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## Discover a new field of science with the latest no-prerequisite articles:

• Proof by Induction By Lê Nguyên Hoang | Updated:2013-06 | Views: 618
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Spacetime of General Relativity By Lê Nguyên Hoang | Updated:2013-06 | Views: 679
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Does God play dice? By Arthur Marronnier | Updated:2013-05 | Views: 122
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 Researsh 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)

• Hypothesis Test with Statistics: Get it Right! By Lê Nguyên Hoang | Updated:2013-05 | Views: 890
How does the scientific method really work? 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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• The Amazing Physics of Water in Trees By Lê Nguyên Hoang | Updated:2013-04 | Views: 1196
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Dynamics, Chaos, Fractals (pt 2) By Scott McKinney | Updated:2013-04 | Views: 261
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 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.
• A Model of Football Games By Lê Nguyên Hoang | Updated:2013-05 | Views: 751
Back then, I simulated the outcome of the 2006 World Cup, based on a modeling of football games. This article explains this model and presents its results.
, by Lê Nguyên Hoang PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Dynamics, Chaos, Fractals (pt 1) By Scott McKinney | Updated:2013-04 | Views: 622
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 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.
• Poincaré Conjecture By Lê Nguyên Hoang | Updated:2013-05 | Views: 1092
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Shannon’s Information Theory By Lê Nguyên Hoang | Updated:2013-06 | Views: 1405
Claude Shannon may be considered as the single most influential person of the 20th Century, as he laid out the foundation of the revolutionary information theory. Yet, unfortunately, he is virtually unknown to the public. This article is a tribute to him. And the best way I’ve found is to explain some of the brilliant ideas he had.
, by Lê Nguyên Hoang PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Space Deformation and Group Representation By Lê Nguyên Hoang | Updated:2013-04 | Views: 605
All along the 20th century, pure algebraists have dug deep into the fundamental structures of mathematics. In this extremely abstract effort, they were greatly help by the possibility of representing these structures by space deformations, which could then be understood much better. This has led to breakthroughs, including the proof of Fermat’s las theorem. This article introduces the ideas of group representations.
, by Lê Nguyên Hoang PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Conditional Probabilities: Know what you Learn By Lê Nguyên Hoang | Updated:2013-05 | Views: 1047
Suppose a man has two children, one of them being a boy. What’s the probability of the other one being a boy too? This complex question has intrigued thinkers for long until mathematics eventually provided a great framework to better understanding of what’s known as conditional probabilities. In this article, we present the ideas through the two-children problem and other fun examples.
, by Lê Nguyên Hoang PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Geometry and General Relativity By Scott McKinney | Updated:2013-01 | Views: 662
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 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 Essence of Quantum Mechanics By Lê Nguyên Hoang | Updated:2013-06 | Views: 1735
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Glaciers: The Forces that Shape the Earth By Lê Nguyên Hoang | Updated:2013-04 | Views: 378
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Non-Euclidean Geometry and Map-Making By Scott McKinney | Updated:2013-01 | Views: 698
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 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.
• Euclidean Geometry and Navigation By Scott McKinney | Updated:2013-01 | Views: 583
This is the first of a series of three posts. In this post we’ll see how the Greeks developed a system of geometry – literally “Earth measure” – to assist with planetary navigation. We then will see why their assumption that the Earth is flat means that Euclidean geometry is insufficient for studying the Earth. The Earth’s spherical surface looks flat from our perspective, but is actually qualitatively different from a flat surface. In the ensuing posts, we’ll see why this implies that it is impossible to make a perfectly accurate map of the Earth, and build on this idea to get a glimpse into Einstein’s revolutionary theories regarding the geometry of the space-time universe.
, by 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.
• Cryptography and Quantum Physics By Scott McKinney | Updated:2012-12 | Views: 327
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 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.
• Topology: from the Basics to Connectedness By Lê Nguyên Hoang | Updated:2013-05 | Views: 1057
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Cryptography and Number Theory By Scott McKinney | Updated:2012-12 | Views: 535
Over 300 years ago, a mathematician named Fermat discovered a subtle property about prime numbers. In the 1970′s, three mathematicians at MIT showed that his discovery could be used to formulate a remarkably powerful method for encrypting information to be sent online. The RSA algorithm, as it is known, is used to secure ATM transactions, online business, banking, and even electronic voting. Surprisingly, it’s not too difficult to understand, so let’s see how it works.
, by 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.