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Author Archives: mzspivey
A Lesson on Converting Between Different Bases
We’re in the time of COVID19, and that has meant taking far more direct responsibility for my children’s learning than I ever have before. It’s been a lot of work, but it’s also been fun. In fact, I’ve been surprised … Continue reading
Posted in number theory
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A CoinFlipping Problem
One problem that I’ve assigned when discussing Markov chains is to calculate the expected number of flips required for a particular pattern to appear. (Here I mean a pattern such as heads, heads, heads, or HHH.) In this post I’m … Continue reading
Posted in coin flipping, Markov chains, probability
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Strong Induction Wasn’t Needed After All
Lately when I’ve taught the second principle of mathematical induction – also called “strong induction” – I’ve used the following example to illustrate why we need it. Prove that you can make any amount of postage of 12 cents or … Continue reading
Posted in number theory, proof techniques
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Arguments for 0.9999… Being Equal to 1
Recently I tried to explain to my 11yearold son why 0.9999… equals 1. The standard arguments for (at least the ones I’ve seen) assume more math background than he has. So I tried another couple of arguments, and they seemed … Continue reading
Posted in arithmetic, number theory
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Diversity Statements in Hiring
Recently Abigail Thompson, chair of the mathematics department at the University of California, Davis, and a vice president of the American Mathematical Society, published this article in Notices of the American Mathematical Society. The article includes the following statement: Faculty … Continue reading
Posted in campus issues, diversity, politics
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Finding the Area of an Irregular Polygon
Finding the area of an irregular polygon via geometry can be a bit of a chore, as the process depends heavily on the shape of the polygon. It turns out, however, that there’s a formula that can give you the … Continue reading
Posted in analytic geometry, calculus, Green's Theorem
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An observation on the unit circle
We did a quick review of the unit circle in my multivariate calculus class last week, and I pointed out a fact about the sines and cosines of the common angles in the first quadrant that some of the students … Continue reading
Posted in trigonometry
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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
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