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Author: Scott B. Guthery
Publisher: Docent Press
ISBN: 1453810579
Category : Mathematics
Languages : en
Pages : 266
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Book Description
The curious property that John Farey observed in one of Henry Goodwyn's tables has enduring pratical and theoretic interest. This book traces the curious property, the mediant, from its initial sighting by Nicolas Chuquet and Charles Haros to its connection to the Riemann hypothesis by Jerome Franel.
Author: Scott B. Guthery
Publisher: Docent Press
ISBN: 1453810579
Category : Mathematics
Languages : en
Pages : 266
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Book Description
The curious property that John Farey observed in one of Henry Goodwyn's tables has enduring pratical and theoretic interest. This book traces the curious property, the mediant, from its initial sighting by Nicolas Chuquet and Charles Haros to its connection to the Riemann hypothesis by Jerome Franel.
Author: Ivars Peterson
Publisher: Macmillan
ISBN: 0805071598
Category : Mathematics
Languages : en
Pages : 273
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Book Description
In the first edition of The Mathematical Tourist, renowned science journalist Ivars Peterson took readers on an unforgettable tour through the sometimes bizarre, but always fascinating, landscape of modern mathematics. Now the journey continues in a new, updated edition that includes all the latest information on mathematical proofs, fractals, prime numbers, and chaos, as well as new material on * the relationship between mathematical knots and DNA * how computers based on quantum logic can significantly speed up the factoring of large composite numbers * the relationship between four-dimensional geometry and physical theories of the nature of matter * the application of cellular automata models to social questions and the peregrinations of virtual ants * a novel mathematical model of quasicrystals based on decagon-shaped tiles Blazing a trail through rows of austere symbols and dense lines of formulae, Peterson explores the central ideas behind the work of professional mathematicians-- how and where their pieces of the mathematical puzzle fit in, the sources of their ideas, their fountains of inspiration, and the images that carry them from one discovery to another.
Author: Jacob P. Murre
Publisher: American Mathematical Soc.
ISBN: 082189434X
Category : Mathematics
Languages : en
Pages : 163
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Book Description
The theory of motives was created by Grothendieck in the 1960s as he searched for a universal cohomology theory for algebraic varieties. The theory of pure motives is well established as far as the construction is concerned. Pure motives are expected to h
Author: Kit Yates
Publisher: Simon and Schuster
ISBN: 1982111887
Category : Mathematics
Languages : en
Pages : 288
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Book Description
"We are all doing math all the time, from the way we communicate with each other to the way we travel, from how we work to how we relax. Many of us are aware of this. But few of us really appreciate the full power of math - the extent to which its influence is not only in every office and every home, but also in every courtroom and hospital ward. In this eye-opening and extraordinary book, Kit Yates explores the true stories of life-changing events in which the application - or misapplication - of mathematics has played a critical role: patients crippled by faulty genes and entrepreneurs bankrupted by faulty algorithms; innocent victims of miscarriages of justice and the unwitting victims of software glitches. We follow stories of investors who have lost fortunes and parents who have lost children, all because of mathematical misunderstandings. Along the way, Yates arms us with simple mathematical rules and tools that can help us make better decisions in our increasingly quantitative society"--
Author: John de Pillis
Publisher: Cambridge University Press
ISBN: 9780883855409
Category : Mathematics
Languages : en
Pages : 364
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Book Description
Illustrated book showing that there are few degrees of separation between mathematics and topics that provoke interesting conversations.
