# 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**: 1240

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**: 1528

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**: 1340

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.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 1098

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.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2561

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.

Fair Division and Cake-Cutting Fair Division and Cake-Cutting

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2661

Cutting a cake to satisfy everyone is no piece of cake! In the article, we focus on classical definitions of fair divisions. I’ll criticize those definitions and conclude by extrapolating them to fairness in society., 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**: 927

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.

Evolutionary Game Theory Evolutionary Game Theory

By Lê Nguyên Hoang | **Updated:**2014-02 | **Views**: 2347

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.

The Tortuous Geometry of the Flat Torus The Tortuous Geometry of the Flat Torus

By Lê Nguyên Hoang | **Updated:**2015-05 | **Views**: 7765

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!, 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.

Geometry and General Relativity Geometry and General Relativity

By Scott McKinney | **Updated:**2013-01 | **Views**: 1246

From our “intrinsic” point-of-view on the surface of the Earth, it appears to be flat, but if we examine the Earth from the “extrinsic” point of view, somewhere off the Earth’s surface, we can see that it is clearly a curved surface. Amazingly, it is possible to determine that the Earth is spherical simply by taking measurements on its surface, and it is possible to generalize these measurements in order to study the shape of the universe. Mathematicians such as Riemann did just this, and Einstein was able to apply these geometric ideas to his “general theory of relativity”, which describes the relation between gravitation, space, and time., 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.

Homotopy Type Theory and Higher Inductive Types Homotopy Type Theory and Higher Inductive Types

By Lê Nguyên Hoang | **Updated:**2014-04 | **Views**: 1285

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., 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**: 1150

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.

Spacetime of General Relativity Spacetime of General Relativity

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 8379

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.

Optimization by Integer Programming Optimization by Integer Programming

By Lê Nguyên Hoang | **Updated:**2014-05 | **Prerequisites: **Optimization by Linear Programming | **Views**: 3808

Integer programming is arguably the greatest achievement of applied mathematics. Half of the time, it’s what’s used to solve real-world problems!, 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 forces of Nature: from Newton to String Theory The forces of Nature: from Newton to String Theory

By Thibault_Lehouillier | **Updated:**2012-10 | **Views**: 1219

, by Thibault_Lehouillier Thibault_Lehouillier

PhD candidate at Ecole Polytechnique of Montréal (Canada)

Engineer of the ENSIMAG (France)

The Magic of Analysis The Magic of Analysis

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 1061

This article retraces the endless pursuit of the infinite that is at the basis of mathematical analysis. From the first approximations of pi to the shape of our limitless universe, from the essential usefulness of differential equations to the troubles with infinite sums, we present the great ideas of mathematical geniuses all along History., 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.

Optimization by Linear Programming Optimization by Linear Programming

By Lê Nguyên Hoang | **Updated:**2014-05 | **Views**: 3501

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.

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

By Lê Nguyên Hoang | **Updated:**2014-11 | **Views**: 18166

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.

Numbers and Constructibility Numbers and Constructibility

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 3496

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.

Hypothesis Test with Statistics: Get it Right! Hypothesis Test with Statistics: Get it Right!

By Lê Nguyên Hoang | **Updated:**2013-11 | **Views**: 3245

Statistician Johnson recently claimed that up to 25% of published scientific experimental results were just wrong! To see why, let’s get to the bottom of the scientific method! And it’s probably more complicated than you think. In this article, we apply it rigorously to “prove” $\pi=3$. This will highlight the actually mechanism of the scientific method, its limits, and how much messages of experiments are often deformed!, 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 Massive Puzzles of Gravity The Massive Puzzles of Gravity

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 1917

This article follows the footsteps of the giants of physics that have moulded our current understanding of gravity. It is a series of brilliant inspirations, usually accompanied by deceiving misconceptions. After all, even today, gravity is still a slippery concept. , 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.

Dual Variable Stabilization Dual Variable Stabilization

By Lê Nguyên Hoang | **Updated:**2012-07 | **Prerequisites: **Optimization by Linear Programming, Duality in Linear Programming, Primal and Dual Simplex Methods | **Views**: 383

Simplex methods face issues in case of degeneracy. The dual variable stabilization is a very recent state-of-the-art way to deal with degeneracy. An intuitive understanding is given in this article., 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**: 4703

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

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1340

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.

The Surprising Flavor of Infinite Series The Surprising Flavor of Infinite Series

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 5336

1+2+4+8+16+…=-1, as proven by Henry Reich on Minute Physics! Now, as a mathematician, I must say that his proof is far from being rigorous. In fact, anyone familiar with the surprising flavor of infinite series should not find it convincing. Surprisingly though, his proof can be rigorously and naturally justified! Find out how!, 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**: 10050

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 Harmonious Mathematics of Music The Harmonious Mathematics of Music

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1528

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.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 6218

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.

