#### Welcome to Science4All

My name is Lê and 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.

Science4All is also available in French.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 985Glaciers 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.

Primal and Dual Simplex Methods Primal and Dual Simplex Methods

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Prerequisites:**Optimization by Linear Programming, Duality in Linear Programming |**Views**: 10527The 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.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Prerequisites:**The Essence of Quantum Mechanics, Imaginary and Complex Numbers, Linear Algebra and Higher Dimensions |**Views**: 5544On 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!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 2023Our 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!

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

By Scott McKinney |

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 |

**Updated:**2015-12 |**Views**: 1289Dynamical 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.

Probabilistic Algorithms, Probably Better Probabilistic Algorithms, Probably Better

By Lê Nguyên Hoang |

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.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 1296Probabilities 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.

Symmetries and Group Theory Symmetries and Group Theory

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 2047Beauty 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.

The Cubic Ball of the 2014 FIFA World Cup The Cubic Ball of the 2014 FIFA World Cup

By Lê Nguyên Hoang |

I know this sounds crazy. Even stupid. But Adidas did design a cubic ball, called brazuca, for the 2014 World Cup. And, yet, this cubic ball is rounder than any previous ball in football History. How is it possible? This article explains it.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 5121I know this sounds crazy. Even stupid. But Adidas did design a cubic ball, called brazuca, for the 2014 World Cup. And, yet, this cubic ball is rounder than any previous ball in football History. How is it possible? This article explains it.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 2003In 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.

The Essence of Quantum Mechanics The Essence of Quantum Mechanics

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 7946Quantum 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.