Mathematics & Science Books

This accessible guide to critical thinking will help you think like a scientist, see through most scams at first glance, and learn how your own brain can trip you up. This fresh and exciting approach to science, skepticism, and critical thinking will...

This fascinating blend of popular science and military history examines the science of war, demonstrating the close connection between the discovery of basic physical principles and the development of weaponry over the ages. Physics has played a critical...

Two leading physicists discuss the importance of the Higgs Boson, the future of particle physics, and the mysteries of the universe yet to be unraveled. n July 4, 2012, the long-sought Higgs Boson--aka "the God Particle"--was discovered at the world's...

How science can convey a profound sense of wonder, connectedness, and optimism about the human condition. Most people appreciate science on an obvious level. Modern medicine, electric lighting, rapid transportation, and long-distance communication are...

This is the fascinating story of one of science's most enduring and triumphant ideas - from its genesis to the 21st century. In this history of atomism - from Democritus, considered by many to be the father of modern science, to the recent discovery of...

Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science. Veteran math educators demonstrate how some ""magnificent mistakes"" had...

Nobel laureate Steven Weinberg has written that "all that has happened since 1687 is a gloss on the Principia." Now you too can appreciate the significance of this stellar work, regarded by many as the greatest scientific contribution of all time...

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the...

Solitons are nonlinear waves which behave like interacting particles. When first proposed in the 19th century, leading mathematical physicists denied that such a thing could exist. Now they are regularly observed in nature, shedding light on phenomena...

This is the first truly comprehensive and thorough history of the development of mathematics and a mathematical community in the United States and Canada. This first volume of the multi-volume work takes the reader from the European encounters with North...

One of the great charms of mathematics is uncovering unexpected connections. In Numbers and Figures, Giancarlo Travaglini provides six conversations that do exactly that by talking about several topics in elementary number theory and some of their...

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18-20, 2022, at the Universite de Grenoble-Alpes, Grenoble, France. The articles present some developments...

This book provides a gentle introduction to fractional Sobolev spaces which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It...

How do we understand the world? While some look to the heavens for intelligent design, others argue that it is determined by information encoded in DNA. Science serves as an important activity for uncovering the processes and operations of nature, but it...

As the title of the book indicates, this is primarily a book on partial differential equations (PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional derivatives. The standard paradigm, or direct problem, is to take a...

The Mathematical Neighborhoods of School Mathematics visits regions beyond, but proximal to and accessible from school mathematics. Its aim is to give readers a glimpse of not just the rich diversity and adaptability of mathematics, but, most...

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the...

This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number Re. In this work, we show that there is constant 0 0 exist at least until t...

Number Theory Through the Eyes of Sophie Germain: An Inquiry Course is an innovative textbook for an introductory number theory course. Sophie Germain (1776-1831) was largely self-taught in mathematics and, two centuries ago, in solitude, devised and...

Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces...

This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including the...

This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The...

The circle method, pioneered by Ramanujan and Hardy in the early 20th century, has over the past 100 years become part of the standard tool chest of analytic number theory. Its scope of applications is ever-expanding, and the subject continues to see...

This book gives a self-contained introduction to the modern ideas and problems of harmonic analysis. Intended for third- and fourth-year undergraduates, the book only requires basic knowledge of real analysis, and covers necessary background in measure...

The theory of geometric structures on manifolds which are locally modeled on a homogeneous space of a Lie group traces back to Charles Ehresmann in the 1930s, although many examples had been studied previously. Such locally homogeneous geometric...

The central topic of this book is the spectral theory of bounded and unbounded self-adjoint operators on Hilbert spaces. After introducing the necessary prerequisites in measure theory and functional analysis, the exposition focuses on operator theory...

This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context...

The State of Play presents an essential first step in understanding how new digital worlds will change the future of our universe. Millions of people around the world inhabit virtual words: multiplayer online games where characters live, love, buy,...

The State of Play presents an essential first step in understanding how new digital worlds will change the future of our universe. Millions of people around the world inhabit virtual words: multiplayer online games where characters live, love, buy,...

The State of Play presents an essential first step in understanding how new digital worlds will change the future of our universe. Millions of people around the world inhabit virtual words: multiplayer online games where characters live, love, buy,...

The Biology of Small Mammals is the first exploration of the lives of small mammals undertaken in decades. Mammalogist Joseph F. Merritt offers an engaging, in-depth discussion about a diverse array of small mammals, from the rare Kitti's hog-nosed bat...

Is there a universal set of rules for discovering and testing scientific hypotheses? Since the birth of modern science, philosophers, scientists, and other thinkers have wrestled with this fundamental question of scientific practice. Efforts to devise...

As unique sources of coherent high-power, microwave, and millimeter-wave radiation, gyrotrons are an essential part of the hunt for controlled fusion. Presently, gyrotrons are actively used for electron cyclotron resonance plasma heating and current...

This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum...

This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25-30, 2018, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Reflecting recent...

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This volume contains the proceedings of a conference celebrating the work of Steven Boyer, held from June 2-8, 2018, at Universite du Quebec a Montreal, Montreal, Quebec, Canada. Boyer's contributions to research in low-dimensional geometry and topology,...

This book is a collection of articles on abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian...

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric...

Graph Theory presents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The format is similar to the companion text, Combinatorics: A Problem Oriented Approach also by Daniel A. Marcus, in...

A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of...

This set contains the Collected Works of William P. Thurston with Commentary, Volumes I-III, and The Geometry and Topology of Three-Manifolds. William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects...

The Seventh ARTA ('Advances in Representation Theory of Algebras VII') conference took place at the Instituto de Matematicas of the Universidad Nacional Autonoma de Mexico, in Mexico City, from September 24-28, 2018, in honor of Jose Antonio de la Pena's...

Alexander V. Kolesnikov, Higher School of Economics, Moscow, Russia. Emanuel Milman, Israel Institute of Technology, Haifa, Israel.

Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence...

We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions only, and we...