Mathematics and Science

Written by Arthur Ogus on the basis of notes from Pierre Berthelot's seminar on crystalline cohomology at Princeton University in the spring of 1974, this book constitutes an informal introduction to a significant branch of algebraic geometry.

This book presents a new result in 3-dimensional topology.

Trains pull into a railroad station and must wait for each other before leaving again in order to let passengers change trains.

In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration.

The authors, leading researchers in the fields of mathematical economics and methodology, present the first comprehensive synthesis of literature on qualitative and other nonparametric techniques, which are important elements of comparative statics and stability analysis in economic theory.

The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds.

One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems.

Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade.

Genomic signal processing (GSP) can be defined as the analysis, processing, and use of genomic signals to gain biological knowledge, and the translation of that knowledge into systems-based applications that can be used to diagnose and treat genetic diseases.

Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory.

Today's standard textbooks treat the theoretical structure of electric and magnetic fields, but their emphasis is on electromagnetic radiation and static-electric and magnetic fields.

Various approaches have been developed to evaluate the consequences of spatial structure on evolution in subdivided populations.

This book seeks to describe the rapid development in recent decades of sieve methods able to detect prime numbers.

Memory is perhaps the most extraordinary phenomenon in the natural world.

This book provides a comprehensive, self-contained introduction to one of the most exciting frontiers in astrophysics today: the quest to understand how the oldest and most distant galaxies in our universe first formed.

Formal verification increasingly has become recognized as an answer to the problem of how to create ever more complex control systems, which nonetheless are required to behave reliably.

From the Internet to networks of friendship, disease transmission, and even terrorism, the concept--and the reality--of networks has come to pervade modern society.

This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics.

In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures.

The first interdisciplinary textbook to introduce students to three critical areas in applied logicDemonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic.

The original goal that ultimately led to this volume was the construction of "e;motivic cohomology theory,"e; whose existence was conjectured by A.

This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrodinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations.

This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it.

Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place.

Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years.

We humans share Earth with 1.

Spatial patterns of movement are fundamental to the ecology of animal populations, influencing their social organization, mating systems, demography, and the spatial distribution of prey and competitors.

This classic book is an introduction to dynamic programming, presented by the scientist who coined the term and developed the theory in its early stages.

This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems.

Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra.

This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q.

In Hadamard Matrices and Their Applications, K.

This book is a spectacular introduction to the modern mathematical discipline known as the Theory of Games.

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis.

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible.

Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure.

Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology.

In The Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986.

This book presents the analytic foundations to the theory of the hypoelliptic Laplacian.

Glimpses of Creatures in Their Physical Worlds offers an eye-opening look into how the characteristics of the physical world drive the designs of animals and plants.

Stability and Stabilization is the first intermediate-level textbook that covers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations.

Earthquake and Volcano Deformation is the first textbook to present the mechanical models of earthquake and volcanic processes, emphasizing earth-surface deformations that can be compared with observations from Global Positioning System (GPS) receivers, Interferometric Radar (InSAR), and borehole strain- and tiltmeters.

Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven.

This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms.

If classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants?

Kiyosi Ito's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes.

A pioneer in evolutionary game theory looks at selfishness and cooperationHow does cooperation emerge among selfish individuals?

This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology.

Outer billiards is a basic dynamical system defined relative to a convex shape in the plane.

Modeling with Data fully explains how to execute computationally intensive analyses on very large data sets, showing readers how to determine the best methods for solving a variety of different problems, how to create and debug statistical models, and how to run an analysis and evaluate the results.