Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects.

Many of the tools used in differential topology are introduced and the...

As a programmer working for Logica UK in London in the mid-1980’s, I became a passionate advocate of formal methods. Extrapolating from small successes with VDM and JSP, I was sure that widespread use of formal methods would bring an end to the software crisis.

One approach especially intrigued me. John Guttag and Jim...

A Bayesian approach can contribute to an understanding of the brain on multiple levels, by giving normative predictions about how an ideal sensory system should combine prior knowledge and observation, by providing mechanistic interpretation of the dynamic functioning of the brain circuit, and by suggesting optimal ways of deciphering...

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the...

Want to calculate the probability that an event will happen? Be able to spot fake data? Prove beyond doubt whether one thing causes another? Or learn to be a better gambler? You can do that and much more with 75 practical and fun hacks packed into Statistics Hacks. These cool tips, tricks, and...

This book provides a completely revised and expanded version of the previous classic edition ‘General Relativity and Relativistic Astrophysics’. In Part I the foundations of general relativity are thoroughly developed, while Part II is devoted to tests of general relativity and many of its applications. Binary pulsars – our...

In the first part of the...

This book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and...

Written by the author of the best-selling E & M text, this text is designed to teach students how to DO quantum mechanics. Part I covers the basic theory; Part II develops approximation schemes and real-world applications. *offers an unusually readable, consistent, and honest discussion of fundamental ideas. *some books allow students to...

By any measure, the Pythagorean theorem is the most famous statement in all of mathematics, one remembered from high school geometry class by even the most math-phobic students. Well over four hundred proofs are known to exist, including ones by a twelve-year-old Einstein, a young blind girl, Leonardo da Vinci, and a future president of the...