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 Zeros of random polynomials
 Hopf fibration double covers circle bundle of sphere
 Euler’s formula e^ix = cos x + i sin x: a geometric approach
 An inequality for functions on the plane
 Weighted isoperimetric inequalities in warped product manifolds
 FaberKrahn inequality
 Why is a² + b² ≥ 2ab ?
 A remark on the divergence theorem
 The CauchySchwarz inequality and the Lagrange identity
 On the existence of a metric compatible with a given connection
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Archives
Category Archives: Dynamical system
A dynamical proof of Fermat’s little theorem
If you have studied number theory (even just a little bit), you should know the Fermat’s little theorem: for any positive , and for any prime number , we have . Here I will give a proof by using a … Continue reading
Posted in Dynamical system, Number Theory
3 Comments
Poincaré recurrence theorem and its friends
The Poincaré recurrence theorem states that a dynamical system (under suitable conditions) will eventually return to a condition that is very close to the original condition. Slightly more formally, for a compact set in , if is a volume preserving … Continue reading
Posted in Dynamical system, Number Theory
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A meta post, and two articles
1. Is there any way to support MathJax here? It can translate directly the latex code to display math. It is supported on blogspot, I find it more convenient. 2. I believe many of us come across some very good articles … Continue reading
Posted in Dynamical system, Uncategorized
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A dynamical proof of some Diophantine approximations
Diophantine approximations is a field in number theory which asks how good a real number can be approximated by some rational number. Quite a number of classical results are proved by using combinatorics, which is not friendly to people who … Continue reading
Posted in Dynamical system, Number Theory
2 Comments