Nicholas J. Higham

This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Princeton Companion to Applied Mathematics

M. J. Ryan

Presents the Anglo-Saxon period of English history from the fifth century up to the late eleventh century, covering such events as the spread of Christianity, the invasions of the Vikings, the composition of Beowulf, and the Battle of Hastings.

The Anglo-Saxon World

The Princeton Companion to Applied Mathematics

A prominent scholar explores King Arthur’s historical development, proposing that he began as a fictional character developed in the ninth century According to legend, King Arthur saved Britain from the Saxons and reigned over it gloriously sometime around A.D. 500. Whether or not there was a “real” King Arthur has all too often been neglected by scholars; most period specialists today declare themselves agnostic on this important matter. In this erudite volume, Nick Higham sets out to solve the puzzle, drawing on his original research and expertise to determine precisely when, and why, the legend began. Higham surveys all the major attempts to prove the origins of Arthur, weighing up and debunking hitherto claimed connections with classical Greece, Roman Dalmatia, Sarmatia, and the Caucasus. He then explores Arthur’s emergence in Wales—up to his rise to fame at the hands of Geoffrey of Monmouth. Certain to arouse heated debate among those committed to defending any particular Arthur, Higham’s book is an essential study for anyone seeking to understand how Arthur’s story began.

The Making of the Legend

King Arthur

This handy volume, enlivened by anecdotes, unusual paper titles, and humorous quotations, provides even more information on the issues you will face when writing a technical paper or talk, from choosing the right journal in which to publish to handling your references. Its overview of the entire publication process is invaluable for anyone hoping to publish in a technical journal.

Handbook of Writing for the Mathematical Sciences

Handbook of Writing for the Mathematical Sciences provides advice on all aspects of scientific writing, with a particular focus on writing mathematics. Its readable style and handy format, coupled with an extensive bibliography and comprehensive index, make it useful for everyone from undergraduates to seasoned professionals. This third edition revises, updates, and expands the best-selling second edition to reflect modern writing and publishing practices and builds on the author's extensive experience in writing and speaking about mathematics. Some of its key features include coverage of fundamentals of writing, including English usage, revising a draft, and writing when your first language is not English; thorough treatment of mathematical writing, including how to choose notation, how to choose between words and symbols, and how to format equations; and many tips for exploiting LaTeX and BibTeX. Higham also provides advice on how to write and publish a paper, covering the entire publication process, and includes anecdotes, quotes, and unusual facts that enliven the presentation. The new edition has been reorganized to make the book easier to use for reference; treats modern developments in publishing such as open access, DOIs, and ORCID; and contains more on poster design, including e-posters and the poster blitz. The new edition also includes five new chapters on the following topics: · workflow covering text editors, markup languages, version control, and much more; · the principles of indexing and how to prepare an index in LaTeX; · reviewing a paper, book proposal, or book; · writing a book, including advice on choosing a publisher and LaTeX tips particular to books; and · writing a blog post.

Handbook of Writing for the Mathematical Sciences, Third Edition

Nick Higham follows up his successful HWMS volume with this much-anticipated second edition.

A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.

Theory and Computation

Functions of Matrices

Accuracy and Stability of Numerical Algorithms gives a thorough, up-to-date treatment of the behavior of numerical algorithms in finite precision arithmetic. It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. This second edition expands and updates the coverage of the first edition (1996) and includes numerous improvements to the original material. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures.

Nicholas J. Higham

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