I have a new ambitious project for myself. I am going to create a math text that covers every subject of math from high school algebra, geometry, trigonometry, to calculus, boolean algebra, probability and statistics, linear algebra, differential equations, complex analysis, Fourier analysis, and whatever else I can think of. Oh, and I want to make it available online. For free.
I have some ideas about the structure of this text.
Derivations: I will have derivations of useful theorems, formulas, and known problem solving strategies as the main part of the text. Each will be self contained, and will have links to the prerequisite material found in other parts of the text.
Note I said “other parts of the text” and not “previous parts of the text.” The text itself will not follow page numbers like ordinary books that are physically limited to them. Certain areas of mathematics can be learned without knowing about certain other areas of mathematics. For example, you can learn all about elementary linear algebra without knowing any calculus, but you do have to know how to do basic algebra. Likewise, you can learn calculus without knowing any linear algebra. The subjects are simply “independent.” Now, if you want to learn how to solve systems of linear differential equations, then you have to know both calculus and linear algebra, and that will be reflected on the page for that.
Exercises and practice problems: These will consist of a few easy exercises that can serve as definition checks and concept checks. They will be followed by more comprehensive problems designed to combine multiple topics together. I would also like to include some open-ended long term type questions, but I’m not sure how to do that yet. Since this will be available online (and for free!) I would like to have some interactive animations to help illustrate some of the topics. I will include “historical problems of interest” to give the reader an idea of how these things came up in the first place, and some of the challenges that arose in the initial attempts to solve them. Finally, I will include a list of open problems in the subject, to show the reader that there is always more to be done in a given field of study.
As I develop the text, I’m sure some of this will be modified greatly, and I would appreciate input from others on this project. My ultimate goal is to provide a free resource for anybody who wants to learn any subject in math (and hopefully, eventually this format can be extended to any number of other subjects in the future.) Right now it’s just me doing this, although there are others who have created amazing online resources such as the stack exchange . I don’t know how long this is going to take, either, but considering I spend a good chunk of my free time doing math problems for my own amusement anyway, I may as well amuse myself to someone else’s benefit.