Natural Philosophy: The Logic of Physics Volume One: Describing the World with Mathematics Fast paced and profusely illustrated with over 500 hand-drawn figures, Describing the World with Mathematics, is an introductory physics textbook suitable for courses at the university freshman and sophomore level, or for AP and IB high school courses. Physics starts and ends with laboratory data, but a discussion of laboratory data involves mathematics, mostly calculus in the beginning. How can a student, who only knows 8th grade algebra, be brought up to studying physics with calculus and differential equations? In this book, all necessary calculus and differential equations are rigorously developed in the context of physics, leaving no need for outside reference. All theorems are proved rigorously, and all physics formulas are derived from first principles or laboratory data. Several hundred students at Cathedral High School in Indianapolis, Indiana have helped to develop the related course. Highlights include: Viscous fluid flow with Reynolds number in chapter 3. - Treatment of experimental data in chapter 4. - Transfer functions and block diagrams in feedback and control engineering in chapter 5. - Introduction to electrical measurements in chapter 8. - Feynman graphs in chapter 9. - Efficiency of internal combustion engines in chapter 10. - Nuclear magnetic resonance in chapter 12. In every chapter there is far more material than an instructor may want to cover, leaving the student to discover the extent of this vast and interesting subject. Volume Two: The Quantum Theory of Everything is in preparation. This book was written by Marshall Dixon (Ph.D. in Physics, University of Virginia) and his former students Adam Hibshman (B.S. in Physics, Butler University) and James Miller (B.S. in Physics, Rose-Hulman Institute of Technology). This text is the result of the authors experimenting with teaching university level mathematical physics to several hundred students at Cathedral High School.