Science4All

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.
I now run a Robustly Beneficial wiki, mostly on AI ethics, which has come to fascinate me!

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Duality in Linear Programming

Duality in Linear Programming
By Lê Nguyên Hoang | Updated:2016-01 | Prerequisites: Optimization by Linear Programming, Linear Algebra and Higher Dimensions | Views: 19147
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.

The Surprising Flavor of Infinite Series

The Surprising Flavor of Infinite Series
By Lê Nguyên Hoang | Updated:2020-01 | Views: 9206
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!

Multicriteria with MACBETH

Multicriteria with MACBETH
By Lê Nguyên Hoang | Updated:2016-02 | Views: 2591
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.

Self-Reference, Math Foundations and Gödel's Incompleteness

Self-Reference, Math Foundations and Gödel's Incompleteness
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4594
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.

Advanced Game Theory Overview

Advanced Game Theory Overview
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Game Theory and the Nash Equilibrium | Views: 5292
This article gives an overview of recent developments in game theory, including evolutionary game theory, extensive form games, mechanism design, bayesian games and mean field games.

Fourier Analysis: Signals and Frequencies

Fourier Analysis: Signals and Frequencies
By Lê Nguyên Hoang | Updated:2016-01 | Views: 9858
Fourier analysis is a fundamental theory in mathematics with an impressive field of applications. From creating radio to hearing sounds, this concept is a translation between two mathematical worlds: Signals and Frequencies. Here is an introduction to the theory.

Numbers and Constructibility

Numbers and Constructibility
By Lê Nguyên Hoang | Updated:2016-02 | Views: 6521
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!

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics
By Lê Nguyên Hoang | Updated:2016-01 | Views: 22924
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!

Dynamics of the Wave Function: Heisenberg, Schrödinger, Collapse

Dynamics of the Wave Function: Heisenberg, Schrödinger, Collapse
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: The Essence of Quantum Mechanics, Imaginary and Complex Numbers, Linear Algebra and Higher Dimensions | Views: 7629
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!

Evolutionary Game Theory

Evolutionary Game Theory
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4808
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.

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