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Notes:

• Includes bibliographical references (page 267) and index.
• This lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks–a sort of potato-stamp method–Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as color-reversing patterns, three-color patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you’ll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.

Subjects:

• Symmetry (Mathematics)
• Symmetry (Art)

Requested by Haines, M.

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Notes:

• Includes index.
• The magic of numbers — The magic of algebra — The magic of 9 — The magic of counting — The magic of Fibonacci numbers — The magic of proofs — The magic of geometry — The magic of [symbol for pi] — The magic of trigonometry — The magic of i and e — The magic of calculus — The magic of infinity — Aftermath.
• The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples–from ice cream scoops and poker hands to measuring mountains and making magic squares–this book empowers you to see the beauty, simplicity, and truly magical properties behind those formulas and equations that once left your head spinning. You’ll learn the key ideas of classic areas of mathematics like arithmetic, algebra, geometry, trigonometry, and calculus, but you’ll also have fun fooling around with Fibonacci numbers, investigating infinity, and marveling over mathematical magic tricks that will make you look like a math genius! –Amazon.com.

Subjects:

• Mathematics — Study and teaching.

Requested by Haines, M.

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Notes:

• Includes bibliographical references and index.
• Volume 1. Antiquity to the 1500s — Volume 2. The 1500s to the future.
• Every age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals. Volume I covers architecture from antiquity through Egyptian, Mayan, Greek, Roman, Medieval, Inkan, Gothic and early Renaissance eras and styles. The themes that are covered range from symbolism and proportion to measurement and structural stability. From Europe to Africa, Asia and South America, the chapters span different countries, cultures and practices. Volume II covers architecture from the Late Renaissance era, through Baroque, Ottoman, Enlightenment, Modern and contemporary styles and approaches. Key figures covered in this volume include Palladio, Michelangelo, Borromini, Sinan, Wren, Wright, Le Corbusier, Breuer, Niemeyer and Kahn. Mathematical themes which are considered include linear algebra, tiling and fractals and the geographic span of the volume’s content includes works in the United States of America and Australia, in addition to those in Europe and Asia. –Back covers.

Subjects:

• Architecture — Mathematics — History.
• Architectural design — Mathematics — History.
• History. fast (OCoLC)fst01411628

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Notes:

• Includes bibliographical references.

Subjects:

• Mathematics.
• Art — Mathematics.
• Music — Philosophy and aesthetics.

Requested by Bloomberg, M.

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Part of the series Studies in History and Philosophy of Science volume 36;Studies in history and philosophy of science (Dordrecht, Netherlands) v. 36.
Notes:

• Includes bibliographical references and index.

Subjects:

• String figures.
• Mathematics — Study and teaching — Activity programs.

Requested by Bloomberg, M.

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Notes:

• Revision of: The foundations of mathematics / Ian Stewart and David Tall. — Oxford : Oxford University Press, 1977.
• Includes bibliographical references (pages 383-385) and index.
• Part I. The intuitive background — 1. Mathematical thinking — 2. Number systems — Part II. The beginnings of formalisation — 3. Sets — 4. Relations — 5. Functions — 6. Mathematical logic — 7. Mathematical proof — Part III. The development of axiomatic systems — 8. Natural numbers and proof by induction — 9. Real numbers — 10. Real numbers as a complete ordered field — 11. Complex numbers and beyond — Part IV. Using axiomatic systems — 12. Axiomatic systems, structure theorems, and flexible thinking — 13. Permutations and groups — 14. Cardinal numbers — 15. Infinitesimals — Part V. Strengthening the foundations — 16. Axioms for set theory.

Subjects:

• Mathematics.
• Logic, Symbolic and mathematical.

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Notes:

• A Perigee book.
• Previously published in the UK in 2014 by Virgin Books, an imprint of Ebury Publishing –Title-page verso.
• Includes bibliographical references (pages [245]-266) and index.
• An explanation of the title, and other cyberbole — The quantified selves — The match & the spark — Do algorithms dream of electric laws? — The machine that made art — Predicting the future.
• In The Formula, Luke Dormehl takes readers inside the world of numbers, asking how we came to believe in the all-conquering power of algorithms introducing the mathematicians, artificial intelligence experts and Silicon Valley entrepreneurs who are shaping this brave new world, and ultimately asking how we survive in an era where numbers can sometimes seem to create as many problems as they solve.

