Tunneling Through the Math Barrier: The Fledgling Physics Student's Field Guide to Essential Mathematics

TL;DR

This book aims to bridge the gap between high-school and college mathematics for physics students, focusing on conceptual understanding and how to think about math in physics rather than just memorizing algorithms.

Contribution

It provides a conceptual framework for physics students to learn essential mathematics, emphasizing understanding over rote memorization, with references for further study.

Findings

Enhanced conceptual understanding of math for physics students

Practical guidance on learning math as physicists do

References for advanced topics

Abstract

[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe and understand the universe around us. Unfortunately our universe happens to be pretty complicated, at least from a mathematical point-of-view. However, a lot of the underlying physics | the underlying set of rules surrounding how things move and behave | is usually not too complicated. Sure, when we couple things together, everything turns disgusting, and we need to turn to really powerful computers or simulators to get a lot accomplished. But the basic rules are not that bad. My hope is to provide enough of a conceptual framework for you to learn to $read$ math as I saw a lot of other physicists do when I started my undergraduate career. I plan to cover some of the topics that tend to trip up a lot of physics students, although I could not cover these exhaustively. When I found that I should have covered more, but could not due to finite time constraints, I left a reference to other work that I think you may find helpful. However, unlike a lot of works, my focus is to help modify your thinking of how math is used, rather than just pummel you with algorithms for you to memorize without giving you the proper context for such algorithms. Whenever you find my explanations long-winded, feel free to proceed through faster. If you get stuck, you are always free to go back and see what I might have referenced before.