Mathematics

A classic treatment of Riemann surfaces from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

Resolution of singularities is a powerful and frequently used tool in algebraic geometry.

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity.

The theory of infinite loop spaces has been the center of much recent activity in algebraic topology.

The 1918-19 influenza epidemic killed more than fifty million people worldwide.

This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory.

For hundreds of years, the study of elliptic curves has played a central role in mathematics.

Though the search for good selectors dates back to the early twentieth century, selectors play an increasingly important role in current research.

This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic).

Between the seventeenth and nineteenth centuries Japan was totally isolated from the West by imperial decree.

The mysterious beauty, harmony, and consistency of mathematics once caused philosopher Hilary Putnam to term its existence a miracle.

The classic book that shares the enjoyment of mathematics with readers of all skill levelsWhat is so special about the number 30?

A foundational account of a new construction in the p-adic Langlands correspondenceMotivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations.

New mathematical research in arithmetic dynamicsIn The Arithmetic of Polynomial Dynamical Pairs, Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics.

A fascinating exploration of the pentagon and its role in various culturesThe pentagon and its close cousin, the pentagram, have inspired individuals for the last two and half millennia, from mathematicians and philosophers to artists and naturalists.

A definitive proof of global nonlinear stability of Minkowski space-time as a solution of the Einstein-Klein-Gordon equationsThis book provides a definitive proof of global nonlinear stability of Minkowski space-time as a solution of the Einstein-Klein-Gordon equations of general relativity.

New adaptive and event-triggered control designs with concrete applications in undersea construction, offshore drilling, and cable elevatorsControl applications in undersea construction, cable elevators, and offshore drilling present major methodological challenges because they involve PDE systems (cables and drillstrings) of time-varying length, coupled with ODE systems (the attached loads or tools) that usually have unknown parameters and unmeasured states.

A groundbreaking contribution to number theory that unifies classical and modern resultsThis book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus.

Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas.

Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of sl(2), both classical and quantum.

How the concept of proof has enabled the creation of mathematical knowledgeThe Story of Proof investigates the evolution of the concept of proof-one of the most significant and defining features of mathematical thought-through critical episodes in its history.

These notes are based on a course of lectures given at Princeton University during the academic year 19661967.

Simple games are mathematical structures inspired by voting systems in which a single alternative, such as a bill, is pitted against the status quo.

This book starts with the elementary theory of Lie groups of matrices and arrives at the definition, elementary properties, and first applications of cohomological induction, which is a recently discovered algebraic construction of group representations.

This book brings together a number of lectures given between 1993 and 1999 as part of a special series hosted by the Federal University of Pernambuco, in which internationally established researchers came to Recife, Brazil, to lecture on classical or celestial mechanics.

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic.

The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces).

When we learn, we change what we believe and how we interact with the world.

These notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966.

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity.

This monograph on the applications of cube complexes constitutes a breakthrough in the fields of geometric group theory and 3-manifold topology.

These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties.

How do scientists look at chance, or randomness, and chaos in physical systems?

Aimed at a diverse scientific audience, including physicists, astronomers, chemists, geologists, and economists, this book explains the theory underlying the classical statistical methods.

Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas.

Essential mathematical insights into one of the most important and challenging open problems in general relativity-the stability of black holesOne of the major outstanding questions about black holes is whether they remain stable when subject to small perturbations.

A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education.

This book presents a state-of-the-art understanding of semiconductor-electrolyte interfaces.

Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices.

'A joy' Philippe Sands'Glorious' David SpiegelhalterA fascinating, enchanting and personal look at the meaning of luck, and the way in which it has shaped our shared history and continues to inflect our day to day lives.

Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry.

A pseudorandom generator is an easy-to-compute function that stretches a short random string into a much longer string that "e;looks"e; just like a random string to any efficient adversary.

Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples.

This book presents the complete proof of the Bloch-Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry.

The history of mathematics is replete with examples of major breakthroughs resulting from solutions to recreational problems.

This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of L-functions.

Differential Equations on Fractals opens the door to understanding the recently developed area of analysis on fractals, focusing on the construction of a Laplacian on the Sierpinski gasket and related fractals.

Computability theory is a branch of mathematical logic and computer science that has become increasingly relevant in recent years.

An advanced treatment of surgery theory for graduate students and researchersSurgery theory, a subfield of geometric topology, is the study of the classifications of manifolds.

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K.