There are many standard sets of numbers, such as real numbers and integers. Some of the common sets are often hard to keep track of. In other cases, interesting sets of numbers are entirely ignored by standard math education. Sixteen such sets of numbers, their definitions, and (if applicable) their standard notations are presented here.

As of this article, the “teaching tidbits” are now being marked by subject right in the subject line. This will be the last tidbit before our first summer school semester starts on Monday, covering graduate level quantum mechanics with grade school math. In the meantime, enjoy one proof of the Pythagorean Theorem.

The latest teaching tidbit is ready: finding the greatest common factor of two number using subtraction. New topics can be requested and old topics can be found through the Bureau 42 Teaches sidebar.

This is our second topic by e-mail request. I also plan to post a method for determining the greatest common factor of two numbers using only subtraction as an operation shortly. You can learn to calculate logarithms by hand here. Also, check out the sidebar on the right for the new “Bureau 42 Teaches” link compilation page.

This topic chosen to satisfy an e-mail request. It is entirely possible to calculate square roots without the aid of an electronic or mechanical device more advanced than a pencil. More on this, and about choosing content, frequency, and presentation of these lessons comes after the break.

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This summer we’ll see Bureau 42’s first summer school session, which covers graduate level quantum physics with grade school math. I had a blast writing it, and will probably write more educational columns in math, physics, and more. (Summer school topics have already been chosen through 2015, featuring contributions from multiple site authors.) Well, not all topics warrant the full summer course treatment, and cover only single lessons at a time. Those will be posted at random intervals right here. Here’s the first topic: turning repeating decimals into fractions. The algorithm can be followed and applied by just about anybody, though the explanation will be easier to deal with if you’re comfortable with high school math. I am also willing to take requests if there’s something you want to learn. I’m not omniscient, but if it’s math and/or physics, I can probably manage it.