Category Archives: math for everyone

On prisoners and their hats (Part III)


This is the third part of the story. The first and second parts can be found here and here, respectively. Previously, we showed that the lexicographic code we constructed consists exactly of the positions of the game of nim. But, … Continue reading

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On prisoners and their hats (Part II)


This is the second part of the story. Catch up with the first part here. Recall that in the last segment, we related the hat game to the construction of Hamming codes. In order to investigate Hamming codes more deeply, … Continue reading

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On prisoners and their hats (Part I)


It’s storytime! I’m going to tell one of my favorite stories, so please make yourself comfortable. Once upon a time, there was anĀ evil prison warden in charge of a bunch of prisoners. Being evil, the warden decided to force the … Continue reading

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What is a random positive integer?


Let’s try to think about this question: What is the probability that a random positive integer starts with a 1? Without thinking about it too much, we might be inclined to say 1/9. After all, for each , there are … Continue reading

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You could have discovered the Jones polynomial


How do we tell when two knots are the same and when they are different? That is, if we start with one of them and fiddle around with it for a while, might we eventually make it look like the … Continue reading

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Wishful thinking in mathematics


Most of the world thinks of mathematics as having only right and wrong answers, with little room for creativity. However, this perception is inconsistent with the way that mathematics is actually done. Like in most other subjects, there is lots … Continue reading

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Algebraic topology for everyone


I have long thought that much of modern mathematics is accessible, in some form, to anyone who is interested, regardless of prior mathematical background. While mathematics is typically taught in such a way that requires the student to have learned … Continue reading

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