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A course in complex analysis
A comprehensive graduate-level textbook that takes a fresh approach to complex analysisA Course in Complex Analysis explores a central branch of mathematical analysis, with broad applications in mathematics and other fields such as physics and engineering. Ideally designed for a year-long graduat...
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Biomolecular feedback systems
This book provides an accessible introduction to the principles and tools for modeling, analyzing, and synthesizing biomolecular systems. It begins with modeling tools such as reaction-rate equations, reduced-order models, stochastic models, and specific models of important core processes. It the...
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Calculus of variations and optimal control theory
This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with ca...
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Complex adaptive systems
This book provides the first clear, comprehensive, and accessible account of complex adaptive social systems, by two of the field's leading authorities. Such systems--whether political parties, stock markets, or ant colonies--present some of the most intriguing theoretical and practical challenge...
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Discrete and computational geometry
An essential introduction to discrete and computational geometryDiscrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet w...
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Discrete and computational geometry, 2nd edition
The essential introduction to discrete and computational geometry—now fully updated and expandedDiscrete and Computational Geometry bridges the theoretical world of discrete geometry with the applications-driven realm of computational geometry, offering a comprehensive yet accessible introduction...
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Distributed control of robotic networks
This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and i...
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Feedback systems
The essential introduction to the principles and applications of feedback systems—now fully revised and expandedThis textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a ...
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Global warming science
A quantitative, broad, hands-on introduction to the cutting-edge science of global warmingThis textbook introduces undergraduates to the concepts and methods of global warming science, covering topics that they encounter in the news, ranging from the greenhouse effect and warming to ocean acidifi...
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Graph theoretic methods in multiagent networks
This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum ...
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Hot molecules, cold electrons
An entertaining mathematical exploration of the heat equation and its role in the triumphant development of the trans-Atlantic telegraph cableHeat, like gravity, shapes nearly every aspect of our world and universe, from how milk dissolves in coffee to how molten planets cool. The heat equation, ...
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Hybrid dynamical systems
Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems ...
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Hybrid feedback control
A comprehensive introduction to hybrid control systems and designHybrid control systems exhibit both discrete changes, or jumps, and continuous changes, or flow. An example of a hybrid control system is the automatic control of the temperature in a room: the temperature changes continuously, but ...
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Intermittent convex integration for the 3d euler equations
A new threshold for the existence of weak solutions to the incompressible Euler equationsTo gain insight into the nature of turbulent fluids, mathematicians start from experimental facts, translate them into mathematical properties for solutions of the fundamental fluids PDEs, and construct solut...
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Introduction to computational science
The essential introduction to computational science—now fully updated and expandedComputational science is an exciting new field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. Th...
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Invisible in the storm
An accessible book that examines the mathematics of weather predictionInvisible in the Storm is the first book to recount the history, personalities, and ideas behind one of the greatest scientific successes of modern times—the use of mathematics in weather prediction. Although humans have tried ...
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Islands of order
Two pioneering anthropologists reveal how complexity science can help us better understand how societies change over timeOver the past two decades, anthropologist J. Stephen Lansing and geneticist Murray Cox have explored dozens of villages on the islands of the Malay Archipelago, combining ethno...
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Linear systems theory
A fully updated textbook on linear systems theoryLinear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. This updated second edition of Linear Systems Theory covers ...
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Making democracy count
How we can repair our democracy by rebuilding the mechanisms that power itWhat’s the best way to determine what most voters want when multiple candidates are running? What’s the fairest way to allocate legislative seats to different constituencies? What’s the least distorted way to draw voting di...
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Math bytes
An inviting collection of fun, hands-on applications in mathematics and computingThis book provides a fun, hands-on approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie's opening weekend? Ho...
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Mathematics for economists
Self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics starting from a very low level. Topics covered include calculus, matrix algebra, probability, dynamics and static and dynamic optimisation, all illustrated by examples and problems from...
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Mathematics for the life sciences
An accessible undergraduate textbook on the essential math concepts used in the life sciencesThe life sciences deal with a vast array of problems at different spatial, temporal, and organizational scales. The mathematics necessary to describe, model, and analyze these problems is similarly divers...
