Author Archives: mzspivey

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

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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

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Mathematics in Games, Part 2: A Beauty Cold and Austere

Last month I wrote a post on the importance of context when teaching and learning mathematics, especially as it applies to games.  My primary point was that the mathematics needs to be embedded in the gaming experience in order for … Continue reading

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Mathematics in Games, Part 1

When my wife and I were buying our first house many years ago our real estate agent Rita quickly found out that I was a math professor.  She gave a response I have heard frequently over the years: “I’m not … Continue reading

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Proof of the Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic states the following: Every integer greater than 1 can be represented uniquely as the product of prime numbers. Another way to put this is that every integer has a unique factorization.  For example, 60 factors … Continue reading

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Equivalence of Two Binomial Sums

This month’s post entails proving the following equivalence: Identity 1: Despite the fact that these two sums are over the same range and are equal for all values of n they are not equal term-by-term. If you think about the two sides … Continue reading

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A Sum of Ratios of Binomial Coefficients

In this post we evaluate the sum .  Then we’ll generalize it and evaluate . The key tools we need for the first sum are the trinomial revision identity, , and the parallel summation identity, .  Using trinomial revision, we have . … Continue reading

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