Author Archives: mzspivey

Mathematics through Narrative: A Beauty Cold and Austere

Earlier this year I spent some time (well, a lot of time) writing a mathematical computer game.  It’s called A Beauty Cold and Austere (ABCA), and it’s text-based; there are no graphics and no symbolic manipulation (e.g., no solving of … Continue reading

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The Validity of Mathematical Induction

Suppose you have some statement .  Mathematical induction says that the following is sufficient to prove that is true for all natural numbers k. is true. For any natural number k, if is true, then is true. The idea is that the first … Continue reading

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The Divergence of the Harmonic Series

The fact that the harmonic series, , diverges has been known since the time of Nicole Oresme in the 14th century, but this fact is still somewhat surprising from a numerical standpoint.  After all, each successive term only adds a … Continue reading

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The Secretary Problem With the Two Best

The secretary problem is the following: Suppose a manager wants to hire the best person for his secretary out of a group of n candidates.  He interviews the candidates one by one.  After interviewing a particular candidate he must either (1) … Continue reading

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Some Thoughts on Teaching Math for Social Justice

Short version: I’m not in favor of it.  For a teacher to use their position of power to push their political and social views on their students is an abuse of that power. Long version: See the rest of this … Continue reading

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Pascal Matrices and Binomial Inversion

In this post we’ll look at the relationship between a Pascal matrix, its inverse, and binomial inversion.  It turns out that these are the same concepts viewed from two different angles. The Pascal matrix is the matrix containing Pascal’s triangle … Continue reading

Posted in binomial coefficients, matrices | 2 Comments

Counting Poker Hands

For this post I’m going to go through a classic exercise in combinatorics and probability; namely, proving that the standard ranking of poker hands is correct. First, here are the standard poker hands, in ranked order. Straight flush: Five cards of … Continue reading

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