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Mathematics in nature, revised edition
How mathematics unveils the beauty of the natural worldMathematics in Nature reveals how mathematics provides a unifying language for understanding the hidden order of nature. In this richly illustrated book, John Adam guides readers from basic models using everyday arithmetic to the modeling of ...
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Modeling infectious diseases in humans and animals
For epidemiologists, evolutionary biologists, and health-care professionals, real-time and predictive modeling of infectious disease is of growing importance. This book provides a timely and comprehensive introduction to the modeling of infectious diseases in humans and animals, focusing on recen...
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Noncooperative game theory
Noncooperative Game Theory is aimed at students interested in using game theory as a design methodology for solving problems in engineering and computer science. João Hespanha shows that such design challenges can be analyzed through game theoretical perspectives that help to pinpoint each proble...
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Nonlinear dynamical systems and control
Nonlinear Dynamical Systems and Control presents and develops an extensive treatment of stability analysis and control design of nonlinear dynamical systems, with an emphasis on Lyapunov-based methods. Dynamical system theory lies at the heart of mathematical sciences and engineering. The applica...
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Nonlinear optimization
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensiv...
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Numerical analysis
Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for c...
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Numerical methods
A rigorous and comprehensive introduction to numerical analysisNumerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing...
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Optimization algorithms on matrix manifolds
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis ...
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Optimization and learning via stochastic gradient search
An introduction to gradient-based stochastic optimization that integrates theory and implementationThis book explains gradient-based stochastic optimization, exploiting the methodologies of stochastic approximation and gradient estimation. Although the approach is theoretical, the book emphasizes...
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Pde control of string-actuated motion
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 system...
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Phase transitions
Phase transitions--changes between different states of organization in a complex system--have long helped to explain physics concepts, such as why water freezes into a solid or boils to become a gas. How might phase transitions shed light on important problems in biological and ecological complex...
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Probability, markov chains, queues, and simulation
Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to grad...
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Quaternions and rotation sequences
Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applicat...
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Robust optimization
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. Written by the principal developers o...
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Steady aircraft flight and performance
This undergraduate textbook offers a unique introduction to steady flight and performance for fixed-wing aircraft from a twenty-first-century flight systems perspective. Emphasizing the interplay between mathematics and engineering, it fully explains the fundamentals of aircraft flight and develo...
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The delicate art of brute force
Using everyday computational power to tackle complex—and seemingly unsolvable—math problemsConfronted by a math problem of seemingly impenetrable difficulty, what can you do? In The Delicate Art of Brute Force, Paul Nahin shows how even if you can’t solve such a problem, you can still get an answ...
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The fascinating world of graph theory
The history, formulas, and most famous puzzles of graph theoryGraph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph ...
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The football
An illustration-packed dive into the geometry, engineering, and physics of soccer ballsThe Football takes readers on an entertaining and fact-filled exploration of the mathematical secrets of the most popular spherical object on the planet. The football is familiar to billions of fans across the ...
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The mathematical radio
How a modern radio works, told through mathematics, history, and selected puzzlesThe modern radio is a wonder, and behind that magic is mathematics. In The Mathematical Radio, Paul Nahin explains how radios work, deploying mathematics and historical discussion, accompanied by a steady stream of i...
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The mathematics of secrets
Explaining the mathematics of cryptographyThe Mathematics of Secrets takes readers on a fascinating tour of the mathematics behind cryptography—the science of sending secret messages. Using a wide range of historical anecdotes and real-world examples, Joshua Holden shows how mathematical principl...
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Topics in mathematical modeling
Topics in Mathematical Modeling is an introductory textbook on mathematical modeling. The book teaches how simple mathematics can help formulate and solve real problems of current research interest in a wide range of fields, including biology, ecology, computer science, geophysics, engineering, a...
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Totally nonnegative matrices
Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, histo...
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Unlocking justice
How we can challenge social injustice—with data and humanityThe American legal system does not offer equal justice to all; we can see obvious racial disparities in sentencing, policing, and incarceration. In Unlocking Justice, Chad Topaz offers a concrete way forward, demonstrating how a candid d...
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Validated numerics
A comprehensive, self-contained primer on validated numericsThis textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmac...
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Viewpoints
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of es...
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X and the city
What mathematical modeling uncovers about life in the cityX and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaur...
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