Author Archives: mzspivey

Six Proofs of a Binomial Identity

I’m a big fan of proving an identity in multiple ways, as I think each perspective gives additional insight into why the identity is true.  In this post we’ll work through six different proofs of the binomial identity . 1. … Continue reading

Posted in binomial coefficients, calculus, combinatorics, generating functions, probability | Leave a comment

Zeno’s Paradoxes

The ancient Greek philosopher Zeno of Elea is known for proposing several paradoxes related to time, space, motion, and infinity.  In this post we’ll focus on one of Zeno’s paradoxes and discuss how some ideas associated with calculus might or … Continue reading

Posted in calculus, infinity, logic, paradoxes, real analysis, sequences and series | Leave a comment

Five Theses on Mathematics in Games

This past weekend I gave a talk entitled “Mathematics Through Narrative” at the NarraScope conference on narrative games at MIT in Boston.  Much of what I discussed I had also put into a series of blog posts several months ago.  … Continue reading

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The Art of Proving Binomial Identities is Now Available

A couple of months ago I posted that my book, The Art of Proving Binomial Identities, would soon be finished.  Well, it’s out now, and you can buy it straight from the publisher (CRC Press).  It’s up on Amazon as well. … Continue reading

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Sum of the Reciprocals of the Binomial Coefficients

In this post we’re going to prove the following identity for the sum of the reciprocals of the numbers in column k of Pascal’s triangle, valid for integers : Identity 1: The standard way to prove Identity 1 is is … Continue reading

Posted in binomial coefficients, sequences and series | 1 Comment

The Art of Proving Binomial Identities

I recently finished a book, The Art of Proving Binomial Identities, that will be published by CRC Press later this year.  We’re past the page proofs stage, and I think all that’s left on my end is to provide a little … Continue reading

Posted in binomial coefficients, publishing | 1 Comment

Mathematics in Games, Part 3: Junior Arithmancer

In the past two months’ blog posts I’ve talked some about mathematics in games.  December‘s focused on the importance of embedding the mathematics in the game world rather than pulling the player out of the game to solve math problems … Continue reading

Posted in games, teaching | 1 Comment