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Author Archives: Simon
Defeating an IM
I hadn’t played a tournament since May, when I had a disastrous tournament and lost four games before withdrawing in disgust. My tournament this weekend was mostly mediocre, except for one game, in which I scored my first win against … Continue reading
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Why didn’t Euler conjecture the prime number theorem?
It shouldn’t have been too hard, based on what he knew. Let us take a look. Euler knew that the sum of reciprocal primes diverged, and he even knew the growth rate of , where the sum is taken only … Continue reading
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The Wallis Product
I had seen the Wallis product, but I did not know a derivation of it until a few weeks ago, when I discovered this gem when reading the wonderful book Sources in the Development of Mathematics by Ranjan Roy. I’m storing this … Continue reading
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One interesting thing: Counting skew ternary trees
On Monday, I attended Don Knuth’s annual Christmas Tree Lecture, where he talks about the most interesting thing he has learned about trees in the past year. This year, he talked about ternary trees and planar graphs. Among other things, … Continue reading
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Exchange sacrifices galore
Last weekend, I played the BayAreaChess Thanksgiving tournament. My play was pretty bad, but my results (2 wins, 1 draw, 2 losses against all players rated a bit higher than I) were okay, and I hit a new rating high … Continue reading
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One interesting thing: Average polynomial time algorithms
The most celebrated problem in theoretical computer science is undoubtedly the P vs. NP problem. Let me explain what it is asking. (If you already know this, feel free to skip the next few paragraphs.) Suppose we have a general … Continue reading
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One interesting thing: Erdős–Rényi random graphs
I’ve been thinking a lot about random graphs this week, so it is appropriate for my post this week to be about them. One of the most important models of random graphs is the Erdős–Rényi model. Here is the construction: we … Continue reading
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One Interesting Thing: The preponderance of 2groups among finite groups
This is a preliminary discussion of my knowledge about 2groups. There are still many questions I have, and I would appreciate any insights. When we first learn about group theory, we learn some theorems about how to decompose finite groups, … Continue reading
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One Interesting Thing: Homomorphic Encryption
I plan to start writing about one interesting thing I learn each week. This will serve two purposes: forcing me to think about interesting things, and also forcing me to write. Here is the first installment in the series. Suppose … Continue reading
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An experiment in imbalances
Ordinarily, when I play chess, I favor relatively balanced positions, in which the result of the game is more likely to hinge on positional ideas, rather than tactics. Hence, I do not sacrifice material often, unless I have calculated that … Continue reading
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