon's Information Theory http://t.co/XdLEL7JUj7”

— Dr. Bisounours (@BisounoursJp) September 29, 2013

Muy bueno el blog Science4all Le Nguyen Hoang http://t.co/3VfpY7QZ7o esfuerzo para divulgar conceptos de forma sencilla y divertida

— Luis A. Núñez (@nunezluis) October 27, 2013

Always a great blog "@science__4__all: Discover irrational, constructible, transcendental and computable numbers! http://t.co/BRBIf5PrDM"

— James Grime (@jamesgrime) November 7, 2013

Simple, well-explained, well-written article about evolution of science philosophy, from Ptolemy to Stephen Hawking http://t.co/Njf3auyAtP

— Cloud-Big Data-EDD (@Ediscoverycloud) November 12, 2013

How can one not love #math? RT @centerofmath The Beauty of Ellipses, Parabolas and Hyperbolas – http://t.co/SSmmLMhj1B #math

— MathDaily (@MathDaily) November 28, 2013

Barney Stinson's theories to explain linear algebra. It's legen(wait-for-it)dary and awesome.
By @science__4__all
http://t.co/X9SVtDFyHr

— Helene Sarah Becotte (@hbecotte) November 28, 2013

Not just the Traveling Santa Problem. See a discussion of SC's route as a vehicle routing problem http://t.co/iBRQqsDCJS

— AmericanMathSociety (@amermathsoc) December 23, 2013

Wishing everyone a geeky mary christmas. http://t.co/TaAZQ2ZI2P

— InTheNext10Years (@inthenext10year) December 25, 2013

This is a fantastic explanation of Quantum Mechanics http://t.co/FZl9OFQqaH

— Nick Gotch (@pszNicx) December 30, 2013

Wow, really good overview! (The Essence of Quantum Mechanics – S4A) http://t.co/rtr8LeRIXn

— Xavi (@nymiro) December 30, 2013

For no reason, do you know @science__4__all http://t.co/R7G1EhMcg7 They're very good.

— James Grime (@jamesgrime) January 10, 2014

Looks cool! RT @science__4__all: NEW ARTICLE!!! Get an intimate feel of The Greatest Feat of Mathematics: http://t.co/qsb5lAA9IP

— Danica McKellar (@danicamckellar) February 21, 2014

@science__4__all I really like your web site! Great work…I am telling any friends interested in science and mathematics about it.

— Joe Dayton ☮ (@JoeDaytonMN) February 22, 2014

"The Most Amazing Thing About Trees" is, frankly, amazing. http://t.co/amaHMkwSX1 HT: @highlyanne

— Adam Mandelman (@amandelman) February 25, 2014

This is so damn cool! "The Tortuous Geometry of the Flat Torus" http://t.co/gybXXnZP2z – last image = new wallpaper!

— LucasVB (@LucasVB) March 16, 2014

Incredible cool way to visualize imaginary numbers: http://t.co/ZPEDz5yN6e #math #mathchat #mathtip #mathed #edchat #edtech

— Rimwe (@RimweLLC) April 27, 2014

This is the first truly convincing argument I've seen that the 131072 tile is the largest possible for the #2048game. http://t.co/ez0JCxjbTs

— Dave Radcliffe (@daveinstpaul) June 20, 2014

To all students of data, this is a must-read > Shannon’s Information Theory: http://t.co/3fHla3HWl0 by @science__4__all #DataScience

— Kirk Borne (@KirkDBorne) July 8, 2014

http://t.co/YNd1CFXPnd Follow
Lê Nguyên Hoang @science__4__all to read and contribute to "popular" science #Interesting

— anbudan BALA|எஅ.பாலா (@AmmU_MaanU) July 13, 2014

I enjoyed this engaging read by LN Hoang about some #Maths research: The New Big Fish Called Mean-Field Game Theory: http://t.co/OiemfWnT7y

— Anita Hall (@ani2tall) September 24, 2014

@science__4__all Thank you for your articles. Just amazing! Wonder how you compile and relate so many things…

— Prasad Gokhale (@Prasad_Gokhale) September 28, 2014

This is GREAT! Even non-math people will enjoy this. The Tortuous Geometry of the Flat Torus: http://t.co/9eZamXiB5o

— Kim Langen (@KimLangen) October 2, 2014

arguably #ComputerScience owes more to #Shannon than anyone else. An excellent article on Shannon's Info Theory: http://t.co/u5AI6qjbKO

— Numan Sheikh (@numansheikh) October 13, 2014

Good one for interested ones, Puzzles, science, methodologies and manymore: http://t.co/NN31T9JNMe

— Pankaj Saraf (@saraf_pankaj) December 21, 2014

Santa's optimization for Christmas visits! A wonderful explanation to Vehicle Routing Problem. http://t.co/pBfq7wW0aP #OperationsResearch

— Vandana Narasimhan (@vandy_ie) December 25, 2014

@science__4__all Great! Primary colours, wavelengths, cones, vectors and spaces, matrices,…this article is really multidimensional.

— Prasad Gokhale (@Prasad_Gokhale) January 10, 2015

@science__4__all hey, you have a great blog! I'm enjoying reading through your articles

— Cam Davidson-Pilon (@Cmrn_DP) January 25, 2015

Another amazing read! #math http://t.co/04oImebBaT

— Cassie Lynn Holmes (@CassiHolmes) March 1, 2015

실시간으로 결정을 해야하고 한번 결정하면 되돌릴 수 없을때, 수학으로 전략 만들기
“@MathbloggingAll:The Secretary/Toilet Problem and Online Optimization http://t.co/G4nMBhTdIG”

— 상일 (@sioum) April 2, 2015