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This book is about writing in the professional mathematical environment. While the book is nominally about writing, it's also about how to function in the mathematical profession. In many ways, this text complements Krantz's previous bestseller, How to Teach Mathematics. Those who are familiar with Krantz's writing will recognize his lively, inimitable style. In this volume, he addresses these nuts-and-bolts issues: Syntax, grammar, structure, and style Mathematical exposition Use of the computer and TeX E-mail etiquette All aspects of publishing a journal article Krantz's frank and straightforward approach makes this book particularly suitable as a textbook. He does not avoid difficult topics. His intent is to demonstrate to the reader how to successfully operate within the profession. He outlines how to write grant proposals that are persuasive and compelling, how to write a letter of recommendation describing the research abilities of a candidate for promotion or tenure, and what a dean is looking for in a letter of recommendation. He further addresses some basic issues such as writing a book proposal to a publisher or applying for a job. Readers will find in reading this text that Krantz has produced a quality work which makes evident the power and significance of writing in the mathematics profession.

This classic guide contains four essays on writing mathematical books and papers at the research level and at the level of graduate texts. The authors are all well known for their writing skills, as well as their mathematical accomplishments. The first essay, by Steenrod, discusses writing books, either monographs or textbooks. He gives both general and specific advice, getting into such details as the need for a good introduction. The longest essay is by Halmos, and contains many of the pieces of his advice that are repeated even today: In order to say something well you must have something to say; write for someone; think about the alphabet. Halmos's advice is systematic and practical. Schiffer addresses the issue by examining four types of mathematical writing: research paper, monograph, survey, and textbook, and gives advice for each form of exposition. Dieudonne's contribution is mostly a commentary on the earlier essays, with clear statements of where he disagrees with his coauthors. The advice in this small book will be useful to mathematicians at all levels.

The subject of mathematical writing has been infused with life once again by Nick Higham as he follows up his successful HWMS volume with this much-anticipated second edition. As is Higham's style, the material is enlivened by anecdotes, unusual paper titles, and humorous quotations. This handy new volume 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. The original book has been completely revised, making use of feedback from readers as well as Higham's own large file of ideas based on his experiences in reading, writing, editing, examining, and supervising theses.

This iHandbook/i explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practice it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematicalpractitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence isdrawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of themathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, thecontributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood.The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging thepast three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstreamhistory of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.

"[Cheng] does a great service by showing us non-mathematician schlubs how real mathematical creativity works." --Wall Street Journal Whether pondering why some numbers are uncountable, or why infinity + 1 is not the same as 1 + infinity, we've all asked the same question: What is infinity? In Beyond Infinity, Eugenia Cheng takes us on a staggering journey from elemental math to its loftiest abstractions. Along the way she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how this little symbol holds the biggest idea of all.