Subjects:

• Algorithms — Popular works.
• Algorithms — History.
• History. fast (OCoLC)fst01411628
• Popular works. fast (OCoLC)fst01423846

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Part of the series Anneli Lax new mathematical library 45;Anneli Lax new mathematical library v. 45.
Notes:

• Includes bibliographical references (pages 133-134) and index.
• X marks the spot — Entering the matrix — Sum matrices — Fitting the norm — Go forth and multiply — It’s elementary, my dear Watson — Math to the max — Stretch and shrink — Zombie math : decomposing — What are the chances? — Mining for meaning — Who’s number 1? — End of the line.
• From simulating complex phenomenon on supercomputers to storing the coordinates needed in modern 3D printing, data is a huge and growing part of our world. A major tool to manipulate and study this data is linear algebra. This book introduces concepts of matrix algebra with an emphasis on application, particularly in the fields of computer graphics and data mining. Readers will learn to make an image transparent, compress an image and rotate a 3D wireframe model. In data mining, readers will use linear algebra to read zip codes on envelopes and encrypt sensitive information. The book details methods behind web search, utilized by such companies as Google, and algorithms for sports ranking which have been applied to creating brackets for March Madness and predict outcomes in FIFA World Cup soccer.

Subjects:

• Algebras, Linear.
• Matrices.
• Computer graphics — Mathematics.
• Data mining.

Requested by Haines, M. & Doree, S.

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Part of the series Culture and civilization in the Middle East 44;Culture and civilisation in the Middle East 44.
Notes:

• Includes bibliographical references and index.
• This book follows the development of classical mathematics and the relation between work done in the Arab and Islamic worlds and that undertaken by the likes of Descartes and Fermat. ‘Early modern,’ mathematics is a term widely used to refer to the mathematics which developed in the West during the sixteenth and seventeenth century. For many historians and philosophers this is the watershed which marks a radical departure from ‘classical mathematics,’ to more modern mathematics heralding the arrival of algebra, geometrical algebra, and the mathematics of the continuous. In this book, Roshdi Rashed demonstrates that ‘early modern,’ mathematics is actually far more composite than previously assumed, with each branch having different traceable origins which span the millennium. Going back to the beginning of these parts, the aim of this book is to identify the concepts and practices of key figures in their development, thereby presenting a fuller reality of these mathematics. This book will be of interest to students and scholars specialising in Islamic science and mathematics, as well as to those with an interest in the more general history of science and mathematics and the transmission of ideas and culture — Provided by publisher.
• Introduction: Problems of method: 1. The history of science: between epistemology and history — 2. The transmissions of Greek heritage into Arabic — 3. Reading ancient mathematical texts: the fifth book of Apollonius’s Conics — 4. The founding acts and main contours of Arabic mathematics Part I. I. Algebra. 1. Algebra and its unifying role — 2. Algebra and linguistics: the beginnings of combinatorical analysis — 3. The first classification of curves — 4. Descartes’s Géométrie and the distinction between geometrical and mechanical curves — 5. Descartes’s ovals — 6. Descartes and the infinitely small — 7. Fermat and algebraic geometry Part II. Arithmetic. 1. Euclidean, neo-Pythagorean and Diophantine arithmetics: new methods in number theory — 2. Algorithmic methods — 3. Thäbit ibn Qurra and amicable numbers — 4. Fibonacci and Arabic mathematics — 5. Fibonacci and the Latin extension of Arabic mathematics — 6. Al-Yazdï and the equation — 7. Fermat and the modern beginnings of Diophantine analysis Part II: Geometry. 1. The Archimedeans and problems with infiniteimals — 2. The traditions of the Conics and the beginning of research on projections — 3. The continuous drawing of conic curves and the classification of curves — 4. Thä ibn Qurra on Euclid’s fifth postulate Part III. Application of mathematics: astronomy and optics. 1. The celestial kinematics of Ibn al-Haytham — 2. From the geometry of the gaze to the mathematics of the phenomena of light — Conclusion: The philosophy of mathematics.

Subjects:

• Mathematics — History.
• History. fast (OCoLC)fst01411628

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Notes:

• Includes bibliographical references and index.
• 1. An historical account — 2. Even exponents — 3. Cassels’ relations — 4. Cyclotomic fields — 5. Dirichlet L-series and class number formulas — 6. Higher divisibility theorems — 7. Gauss sums and Stickelberger’s theorem — 8. Mihăilescu’s ideal — 9. The real part of Mihăilescu’s ideal — 10. Cyclotomic units — 11. Selmer group and proof of Catalan’s conjecture — 12. The theorem of Thaine — 13. Baker’s method and Tijdeman’s argument — Appendix A: Number fields — Appendix B: Heights — Appendix C: Commutative rings, modules, semi-simplicity — Appendix D: Group rings and characters — Appendix E: Reduction and torsion of finite G-modules — Appendix F: Radical extensions.
• In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In this book we give a complete and (almost) self-contained exposition of Mihăilescu?s work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume very modest background: a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.

Subjects:

• Consecutive powers (Algebra)
• Problem solving.
• Number theory.
• Mihăilescu, Preda, author.
• Catalan, Eugène Charles, 1814-1894.

Requested by Bloomberg, M.