Foreword

TLDR:

As a physicist, you need to learn as much mathematics as possible without becoming a full mathematician. Same is true for all other subjects for physicists. This is why a physicist is 40-50% a Computer Scientist, 70% an Engineer, and 50% a Mathematician, or you customize your own curriculum/capability in your own way. The real question is why would you want to work with a physicist, a character that is not specified in any one domain but a quirky jack-of-all-trades, versus someone specified in one narrow domain, who is often times an expert in that field. In my own opinion, both have their ups and downs, and I don’t see how one is superior to the other – I chose to be a physics major simply because I was influenced by someone’s infectious passion for physics.

Why math?

Initially I planned to jump straight into describing condensed matter. But then I thought, “maybe it would help if I can jog down the physics that give rise to condensed matter!” and realized that maybe I should start with stat mech and quantum. But then I also realized both subjects utilize an abusive amount of linear algebra, which builds on top of the differential equation. Undeniably, the current most effective way, but not limited to the only way, known to mankind when it comes to describing physics is through mathematics. So here it is, linear algebra to the experimentalist’s standard. I just need it enough to address the different topics.

I plan on addressing the mathematics that are commonly used in E&M, QM, stat mech and classical mechanics (both phase and configuration spaces).

Keep in mind also, what you are reading is materials you may already have seen, and you may even find the majority of this work to be trivial. My writing for this is geared towards introducing physics in the most “parameterized” way possible, such that learners (be it high schoolers, freshman college students, illuminati or avid learners) can more easily grasp at the ideas through the mathematical formalism. I will also attempt to introduce the physics in the most vivid way possible, with or without mathematics. For an experimental description, much of it will involve reading lots of words and relatively little math, if anything lots of best fits to find trends locally. To think of physics as a subject of vitality, experimentalist have a language that is likely not in the language of mathematics, but in the language of established models. The reality is just as it is, as it will always be, regardless of however you describe it. It’s the data before the empirical law. One can say that this is an elementary approach and you’re not really learning physics; I say that having the capability to understand things by neatly parameterizing variables is the first step to an organized method of mastery.

As an applied experimentalist at heart, one can say the project Book Of Physics is not of practical use because this is only addressing the mathematics, not the physics! I believe that once the learner has a solid grasp at the mathematical structure behind the physical model, understanding and mastery of the model would come more naturally. Despite the fact that this is merely review, and has no novelty or new fundamental discovery, I can certainly say that having a more profound understanding and being able to deliver the message in a more accessible format is still a good practice. It can certainly be a great foundation for the discovery that lies ahead!