From Integers to the Big Bang

This book offers a concise catalogue of the mathematical subjects underpinning modern theoretical physics. It traces the logical progression of ideas from the primitive beginnings of our earliest number systems to the calculation of the transcendental numbers e and π and their uses in complex analysis. What took the human race thousands of years to accomplish is here presented in a coherent, intuitive sequence. Along the way, the book introduces core topics in mathematical physics, including electromagnetism, statistical mechanics, thermodynamics, relativity, and nuclear fission and fusion, breakthroughs that have been foundational to the sophisticated scientific landscape in which we find ourselves.

Topics that are often taught in isolation, at scattered intervals, are here woven into a unified narrative that prioritises the logical development of ideas, offering an approach grounded in intuitive reasoning. Whether encountering these subjects for the first time or seeking to consolidate earlier learning, readers will benefit from the book's unique perspective on the underlying structure of mathematics and physics, and how these disciplines have guided humanity from its early agrarian roots to the intricate, technologically advanced world of today.