'Fascinating ... so enlightening that suddenly maths doesn't seem so fearsome as it once did' SIMON WINCHESTER From Aristotle to Ada Lovelace: a brief history of the mathematical ideas that have forever changed the world and the everyday people and pioneers behind them. The story of our best invention yet. From our ability to calculate the passing of time to the algorithms that control computers and much else in our lives, numbers are everywhere. They are so indispensable that we forget how fundamental they are to our way of life. In this international bestseller, Mickael Launay mixes history and anecdotes from around the world to reveal how mathematics became pivotal to the story of humankind. It is a journey into numbers with Launay as a guide. In museums, monuments or train stations, he uses the objects around us to explain what art can reveal about geometry, how Babylonian scholars developed one of the first complex written languages, and how 'Arabic' numbers were adopted from India. It All Adds Up also tells the story of how mapping the trajectory of an eclipse has helped to trace the precise day of one of the oldest battles in history, how the course of the modern-day Greenwich Meridian was established, and why negative numbers were accepted just last century. This book is a vital compendium of the great men and women of mathematics from Aristotle to Ada Lovelace, which demonstrates how mathematics shaped the written word and the world. With clarity, passion and wisdom, the author unveils the unexpected and at times serendipitous ways in which big mathematical ideas were created. Supporting the belief that - just like music or literature - maths should be accessible to everyone, Launay will inspire a new fondness for the numbers that surround us and the rich stories they contain.

Based on a highly regarded lecture course at Moscow State University, this is a clear and systematic introduction to gauge field theory. It is unique in providing the means to master gauge field theory prior to the advanced study of quantum mechanics. Though gauge field theory is typically included in courses on quantum field theory, many of its ideas and results can be understood at the classical or semi-classical level. Accordingly, this book is organized so that its early chapters require no special knowledge of quantum mechanics. Aspects of gauge field theory relying on quantum mechanics are introduced only later and in a graduated fashion--making the text ideal for students studying gauge field theory and quantum mechanics simultaneously.

The book begins with the basic concepts on which gauge field theory is built. It introduces gauge-invariant Lagrangians and describes the spectra of linear perturbations, including perturbations above nontrivial ground states. The second part focuses on the construction and interpretation of classical solutions that exist entirely due to the nonlinearity of field equations: solitons, bounces, instantons, and sphalerons. The third section considers some of the interesting effects that appear due to interactions of fermions with topological scalar and gauge fields. Mathematical digressions and numerous problems are included throughout. An appendix sketches the role of instantons as saddle points of Euclidean functional integral and related topics.

Perfectly suited as an advanced undergraduate or beginning graduate text, this book is an excellent starting point for anyone seeking to understand gauge fields.