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This new text from Jöran Friberg, the leading expert on Babylonian mathematics, presents 130 previously unpublished mathematical clay tablets from the Norwegian Schøyen collection, and provides a synthesis of the author's most important work. Through a close study of these tablets, Friberg has made numerous amazing discoveries, including the first known examples of pre-Classical labyrinths and mazes, a new understanding of the famous table text Plimpton 322, and new evidence of Babylonian familiarity with sophisticated mathematical ideas and objects, such as the three-dimensional Pythagorean equation and the icosahedron. In order to make the text accessible to the largest possible audience, the author has included an introductory chapter entitled, "How to get a better understanding of mathematical cuneiform texts." Throughout the text he avoids anachronisms and makes every effort to teach the reader to do the same. The approach in this book is inherently pedagogical, as Friberg illustrates all the steps of the process of interpretation and clearly explains the mathematical ideas, including terminology, metrological systems, and methods of calculation. Drawings and color photos of a large selection of tablets are also included. Particularly beautiful hand copies of the most complicated texts were made by Farouk Al-Rawi, professor of Ancient Languages and Archaeology at Baghdad University. While the book is reader-friendly, it remains as detailed and exhaustive as possible. It is the most comprehensive treatment of a set of Babylonian mathematical texts ever published and will open up this subject to a new generation of students, mathematicians, and historians of science. Jöran Friberg is Professor Emeritus of Mathematics at Chalmers University of Technology, Sweden. He has recently published the book Unexpected Links Between Egyptian and Babylonian Mathematics (World Scientific 2005), and its sequel Amazing Traces of a Babylonian Origin in Greek Mathematics (World Scientific 2007).

Mathematics, Babylonian. --- Mathematics, Ancient. --- Ancient mathematics --- Mathematics. --- History. --- History of Mathematical Sciences. --- Annals --- Auxiliary sciences of history --- Math --- Science --- Schøyen, Martin --- Private collections.

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In the city republics of Renaissance Italy, it was a common practice among the merchant class to send sons for a two-year course of study at an "abbacus school", where they learned practical, mostly commercial mathematics, known as abbaco. From this school institution, several hundred manuscripts survive, all in Italian, often containing not only what the masters needed in their teaching but also algebra or other advanced mathematical material. A signal feature of the book by Jens Høyrup is the first translation of one of these abbacus manuscripts into English. The abbacus books have long been supposed to be reduced versions of Leonardo Fibonacci’s Liber abbaci. Analysis of early abbacus books, not least of the first specimen treating of algebra – Jacopo da Firenze’s Tractatus algorismi from 1307 – shows instead that abbacus mathematics was an exponentof a more widespread culture of commercial mathematics, already known by Fibonacci, and probably flourishing in Provence and/or Catalonia before it reached Italy. Abbacus algebra – eventually the main inspiration for the algebraic breakthrough of the 16th and 17th centuries – was inspired from a Romance-speaking region outside Italy, most likely located in the Provençal-Catalan area, and ultimately from a similar practitioners’ level of Arabic mathematics. The book contains, along with the English translation, an edition of Jacopo’s Tractatus and a commentary analyzing Jacopo’s mathematics and its links to Provençal, Catalan, Arabic, Indian and Latin medieval mathematics. It will provide historians of mathematics and mathematics teachers with a new perspective on a period and on processes which eventually reshaped the whole mathematical enterprise in the 17th century.

Algebra --- History. --- Jacopo, --- Mathematics --- Mathematical analysis --- Mathematics. --- History of Mathematical Sciences. --- Applications of Mathematics. --- Math --- Science --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Annals --- Auxiliary sciences of history

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Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students in mathematics but will also appeal to the reader with a general interest in the history of mathematics. Emphasis is placed on understanding the historical significance of the new mathematics: Why was it done? How - if at all - was it appreciated? What new questions did it generate? Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker's equations) and their role in resolving a paradox in the theory of duality; to Riemann's work on differential geometry; and to Beltrami's role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry, as exemplified by Klein's Erlangen Program, rose to prominence, and looks at Poincaré's ideas about non-Euclidean geometry and their physical and philosophical significance. It then concludes with discussions on geometry and formalism, examining the Italian contribution and Hilbert's Foundations of Geometry; geometry and physics, with a look at some of Einstein's ideas; and geometry and truth. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for. The Springer Undergraduate Mathematics Series (SUMS) is designed for undergraduates in the mathematical sciences. From core foundational material to final year topics, SUMS books take a fresh and modern approach and are ideal for self-study or for a one- or two-semester course. Each book includes numerous examples, problems and fully-worked examples.

Geometry --- Mathematics --- geschiedenis --- wiskunde --- geometrie --- Mathematics. --- Geometry. --- History. --- History of Mathematical Sciences. --- Math --- Science --- Euclid's Elements --- Annals --- Auxiliary sciences of history

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Revisits successive periods in the reception of the Disquisitiones as it studies which parts were taken up and when, which themes were further explored. This work also focuses on how specific mathematicians reacted to Gauss' book: Dirichlet and Hermite, Kummer and Genocchi, Dedekind and Zolotarev, Dickson and Emmy Noether, among others.

Number theory. --- Gauss, Carl Friedrich, --- Number study --- Numbers, Theory of --- Algebra --- Algebra. --- Number Theory. --- History of Mathematical Sciences. --- Mathematics --- Mathematical analysis --- Mathematics. --- History. --- Annals --- Auxiliary sciences of history --- Math --- Science

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This monograph describes how the understanding of the geometry behind perspective evolved between the years 1435 and 1800 and how new insights within the mathematical theory of perspective influenced the way the discipline was presented in textbooks. In order to throw light on these issues, the author has chosen to focus on a number of key questions, including: • What were the essential innovations in the mathematical theory of perspective? • Was there any interplay between the developments of the mathematical theory of perspective and other branches of geometry? • What were the driving forces behind working out an advanced mathematical theory of perspective? • Were there regional differences in the mathematical approach to perspective? And if so, how did they relate to local applications of perspective? • How did mathematicians and practitioners of perspective interact? In fact, the last issue is touched upon so often that a considerable part of this book could be seen as a case study of the difficulties in bridging the gap between those with mathematical knowledge and the mathematically untrained practitioners who wish to use this knowledge. The author has based her work on more than 200 books, booklets, and pamphlets on perspective. She starts with the first treatise known to deal with geometrical perspective, Leon Alberti Battista’s De pictura, and ends around 1800, when the theory of mathematical perspective as an independent discipline was absorbed first into descriptive geometry and later into projective geometry. The prominent protagonists are Guidobaldo del Monte, Simon Stevin, Willem ’sGravesande, Brook Taylor, and Johann Heinrich Lambert. As far as data were available, the author has provided brief biographies of all the writers on perspective whose work she studied. The book also contains an extensive bibliography divided into two parts, one for primary sources on perspective, and the second for all other literature. Kirsti Andersen is Associate Professor of History of Science at the University of Aarhus, Denmark. She is the author of Brook Taylor’s Work on Linear Perspective, also published by Springer. .

Perspective. --- Architectural drawing. --- Drawing, Architectural --- Plans --- Architectural design --- Communication in architectural design --- Drawing --- Mechanical drawing --- Architectural perspective --- Linear perspective --- Mechanical perspective --- Optics --- Space (Art) --- Space perception --- Projection --- Proportion (Art) --- Shades and shadows --- Geometry. --- History of Mathematical Sciences. --- Mathematics --- Euclid's Elements --- Mathematics. --- History. --- Annals --- Auxiliary sciences of history --- Math --- Science