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On the unreasonable efficiency of mathematical writing, part II

The writing of mathematics is very efficient. Perhaps the teaching of mathematics can afford a little more redundancy. Here is a key example: Mathematical induction-the champion of efficiency. The beautiful idea: Induction is often used (and usually taught) to prove … Continue reading

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On the unreasonable efficiency of mathematical writing

In literary writing, we are taught to provide an introduction, a body and a conclusion. We are encouraged to—inefficiently—relate parts of an essay to a central idea. In mathematics, our writing is at times too efficient. Perhaps the teacher can … Continue reading

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On Teaching Loving Mathematics

I love math—not because I think I’m good at it, but because it’s powerful, it’s supremely beautiful and it’s everywhere. Mathematicians and many others agree! However, it happens all too often that people claim not to agree. Teachers can change … Continue reading

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On the Value of Making up Your Own Question

First, we consider an example of how one might make up a question. Here is a nice fact: (1/2)+(1/3)+(1/6)=1 Let’s have some fun with this fact by making it the answer of a question. Think of it as a mystery … Continue reading

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Squaring the Superhero

I teach many different courses in mathematics. All of these courses contain wonderful material. I love math. Last year, my son asked me why some of the students at his elementary school did not seem to share my view regarding … Continue reading

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On Trigonometric Nostalgia

When my son asks me how something works, I often don’t have a satisfactory answer. After all, I can’t rip open my digital device and show him the parts in action. In sharp contrast, we can see exactly how a … Continue reading

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A Perfect Square Discovers Pi

Pi is defined as the ratio of the circumference of a circle, to its diameter. It follows (how?) that the same constant pi is also the number of r x r squares that have the same total area as a … Continue reading

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Welcome.

Dan McQuillan, Associate Professor of Mathematics Department of Mathematics Norwich University Northfield, VT 05663 802 485-2323 dmcquill [at] norwich.edu There is a menu on the bottom of the above picture of Norwich University. Please explore various pages of this site … Continue reading

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