Tuesday, January 1, 2019
--- A course in mathematics ---
Do you want a self education in mathematics? I have three curricula for you according to how deep you want to go and how long you want to take.
If you just want a brief overview I'll plug my own work.
The Stat files (on the Therian Timeline site) are about statistics, but I begin by breezing through arithmetic, algebra, geometry, pre-calculus, calculus and differential equations - and then I throw in a little complex mathematics, vectors, linear algebra, logic, and simple statistics. The purpose of this section is to bring budding amateur researchers and statistician up to speed in the preliminaries, but the section, The Basics, would serve as an overview of mathematics, too. Here's the address:
If you want a little more depth and, maybe, some hands-on experience, check out the Excursions section where I explain counting on your fingers (fingermath), standards of measurement (including the measuring tools you carry around with you everywhere - your body), lattice multiplication, and building a slide rule from scratch using index cards.
If you want a lot more depth, you might want to follow my mathematics LabBook. It's a mathematics tutorial with lots of personal involvement. At the current writing, I've only covered the very basics of mathematics - the logic behind math, counting, and whole numbers, but my intention here is to look inside mathematics and really see how it works. Do you really know how numbers work?
If I live long enough, I'll make it to differential equations.
The LabBooks are LibreOffice Calc spreadsheet documents but, fortunately, LibreOffice is a free download.
Level two is conversational math. You can pick up an understanding of mathematics to the point that you could sit through a lecture on, say, tensor analysis and understand what the presenter is talking about. You probably wouldn't be able to use tensors to solve an engineering problem though. You could achieve that level in about a year with the Teaching Company mathematics courses.
The Teaching company sells college level courses in a wide range of subjects. The video sets are pretty pricey. The key is that every set they sell goes on sale at least once during the year at a substantial discount. Also, the Denver Public Library has many of the products. Check your own local library if you want to go that way, but there is considerable advantage of owning your own. For one thing, there's no time limit.
The Teaching Company website is here:
For a complete course of mathematics, I would recommend:
Secrets of Mental Math - Arthur Benjamin
Algebra I - James A. Sellers
Algebra II - James A. Sellers
Geometry: An Interactive Journey to Mastery - James S. Tanton
Precalculus (including trigonometry)
Mathematics Describing the Real World: Precalculus and Trigonometry - Bruce Edwards
Change and Motion: Calculus Made Clear - Michael Starbird
Mastering Differential Equations: the visual method - Robert L. Devaney
There are several other sets for fields like discrete mathematics, probability, statistics, combinatorics, etc. but that might take you into a second year of study.
Now, if you want to take a few years and really have a mastery of mathematics, I would recommend beginning with the CK12 textbooks and then switch to the MIT OpenCourseWare courses for the college level mathematics.
CK12 is an organization that offers excellent free textbooks and other learning materials for grades kindergarten to high school (thus "CK12"). The website is here:
And the MIT website is here:
If you can get your hands on a copy of the old educational mathematics textbook Basic Mathematical Concepts, by F. Lynwood Wren it's one of the best mathematical texts for explaining elementary concepts I have seen. Some other great resources are:
The Universal Encyclopedia of Mathematics by James R. Newman
Secrets of Mental Math by Arthur Benjamin
The Handbook of Essential Mathematics: Formulas, Processes, and Tables Plus Applications in Personal Finance edited by Donald D. Gregory and Vincent R. Miller
This last reference is an Air Force Research Laboratory text that has been released for public distribution and can be found on the Internet here:
Also be sure to check out the Interactive Mathematics website (http://www.cut-the-knot.org).