Part six of lots: Permutation Groups.
We now have part five of oodles: Structuring Symmetry, with the first application of the group axioms.
This lesson defines “algebra” and starts to deal with a particular type of algebra. Lesson four: The Group Axioms is available here.
Here it is, part three of many: Defining Whole (and Natural) Numbers.
Part two in our tri-weekly series is here. This week’s topic: Set Theory. For past topic, click the “math from scratch” tag below. There will be too many of these to include links in every article.
Bureau 42’s biggest educational project to date begins here. The ultimate goal: teach everything we possibly can in math from the ground up in a sequence of comprehensive lessons, released no more than three weeks apart. This project will likely take years. The first lesson, defining mathematical relations, is available here.
As mentioned last week, I wasn’t pleased with how the linear algebra summer school modules were turning out, so the project has mutated into something else entirely. Those who are interested can read the portions that were completed here. All intended content will eventually become a part of the Math From Scratch project, but as the first lesson was the only one I was really satisfied with in this format, I’m changing the plans. Consider this a preview of the “Math From Scratch” project that will start in early 2011.
The previously announced plans for future Summer School sessions may change somewhat. Feedback is requested, and details are offered after the break.
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.