What is the systematic prerequisite sequences of learning that must be mastered before approaching the subject of learning Quaternions, and then Clifford Algebra? My ultimate goal is to learn and study Maxwell’s equations in their original Quaternion form, plus other obscure scientific papers that utilize Clifford Algebra and Octonians. But before I can approach that, I need the solid mathematical background that comes before studying and understanding Quaternions and Clifford (Geometric) Algebra, beginning with a recommended syllabus that starts with pre-algebra mathematics.
I know that there is a systematic approach to learning mathematics in general. For example: Multiplication and division at the foundation, then fractions, then pre-algebra, then algebra, then geometry, then trigonometry, and so on. With each division of mathematics itself having a systematic sequence of learning the subject from its fundamentals to their ultimate advanced topics. So to state my question differently, what I want to know is this:
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What is the best sequence of mathematical prerequisites (the syllabus) to master before I begin studying Quaternions, and then advance to Clifford (Geometric) Algebra?
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Where does Quaternion and Clifford (Geometric) algebra fit in the sequence of learning algebra, and what will be their prerequisites necessary to have been already mastered before entering these subjects?
Also, can someone recommend a track of material that would properly prepare me for the topic of Quaternions and Clifford (Geometric) Algebra from a pre-algebra starting point? i.e. Completed knowledge of addition/subtraction, multiplication/division, fractions and percentages.
Best Answer
You learn arithmetic, basic geometry, then what is called "prealgebra", then algebra 1 and algebra 2. Once you have gotten through the chapter on complex numbers, you want to learn at least a little bit about matrices. You might get a taste in your algebra 2 class or precalculus, but the subject is called "linear algebra" and the more of it you know the better--it doesn't require calculus.
Once you have complex numbers and matrices, you are good to go. I actually would not recommend Conway; I own it and found it frustrating. I have hunted for good materials to learn quaternions and there mostly aren't any books that explain them well. But YouTube videos fill the gap; since quaternions get used in computer programming to handle rotations in three dimensions, there is some demand. Good luck!