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cameroncounts.wordpress.com | ||
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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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www.jeremykun.com
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| | | | | This proof assumes knowledge of complex analysis, specifically the notions of analytic functions and Liouville's Theorem (which we will state below). The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way. This series of proofs of the fundamental theorem also highlights how in mathematics there are many many ways to prove a single theorem... | |
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gilkalai.wordpress.com
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| | | | | Frankl's conjecture Frankl's conjecture is the following: Let $latex \cal A$ be a finite family of finite subsets of $latex N=\{1,2,\dots,n\}$ which is closed under union, namely, if $latex S,T \in {\cal A}$ thenalso $latex S \cup T \in {\cal A}$. Then there exists an element $latex x$ which belongs to at least half the... | |
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qchu.wordpress.com
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| | | As a warm-up to the subject of this blog post, consider the problem of how to classify$latex n \times m$ matrices $latex M \in \mathbb{R}^{n \times m}$ up to change of basis in both the source ($latex \mathbb{R}^m$) and the target ($latex \mathbb{R}^n$). In other words, the problem is todescribe the equivalence classes of the... | ||
