Part seven of a number that just keeps getting bigger: Subgroups. Remember, past lessons can all be found by clicking on the “math from scratch” tag below.
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.
On January 1, the first lesson in a series of triweekly lessons launches. The concept is to cover all of the math I know and can learn in a logical sequence, with no assumptions of any kind, until a full tapestry of math has been produced. The bibliography for this will be huge. Instead of formal citations, as this will likely involve every book I own today and whatever else I buy in the next few years, I will list the bibliography as follows. My book collection is listed here. Every relevant book in that collection will be used at some point in the development of these lessons. In addition, I also have been referencing Wikipedia, Wolfram’s MathWorld and PlanetMath. The book collection I own will be updated periodically, while additional websites will be added to this article as they are incorporated in my research.
As previously announced, starting January 1, 2011, there will be a new math lesson posted here every three weeks until all the math that I know has been posted. Half of the lessons for 2011 are now written, and several other lessons heading into 2013 are roughed out on my outline. This is a call for input: at this stage in the planning, the real numbers and basic algebras have been put in place. Based on that, the next lessons can establish geometry, linear algebra, calculus, and more. Which topics do you, our readers, want to see prioritized? Speak your piece below or by direct e-mail. Users of the free (and Free, and highly recommended) yEd software can download the current plan from this link. (Right-click and save to make sure it loads in yEd.) Numbered blocks have specific lessons associated with them, blue blocks are lessons which have been written, and arrows lead from prerequisite topics to later topics. Some topics may be combined into single lessons or divided into multiple lessons as I get to the actual writing. I’ll try to keep that link up to date, along with the Bureau 42 event calendar.
The previously announced plans for future Summer School sessions may change somewhat. Feedback is requested, and details are offered after the break.