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Algebra And Tiling
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Author :Sherman K. Stein Publisher :Mathematical Association of America (MAA) ISBN 13 :9781614440246 Total Pages :222 pages Book Rating :4.4/5 (42 download)
Book Synopsis Algebra and Tiling by : Sherman K. Stein
Download or read book Algebra and Tiling written by Sherman K. Stein and published by Mathematical Association of America (MAA). This book was released on 2014-05-10 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.
Book Synopsis Algebra and Tiling by : Sherman Stein
Download or read book Algebra and Tiling written by Sherman Stein and published by Cambridge University Press. This book was released on 1994 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.
Book Synopsis Topology of Tiling Spaces by : Lorenzo Adlai Sadun
Download or read book Topology of Tiling Spaces written by Lorenzo Adlai Sadun and published by American Mathematical Soc.. This book was released on 2008 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces." "The text contains a generous supply of examples and exercises."--BOOK JACKET.
Download or read book Miles of Tiles written by Charles Radin and published by American Mathematical Soc.. This book was released on 1999 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Miles of Tiles" is a mathematics lesson for middle school classes requiring students to calculate the number and cost of tiles needed to cover the floor of the classroom. This lesson includes Internet activities. "Miles of Tiles" is presented as a service of the Link-to-Learn Professional Development Project of Pennsylvania, a state-sponsored educational technology initiative.
Book Synopsis Aperiodic Order: Volume 1, A Mathematical Invitation by : Michael Baake
Download or read book Aperiodic Order: Volume 1, A Mathematical Invitation written by Michael Baake and published by Cambridge University Press. This book was released on 2013-08-22 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. In particular, the authors provide a systematic exposition of the mathematical theory of kinematic diffraction. Numerous illustrations and worked-out examples help the reader to bridge the gap between theory and application. The authors also point to more advanced topics to show how the theory interacts with other areas of pure and applied mathematics.
Book Synopsis Non-Euclidean Geometries by : András Prékopa
Download or read book Non-Euclidean Geometries written by András Prékopa and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: "From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.
Book Synopsis Zome geometry : hands-on learning with Zome models by : George W. Hart
Download or read book Zome geometry : hands-on learning with Zome models written by George W. Hart and published by Key Curriculum Press. This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by George W. Hart, a mathematician and artist, and Henri Picciotto, an innovative teacher, the activities are based on a deep understanding of polyhedra and practical classroom experience. Students discover relationships in something they have built themselves, they understand and remember the concepts.
Book Synopsis Tilings and Patterns by : Branko Grünbaum
Download or read book Tilings and Patterns written by Branko Grünbaum and published by W H Freeman & Company. This book was released on 1989 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tilings and Patterns: An Introduction presents in convenient paperback form the first half of Tilings and Patterns. Omitting the more specialized material of the earlier volume, this abbreviated edition make's the authors' contributions to tiling theory and its practical applications accessible to a wide audience.
Download or read book Tessalation! written by Emily Grosvenor and published by Mascot Books. This book was released on 2016-07-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: As Tessa Truman-Ling explores the outdoors, she sees patterns everywhere and in everything.
Book Synopsis Thirty-three Miniatures by : Jiří Matoušek
Download or read book Thirty-three Miniatures written by Jiří Matoušek and published by American Mathematical Soc.. This book was released on 2010 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53)
Book Synopsis Substitution and Tiling Dynamics: Introduction to Self-inducing Structures by : Shigeki Akiyama
Download or read book Substitution and Tiling Dynamics: Introduction to Self-inducing Structures written by Shigeki Akiyama and published by Springer Nature. This book was released on 2020-12-05 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings.
Book Synopsis The Modified Algorithm of Jacobi-Perron by : Robert Berger
Download or read book The Modified Algorithm of Jacobi-Perron written by Robert Berger and published by American Mathematical Soc.. This book was released on 1966 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proofs that Really Count by : Arthur T. Benjamin
Download or read book Proofs that Really Count written by Arthur T. Benjamin and published by American Mathematical Society. This book was released on 2022-09-21 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.
Book Synopsis Common Core Math For Parents For Dummies with Videos Online by : Christopher Danielson
Download or read book Common Core Math For Parents For Dummies with Videos Online written by Christopher Danielson and published by John Wiley & Sons. This book was released on 2015-04-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Help your child succeed with a better understanding of Common Core Math Common Core Math For Parents For Dummies is packed with tools and information to help you promote your child's success in math. The grade-by-grade walk-through brings you up to speed on what your child is learning, and the sample problems and video lessons help you become more involved as you study together. You'll learn how to effectively collaborate with teachers and keep tabs on your child's progress, so minor missteps can be corrected quickly, before your child falls behind. The Common Core was designed to improve college- and career-readiness, and to prepare U.S. students to be more competitive on an international stage when it's time to enter the workforce. This guide shows you how the standards were created, and how they've evolved over time to help ensure your child's future success. The Common Core Math Standards prepare students to do real math in the real world. Many new teaching methods are very different from the way most parents learned math, leading to frustration and confusion as parents find themselves unable to help with homework or explain difficult concepts. This book cuts the confusion and shows you everything you need to know to help your child succeed in math. Understand the key concepts being taught in your child's grade Utilize the homework tools that help you help your child Communicate more effectively with your child's teacher Guide your child through sample problems to foster understanding The Common Core was designed to ensure that every student, regardless of location or background, receives the education they need. Math skills are critical to real-world success, and the new standards reflect that reality in scope and rigorousness. Common Core Math For Parents For Dummies helps you help your child succeed.
Book Synopsis The Knot Book by : Colin Conrad Adams
Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Book Synopsis Open Middle Math by : Robert Kaplinsky
Download or read book Open Middle Math written by Robert Kaplinsky and published by Taylor & Francis. This book was released on 2023-10-10 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.
Book Synopsis An Invitation to Abstract Mathematics by : Béla Bajnok
Download or read book An Invitation to Abstract Mathematics written by Béla Bajnok and published by Springer Nature. This book was released on 2020-10-27 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH
