Other Titles in Applied Mathematics – serie

Since its original appearance in 1997, Numerical Linear Algebra has been a leading textbook in its field, used in universities around the world. It is noted for its 40 lecture-sized short chapters and its clear and inviting style. It is reissued here with a new foreword by James Nagy and a new afterword by Yuji Nakatsukasa about subsequent developments.

This second edition has been almost completely rewritten to create a textbook designed so instructors can determine the degree of rigor and flexible enough for a one- or two-semester course. The author achieves this by increasing the level of sophistication as the text proceeds from traditional first principles in the early chapters to theory and applications in the later ones, and by ensuring that material at any point is not dependent on subsequent developments. While theorems and proofs are highlighted, the emphasis is on applications.The author provides carefully constructed exercises ranging from easy to moderately challenging to difficult, many of which condition students for topics that follow. An accompanying book, Matrix Analysis and Applied Linear Algebra, Second Edition, Study and Solutions Guide, contains complete solutions and discussions of each exercise; and historical remarks that focus on the personalities of the individuals who created and contributed to the subject's development.This book is designed for use in either a one- or two-term linear algebra course. It can also serve as a reference to anyone who needs to use or apply linear algebra.

Jobs using mathematics, statistics, and operations research are projected to grow by almost 30% over the next decade. BIG Jobs Guide helps job seekers at every stage of their careers in these fields explore opportunities in business, industry, and government (BIG). Written in a conversational and practical tone, BIG Jobs Guide offers insight on topics such as: What skills can I offer employers? How do I write a high-impact resumé? Where can I find a rewarding internship? What kinds of jobs are out there for me? The Guide also offers insights to advisors and mentors on topics such as how departments can help students get BIG jobs and how faculty members and internship mentors can build institutional relationships.Whether you’re an undergraduate or graduate student or a job seeker in applied mathematics, statistics, computer science, or operations research, this hands-on book will help you reach your goal, whether landing an internship, getting your first job or transitioning to a new one.

In just over 100 pages, this book provides basic, essential knowledge of some of the tools of real analysis: the Hardy–Littlewood maximal operator, the Calderón–Zygmund theory, the Littlewood–Paley theory, interpolation of spaces and operators, and the basics of H1 and BMO spaces. This concise text offers brief proofs and exercises of various difficulties designed to challenge and engage students. An Introduction to Singular Integrals is meant to give first-year graduate students in Fourier analysis and partial differential equations an introduction to harmonic analysis. While some background material is included in the appendices, readers should have a basic knowledge of functional analysis, some acquaintance with measure and integration theory, and familiarity with the Fourier transform in Euclidean spaces.

This textbook presents a special solution of underdetermined linear systems where the number of nonzero entries in the solution is very small compared to the total number of entries. This is called sparse solution. As underdetermined linear systems can be very different, the authors explain how to compute a sparse solution by many approaches.Sparse Solutions of Underdetermined Linear Systems:Contains 72 algorithms for finding sparse solutions of underdetermined linear systems and their applications for matrix completion, graph clustering, and phase retrieval.Provides a detailed explanation of these algorithms including derivations and convergence analysis.Includes exercises for each chapter to help the reader understand the material.This textbook is appropriate for graduate students in math and applied math, computer science, statistics, data science, and engineering. Advisors and postdocs will also find the book of interest.It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

Expositions of quantitative methods and algorithms for biological data tend to be scattered through the technical literature, often across different fields, and are thus awkward to assimilate. This book documents one example of this: the relationship between the cell biology idea of metabolic networks and the mathematical idea of polyhedral cones. Such cones can be used to describe the set of steady-state admissible fluxes through metabolic networks, and consequently have become important constructs in the field of microbiology.Via convex cone concepts, fundamental objects called elementary flux modes (EFMs) can be described mathematically. The fundamental algorithm of this relationship is the double description method, which has an extended history in the field of computational geometry. This monograph addresses its relatively recent use in the context of cellular metabolism. Metabolic Networks, Elementary Flux Modes, and Polyhedral Cones:Addresses important topics in the mathematical description of metabolic activity that have not previously appeared in unified form.Introduces a central topic of mathematical systems biology in a manner accessible to nonmathematicians with some mathematical and computational experience. Presents a careful study of the double description method, a fundamental algorithm of computational geometry, in the context of metabolic analysis.The core audience for this book includes mathematicians, engineers, and biologists interested in cell metabolism. Computational geometers will also find it of interest.

Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient. The style is friendly and approachable and cartoon characters guide the way.Inside this book, readers will finddetailed descriptions of algorithms,implementations in Julia that illustrate concepts and allow readers to explore methods on their own, andillustrations and graphics that emphasize core concepts and demonstrate algorithms. Numerical Linear Algebra with Julia is a textbook for undergraduate and graduate students. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. The book may also serve as a reference for researchers in various fields such as computational engineering, statistics, data-science, and machine learning, who depend on numerical solvers in linear algebra.

Partial differential equations (PDEs) are the main tool to describe spatially and temporally extended systems in nature. PDEs usually come with parameters, and the study of the parameter dependence of their solutions is an important task. Letting one parameter vary typically yields a branch of solutions, and at special parameter values, new branches may bifurcate.Numerical Continuation and Bifurcation in Nonlinear PDEs:Presents hands-on approach to numerical continuation and bifurcation for nonlinear PDEs, in 1D, 2D and 3D.,Provides a concise but sound review of analytical background and numerical methods.Explains the use of the free MATLAB package pde2path via a large variety of examples with ready to use code.Contains demo codes that can be easily adapted to the reader's given problem.This book will be of interest to applied mathematicians and scientists from physics, chemistry, biology, and economics interested in the numerical solution of nonlinear PDEs, particularly the parameter dependence of solutions. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

Matrix Analysis and Computations introduces the basics of matrix analysis and presents representative methods and their corresponding theories in matrix computations. In this textbook, readers will find:The matrix theory necessary for direct and iterative methods for solving systems of linear equations.Systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods.Current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems.Exercises at the end of each chapter for applying learned methods.This book is intended for graduate students, researchers, and engineers interested in matrix analysis and matrix computations. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

This self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, Fourier transform, Hilbert transform, and Calderon-Zygmund singular integrals. An ideal introduction to more advanced texts, the book complements Ciarlet's Linear and Nonlinear Functional Analysis with Applications (SIAM), where the titular topics were not treated. Pedagogical features such as detailed theorems and 93 problems make the book ideal for a one-semester first-year graduate course or for self-study.The book is intended for advanced undergraduates and first-year graduate students and researchers. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory

Based on a master's program course at the University of Southern California, the main goal of Mathematics and Tools for Financial Engineering is to train students to use mathematical and engineering tools to understand and solve financial problems. The book contains numerous examples and problems and is divided into two parts:Part I covers mathematical preliminaries (set theory, linear algebra, sequences and series, real functions and analysis, numerical approximations and computations, basic optimization theory, and stochastic processes).Part II addresses financial topics, ranging from low- to high-risk investments.Mathematics and Tools for Financial Engineering is intended for senior undergraduate or graduate students in finance or financial engineering. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. Readers with no prior knowledge in finance can use the book to learn about various mathematical theories and tools.

Fit for students just starting to build a background in mathematics, this textbook provides an introduction to numerical methods for linear algebra problems.Introduction to Numerical Linear Algebrais ideal for a flipped classroom, as it provides detailed explanations that allow students to read on their own and instructors to go beyond lecturing, assumes that the reader has taken a course on linear algebra, but reviews background as needed, andcovers several topics not commonly addressed in related introductory books, including diffusion, a toy model of computed tomography, global positioning systems, the use of eigenvalues in analyzing stability of equilibria, a detailed derivation and careful motivation of the QR method for eigenvalues starting from power iteration, a discussion of the use of the SVD for assigning grades, and multigrid methods.This textbook is appropriate for undergraduate and beginning graduate students in mathematics and related fields. It can be used in the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory

Building on the authors' many years of experience running creativity workshops, How to Be Creative: A Practical Guide for the Mathematical Sciences:Gives a six-step process for generating great ideas that can be used by individuals or groups.Provides examples demonstrating how these concepts have been or might be used in practice in the mathematical sciences.Presents seven cases of tried and tested briefs that can be used at creativity workshops.With mathematically oriented models, this book is for anyone in the mathematical sciences who wants to be more creative or who wishes to train others in creativity.

Collecting a set of classical and emerging methods that otherwise would not be available in a single treatment, Foundations of Computational Imaging: A Model-Based Approach is the first book to define a common foundation for the mathematical and statistical methods used in computational imaging. The book is designed to bring together an eclectic group of researchers with a wide variety of applications and disciplines including applied math, physics, chemistry, optics, and signal processing, to address a collection of problems that can benefit from a common set of methods. Inside, readers will find:Basic techniques of model-based image processing.A comprehensive treatment of Bayesian and regularized image reconstruction methods.An integrated treatment of advanced reconstruction techniques such as majorization, constrained optimization, ADMM, and Plug-and-Play methods for model integration.Foundations of Computational Imaging can be used in courses on Model-Based or Computational Imaging, Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. It is also for researchers or practitioners in medical imaging, scientific imaging, commercial imaging, or industrial imaging.

This expansive volume describes the history of numerical methods proposed to solve linear algebra problems,, from antiquity to the present day. The authors focus on methods for solving linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of the main important contributors to the field.A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, and to applied mathematiciansas well as to and historians of mathematics as well.

In recent years, there has been an explosion of interest in network-based modeling in many branches of science. This book synthesizes some of the common features of many such models, providing a general framework analogous to the modern theory of nonlinear dynamical systems. How networks lead to behavior not typical in a general dynamical system and how the architecture and symmetry of the network influence this behavior are the book's main themes.Dynamics and Bifurcation in Networks: Theory and Applications of Coupled Differential Equations is the first book to describe the formalism for network dynamics developed over the past 20 years. In it, the authors introduce a definition of a network and the associated class of "admissible" ordinary differential equations, in terms of a directed graph whose nodes represent component dynamical systems and whose arrows represent couplings between these systems. They also develop connections between network architecture and the typical dynamics and bifurcations of these equations and discuss applications of this formalism to various areas of science, including gene regulatory networks, animal locomotion, decision-making, homeostasis, binocular rivalry, and visual illusions.This book will be of interest to scientific researchers in any area that uses network models, which includes many parts of biology, physics, chemistry, computer science, electrical and electronic engineering, psychology, and sociology.

This second edition has been almost completely rewritten to create a textbook designed to provide flexibility for nearly any desired degree of rigor and depth of coverage. This is achieved with a linear development ensuring that material at any point is not dependent on subsequent developments and by means of graduated levels of sophistication. The text moves from traditional first principles in early chapters to deeper topics involving both theory and applications in later chapters. This allows for a traditional single-term course based on roughly half of the text without having to refer to more advanced topics while the later portion of the book facilitates a seamless two-term course covering the range of theory and applications generally reserved for discussions beyond fundamentals.Rigor is present throughout, but the level is adaptable because all major theorems have ample accompanying discussions and illustrative examples designed to convince readers and students of the validity of a result without a deep dive into the proof. Moreover, there is an expanded emphasis on both the depth and breadth of applications that are designed to illuminate the utility of the subject across broad areas of science and engineering. At major junctures there are photos and historical remarks concerning the personalities who created and contributed to the subject's development. Throughout there are carefully constructed exercises ranging from easy to moderately challenging to difficult, many of which condition students for topics that follow. Matrix Analysis and Applied Linear Algebra, Second Edition, Study and Solutions Guide contains discussions of each exercise that are designed to guide the development as one moves through the subject.

This text presents a unique treatment of network control systems. Drawing from fundamental principles of dynamical systems theory and dynamical thermodynamics, the authors develop a continuous-time, discrete-time, and hybrid dynamical system and control framework for linear and nonlinear large-scale network systems. The proposed framework extends the concepts of energy, entropy, and temperature to undirected and directed information networks. Continuous-time, discrete-time, and hybrid thermodynamic principles are used to design distributed control protocol algorithms for static and dynamic networked systems in the face of system uncertainty, exogenous disturbances, imperfect system network communication, and time delays.Network Information Systems: A Dynamical Systems Approach is written for applied mathematicians, dynamical systems theorists, control theorists, and engineers. Researchers and graduate students in a variety of fields who seek a fundamental understanding of the rich behavior of controlled large-scale network systems will also find this book useful.This book can be used for a first course on control design of large-scale network systems, such as control protocols for network systems, network information systems, a dynamical systems approach to network systems, and network thermodynamic systems. The prerequisites are a first course in nonlinear systems theory and a first course in advanced (multivariable) calculus.

