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#algebra
What is a variety?
Of course, I am not talking about the English word “variety” here, which everyone knows the meaning. I am referring to algebraic varieties. These are the primary objects one studies in algebraic geometry. I am no expert on the subject, but I have a little understanding of the concept. I would like to share my thoughts and insights by showing some elementary and common examples everyone would have seen sometime or the other - completely unaware that they are varieties in disguise!
Read more...Sprague-Grundy: Why is it XOR?
I have always wondered why the correct way to combine nim games is taking the XOR of their grundy numbers. But never got around to learning the theory behind it.
Recently, I had a very enlightening conversation with Siddharth Bhat. He showed me a very simple and elegant proof for this.
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