Mathematics from Manuscript to Print, 1300-1600


Book Description

Eighteen essays under four topical heads (Italian and Provincal mathematics; Nicholas Chuquet and French mathematics; Mathematics in the 16th century; Mathematics and its ramifications) comprise the attractively produced proceedings of a conference which took place at Oxford in September, 1984. Valuable as a contribution to the scholarly literature on the history of mathematics, and quite a number of the essays would interest general scientific readers. (NW) Annotation copyrighted by Book News, Inc., Portland, OR




Rewriting the History of School Mathematics in North America 1607-1861


Book Description

The focus of this book is the fundamental influence of the cyphering tradition on mathematics education in North American colleges, schools, and apprenticeship training classes between 1607 and 1861. It is the first book on the history of North American mathematics education to be written from that perspective. The principal data source is a set of 207 handwritten cyphering books that have never previously been subjected to careful historical analysis.




Medieval Latin


Book Description

Organized with the assistance of an international advisory committee of medievalists from several disciplines, Medieval Latin: An Introduction and Bibliographical Guide is a new standard guide to the Latin language and literature of the period from c. A.D. 200 to 1500. It promises to be indispensable as a handbook in university courses in Medieval Latin and as a point of departure for the study of Latin texts and documents in any of the fields of medieval studies. Comprehensive in scope, the guide provides introductions to, and bibliographic orientations in, all the main areas of Medieval Latin language, literature, and scholarship. Part One consists of an introduction and sizable listing of general print and electronic reference and research tools. Part Two focuses on issues of language, with introductions to such topics as Biblical and Christian Latin, and Medieval Latin pronunciation, orthography, morphology and syntax, word formation and lexicography, metrics, prose styles, and so on. There are chapters on the Latin used in administration, law, music, commerce, the liturgy, theology and philosophy, science and technology, and daily life. Part Three offers a systematic overview of Medieval Latin literature, with introductions to a wide range of genres and to translations from and into Latin. Each chapter concludes with a bibliography of fundamental works--texts, lexica, studies, and research aids. This guide satisfies a long-standing need for a reference tool in English that focuses on medieval latinity in all its specialized aspects. It will be welcomed by students, teachers, professional latinists, medievalists, humanists, and general readers interested in the role of Latin as the learned lingua franca of western Europe. It may also prove valuable to reference librarians assembling collections concerned with Latin authors and texts of the postclassical period. ABOUT THE EDITORS F. A. C. Mantello is professor of Medieval Latin at The Catholic University of America. A. G. Rigg is professor of English and medieval studies and chairman of the Medieval Latin Committee at the University of Toronto's Centre for Medieval Studies. PRASIE FOR THE BOOK "This extraordinary volume, joint effort of dozens of scholars in eight countries, will be in constant use for research, for advising students and designing courses, and for answering the queries of nonmedievalist colleagues. . . . Medieval Latin provides a foundation for advances in research and teaching on a wide front. . . . Though Mantello and Rigg's Medieval Latin is a superb reference volume, I recommend that it also be read from beginning to end--in small increments, of course. The rewards will be sheaves of notes and an immensely enriched appreciation of Medieval Latin and its literature."--Janet M. Martin, Princeton University, Speculum "A remarkable achievement, and no one interested in medieval Latin can afford to be without it."--Journal of Ecclesiastical History "Everywhere there is clarity, conclusion, judicious illustration, and careful selection of what is central. This guide is a major achievement and will serve Medieval Latin studies extremely well for the foreseeable future."--The Classical Review




The History of Mathematics


Book Description

Praise for the Second Edition "An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential." —CHOICE This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include: Material arranged in a chronological and cultural context Specific parts of the history of mathematics presented as individual lessons New and revised exercises ranging between technical, factual, and integrative Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book) An emphasis on geography, culture, and mathematics In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.




Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition


Book Description

Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.




Mathematical Discourse


Book Description

An examination of mathematical discourse from the perspective of Michael Halliday's social semiotic theory.




The Art of Conjecturing, Together with Letter to a Friend on Sets in Court Tennis


Book Description

"Part I reprints and reworks Huygens's On Reckoning in Games of Chance. Part II offers a thorough treatment of the mathematics of combinations and permutations, including the numbers since known as "Bernoulli numbers." In Part III, Bernoulli solves more complicated problems of games of chance using that mathematics. In the final part, Bernoulli's crowning achievement in mathematical probability becomes manifest he applies the mathematics of games of chance to the problems of epistemic probability in civil, moral, and economic matters, proving what we now know as the weak law of large numbers."




The Development of Mathematics in Medieval Europe


Book Description

The Development of Mathematics in Medieval Europe complements the previous collection of articles by Menso Folkerts, Essays on Early Medieval Mathematics, and deals with the development of mathematics in Europe from the 12th century to about 1500. In the 12th century European learning was greatly transformed by translations from Arabic into Latin. Such translations in the field of mathematics and their influence are here described and analysed, notably al-Khwarizmi's "Arithmetic" -- through which Europe became acquainted with the Hindu-Arabic numerals -- and Euclid's "Elements". Five articles are dedicated to Johannes Regiomontanus, perhaps the most original mathematician of the 15th century, and to his discoveries in trigonometry, algebra and other fields. The knowledge and application of Euclid's "Elements" in 13th- and 15th-century Italy are discussed in three studies, while the last article treats the development of algebra in South Germany around 1500, where much of the modern symbolism used in algebra was developed.




From Discrete to Continuous


Book Description

In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways. This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.




The Growth of Mathematical Knowledge


Book Description

Mathematics has stood as a bridge between the Humanities and the Sciences since the days of classical antiquity. For Plato, mathematics was evidence of Being in the midst of Becoming, garden variety evidence apparent even to small children and the unphilosophical, and therefore of the highest educational significance. In the great central similes of The Republic it is the touchstone ofintelligibility for discourse, and in the Timaeus it provides in an oddly literal sense the framework of nature, insuring the intelligibility ofthe material world. For Descartes, mathematical ideas had a clarity and distinctness akin to the idea of God, as the fifth of the Meditations makes especially clear. Cartesian mathematicals are constructions as well as objects envisioned by the soul; in the Principles, the work ofthe physicist who provides a quantified account ofthe machines of nature hovers between description and constitution. For Kant, mathematics reveals the possibility of universal and necessary knowledge that is neither the logical unpacking ofconcepts nor the record of perceptual experience. In the Critique ofPure Reason, mathematics is one of the transcendental instruments the human mind uses to apprehend nature, and by apprehending to construct it under the universal and necessary lawsofNewtonian mechanics.