Imaginary and Complex Numbers Imaginary and Complex Numbers

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 3626

My first reaction to imaginary numbers was… What the hell is that? Even now, I have trouble getting my head around these mathematical objects. Fortunately, I have a secret weapon: Geometry! This article proposes constructing complex numbers with a very geometrical and intuitive approach, which is probably very different from what you’ve learned (or will learn)., 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.

Symmetries and Group Theory Symmetries and Group Theory

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 1538

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.

Colors: It’s not just about Wavelengths! Colors: It’s not just about Wavelengths!

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2087

Colors… What are they really? Are there the same for all of us? And for other animals? How does color addition or subtraction work? How do they work on computers? And on printers? The mysterious (but not dark) world of colors is actually very colorful!, 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.

Poincaré Conjecture and Homotopy Poincaré Conjecture and Homotopy

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 4730

Poincaré conjecture is the most recent major proven theorem. Posited a century ago by Henri Poincaré, this major conjecture of topology was solved by Gregori Perelman. It has revolutionized our understanding of space and raised intriguing questions regarding the global structure of our Universe., 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**: 3296

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.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 3529

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.

Model-Dependent Realism Model-Dependent Realism

By Lê Nguyên Hoang | **Updated:**2013-11 | **Views**: 2455

Introduced by the two renowned theoretical physicists Stephen Hawking and Leonard Mlodinov in their book The Grand Design in 2010, model-dependent realism is a new controversial understanding of the universe. Based on solid logical reasonings and recent developments in physics, this concept may well be an incredible breakthrough for philosophy and science, as well as metaphysics., 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**: 15398

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.

The Addictive Mathematics of the 2048 Tile Game The Addictive Mathematics of the 2048 Tile Game

By Lê Nguyên Hoang | **Updated:**2014-06 | **Views**: 7098

2048 is the Internet sensation of the year. This very addictive game has been downloaded hundred of millions of times. Interestingly, this game raises plenty of intriguing mathematical questions. This article unveils some of them!, 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 Thrilling Physics of Resonance The Thrilling Physics of Resonance

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 8734

From the destruction of bridges and buildings to the foundations of electromagnetism and quantum mechanics, through their uses by radios or our ears,resonance is a counter-intuitive underlying phenomenon which shapes our reality. But amazingly, they can be made amazingly visual by playing with head massagers!, 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 Biology Civil War Opposing Kin to Group Selection The Biology Civil War Opposing Kin to Group Selection

By Lê Nguyên Hoang | **Updated:**2014-03 | **Views**: 1685

In 2010, a controversial article published in Nature violently criticized the last 40 years of developments in evolutionary biology, triggering an ongoing war within the scientific community. This article explains the essence of the controversy!, 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.

Construction and Definition of Numbers Construction and Definition of Numbers

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 3690

Although they have been used for thousands of years, an actual definition of numbers was given less than a century ago! From the most fundamental level of set theory, this article takes you to the journey of the construction of natural, integer, rational, real and complex 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.

Linear Algebra and Higher Dimensions Linear Algebra and Higher Dimensions

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2661

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.

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**: 2950

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.

Darwin’s Theory of Evolution Darwin’s Theory of Evolution

By Lê Nguyên Hoang | **Updated:**2013-12 | **Views**: 7565

Darwin’s theory of evolution is one of the greatest of all time. It’s also one of the most controversial. This article presents the most fundamental concepts of the theory. We’ll also provide results of modern science and discuss to which extend to they confirm Darwin’s postulates., 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**: 5147

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.

Mechanism Design and the Revelation Principle Mechanism Design and the Revelation Principle

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2410

Whenever you need to make a group of people interact, you are designing a mechanism. If you want to achieve a good interaction, you need to make sure your mechanism is well designed. In this article, I’ll show you main features of mechanisms through various examples. I’ll also talk about a great mathematical tool for mechanism design: the revelation principle., 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**: 4364

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.

Multicriteria with MACBETH Multicriteria with MACBETH

By Lê Nguyên Hoang | **Updated:**2013-07 | **Views**: 1555

As more and more complex problems are dealt with in our societies, developing models such as multi-criteria analysis is crucial to better understand these problems. MACBETH is a state-of-the-art method to do just that. Its functioning is described in this article., 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 New Big Fish Called Mean-Field Game Theory The New Big Fish Called Mean-Field Game Theory

By Lê Nguyên Hoang | **Updated:**2014-06 | **Views**: 5330

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!, 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**: 2412

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.

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

By Lê Nguyên Hoang | **Updated:**2015-04 | **Views**: 1240

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.

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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