Author: Robert Fathauer
Publisher: CRC Press
ISBN: 0429589239
Category : Mathematics
Languages : en
Pages : 450
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Book Description
Tessellations: Mathematics, Art and Recreation aims to present a comprehensive introduction to tessellations (tiling) at a level accessible to non-specialists. Additionally, it covers techniques, tips, and templates to facilitate the creation of mathematical art based on tessellations. Inclusion of special topics like spiral tilings and tessellation metamorphoses allows the reader to explore beautiful and entertaining math and art. The book has a particular focus on ‘Escheresque’ designs, in which the individual tiles are recognizable real-world motifs. These are extremely popular with students and math hobbyists but are typically very challenging to execute. Techniques demonstrated in the book are aimed at making these designs more achievable. Going beyond planar designs, the book contains numerous nets of polyhedra and templates for applying Escheresque designs to them. Activities and worksheets are spread throughout the book, and examples of real-world tessellations are also provided. Key features Introduces the mathematics of tessellations, including symmetry Covers polygonal, aperiodic, and non-Euclidean tilings Contains tutorial content on designing and drawing Escheresque tessellations Highlights numerous examples of tessellations in the real world Activities for individuals or classes Filled with templates to aid in creating Escheresque tessellations Treats special topics like tiling rosettes, fractal tessellations, and decoration of tiles
Author: Sebastian M. Cioabă
Publisher: American Mathematical Society
ISBN: 1470471485
Category : Mathematics
Languages : en
Pages : 544
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Book Description
Most introduction to proofs textbooks focus on the structure of rigorous mathematical language and only use mathematical topics incidentally as illustrations and exercises. In contrast, this book gives students practice in proof writing while simultaneously providing a rigorous introduction to number systems and their properties. Understanding the properties of these systems is necessary throughout higher mathematics. The book is an ideal introduction to mathematical reasoning and proof techniques, building on familiar content to ensure comprehension of more advanced topics in abstract algebra and real analysis with over 700 exercises as well as many examples throughout. Readers will learn and practice writing proofs related to new abstract concepts while learning new mathematical content. The first task is analogous to practicing soccer while the second is akin to playing soccer in a real match. The authors believe that all students should practice and play mathematics. The book is written for students who already have some familiarity with formal proof writing but would like to have some extra preparation before taking higher mathematics courses like abstract algebra and real analysis.
Author: sarah-marie belcastro
Publisher: CRC Press
ISBN: 1439865132
Category : Mathematics
Languages : en
Pages : 205
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Book Description
Mathematical craftwork has become extremely popular, and mathematicians and crafters alike are fascinated by the relationship between their crafts. The focus of this book, written for mathematicians, needleworkers, and teachers of mathematics, is on the relationship between mathematics and the fiber arts (including knitting, crocheting, cross-stitch, and quilting). Each chapter starts with an overview of the mathematics and the needlework at a level understandable to both mathematicians and needleworkers, followed by more technical sections discussing the mathematics, how to introduce the mathematics in the classroom through needlework, and how to make the needlework project, including patterns and instructions.
Author: William Higginson
Publisher: Routledge
ISBN: 113471131X
Category : Education
Languages : en
Pages : 187
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Book Description
Exploring the ways in which maths skills can be learned through cross-curricular projects on arts and music, this book presents maths as a meaningful and exciting subject which holds no fear for children.
Author: Carlo Mazza
Publisher: American Mathematical Soc.
ISBN: 9780821838471
Category : Mathematics
Languages : en
Pages : 240
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Book Description
The notion of a motive is an elusive one, like its namesake "the motif" of Cezanne's impressionist method of painting. Its existence was first suggested by Grothendieck in 1964 as the underlying structure behind the myriad cohomology theories in Algebraic Geometry. We now know that there is a triangulated theory of motives, discovered by Vladimir Voevodsky, which suffices for the development of a satisfactory Motivic Cohomology theory. However, the existence of motives themselves remains conjectural. This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, etale cohomology, and Chow groups. The book is divided into lectures, grouped in six parts. The first part presents the definition of Motivic Cohomology, based upon the notion of presheaves with transfers. Some elementary comparison theorems are given in this part. The theory of (etale, Nisnevich, and Zariski) sheaves with transfers is developed in parts two, three, and six, respectively. The theoretical core of the book is the fourth part, presenting the triangulated category of motives. Finally, the comparison with higher Chow groups is developed in part five. The lecture notes format is designed for the book to be read by an advanced graduate student or an expert in a related field. The lectures roughly correspond to one-hour lectures given by Voevodsky during the course he gave at the Institute for Advanced Study in Princeton on this subject in 1999-2000. In addition, many of the original proofs have been simplified and improved so that this book will also be a useful tool for research mathematicians. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
