Paul Davies

Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity. The book contains two intertwined but distinct halves.Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible. The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.

The goal of this book is to expose the reader to the indispensable role that mathematics plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fibre bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras, fibre bundles, and gauge theories. The spirit of the first edition, namely the balance between rigour and physical application, has been maintained, as is the abundance of historical notes and worked out examples that demonstrate the "unreasonable effectiveness of mathematics" in modern physics.

"A riveting tour of the cosmos from one of the brightest minds in astrophysics." —The Washington Post A revolutionary new account of our universe’s creation—and a breathtaking exploration of the landscape from which we sprang—from one of the world’s most celebrated cosmologists What came before the Big Bang, and what exists outside of the universe it created? Until recently, scientists could only guess at what lay past the edge of space-time. However, as pioneering theoretical physicist Laura Mersini-Houghton explains, new scientific tools are now giving us the ability to peer beyond the limits of our universe and to test our theories about what is there. And what we are finding is upending everything we thought we knew about the cosmos and our place in it. Mersini-Houghton is no stranger to boundaries—or to pushing through them. As a child growing up in Communist Albania, she discovered a universe beyond her walled-off world through the study of math and science, and through music. As a female cosmologist in a male-dominated field, she transcended the limits that society and her profession tried to place on her. And as a trailblazing researcher, she helped to revolutionize the study of our universe by revealing that, far from living in a cosmic Albania, with a world that ends at its borders, we are part of a larger family of universes—a multiverse—that holds wonders we are only beginning to unlock. Mersini-Houghton’s groundbreaking research suggests that we sit in a quantum landscape whose peaks and valleys hide a multitude of other universes, and even hold the secret to the origins of existence itself. Recent evidence has revealed the signatures of such sibling universes in our own night sky, confirming Mersini-Houghton’s theoretical work and offering humbling evidence that our universe is just one member of an unending cosmic family. The incredible scientific saga of one woman’s mind-expanding journey through the multiverse, Before the Big Bang will reshape our understanding of humanity’s place in the unfathomable vastness of the cosmos.