Among the many branches of applied mathematics, options pricing theory occupies a unique position: it utilizes a wide range of advanced mathematical concepts, making it appealing to mathematicians, and it is regularly applied at financial institutions, making it indispensable to practitioners. The emergence of artificial intelligence in the financial industry has led to further interest in mathematical finance and has increased the demand for literature on this subject that is accessible to a large audience.This book presents a self-contained introduction to options pricing theory and includes a complete discussion of the required concepts in finance and probability theory; an introduction to basic models, emphasizing both critical thinking and practical applications; and over 200 exercises, several Python codes for the analysis and application of the options pricing models, and numerical projects intended to help close the gap between theory and practice. A First Course in Options Pricing Theory is suitable for an advanced undergraduate course on financial mathematics and options pricing theory in engineering, computer science, and applied mathematics programs. The reader is assumed to be familiar with the standard material in calculus and linear algebra. Stochastic calculus is not used in the book.

Set-valued, convex, and nonsmooth analysis are relatively modern branches of mathematical analysis and increasingly relevant in current control theory and control engineering literature. The first book of this scope and at this level, Set-Valued, Convex, and Nonsmooth Analysis in Dynamics and Control serves as a broad introduction to the field and to applications in dynamical and control systems. Continuous-time and discrete-time multivalued dynamics, modeled by differential and difference inclusions, are treated next to one another and often interchangeably.

This new, considerably expanded edition covers the fundamentals of linear and nonlinear functional analysis, including distribution theory, harmonic analysis, differential geometry, calculus of variations, and degree theory. Numerous applications are included, especially to linear and nonlinear partial differential equations and to numerical analysis. All the basic theorems are provided with complete and detailed proofs.The author has added more than 450 pages of new material and more than 210 problems. The solutions to all of the problems will be made available on an accompanying website. Two entirely new chapters, one on locally convex spaces and distribution theory and the other on the Fourier transform and Calderón–Zygmund singular integral operators, have also been added. In addition, the chapter on the “great theorems” of nonlinear functional analysis has been enlarged and split into two chapters, one on the calculus of variations and the other on Brouwer’s theorem, Brouwer’s degree, and Leray–Schauder’s degree.AudienceIdeal for both teaching and self-study, Linear and Nonlinear Functional Analysis with Applications, Second Edition is intended for advanced undergraduate and graduate students in mathematics, university professors, and researchers. It is also an ideal basis for several courses on linear or nonlinear functional analysis.

This book provides an easily accessible, yet detailed, discussion of computer arithmetic as mandated by the IEEE 754 floating point standard, arguably the most important standard in the computer industry. The result of an unprecedented cooperation between academic computer scientists and industry, the standard is supported by virtually every modern computer. Although the basic principles of IEEE floating point arithmetic have remained largely unchanged since the first edition of this book was published in 2001, the technology that supports it has changed enormously.Every chapter has been extensively rewritten, and two new chapters have been added: one on computations with higher precision than that mandated by the standard, needed for a variety of scientific applications, and one on computations with lower precision than was ever contemplated by those who wrote the standard, driven by the massive computational demands of machine learning.The second edition of Numerical Computing with IEEE Floating Point Arithmetic includes many technical details not readily available elsewhere, along with many new exercises. It explores the rationale for floating point representation, correctly rounded arithmetic, exception handling, and support for the standard provided by floating point microprocessors and programming languages. Key concepts such as cancellation, conditioning and stability are also discussed. The book emphasizes historical development, from the early history of computing, through the 2008 and 2019 revisions of the floating-point standard, to the latest advances in microprocessor support. It also includes a previously unpublished letter by Donald E. Knuth on the value of gradual underflow, a key requirement of the standard.AudienceThis book should be accessible to any reader with an interest in computers and mathematics, including students at all levels. Some basic knowledge of calculus and programming is assumed in the second half. There is enough variety of content that all but the most expert readers will find something of interest.

This is the only book devoted exclusively to Hessenberg and tridiagonal matrices. Hessenberg matrices are involved in Krylov methods for solving linear systems or computing eigenvalues and eigenvectors, in the QR algorithm for computing eigenvalues, and in many other areas of scientific computing (for instance, control theory). Matrices that are both upper and lower Hessenberg are tridiagonal. Their entries are zero except for the main diagonal and the subdiagonal and updiagonal next to it.Hessenberg and Tridiagonal Matrices: Theory and Examples presents known and new results; describes the theoretical properties of the matrices, their determinants, LU factorizations, inverses, and eigenvalues; illustrates the theoretical properties with applications and examples as well as numerical experiments; and considers unitary Hessenberg matrices, inverse eigenvalue problems, and Toeplitz tridiagonal matrices.AudienceThis book is intended for applied mathematicians, especially those interested in numerical linear algebra, and it will also be of interest to physicists and engineers.