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Author : Sherman Stein,Sandor Szabó
Publisher : Cambridge University Press
Page : 236 pages
File Size : 43,8 Mb
Release : 1994
Category : Mathematics
ISBN : 0883850281
A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.
Author : Sherman K. Stein,Sándor Szabó
Publisher : Unknown
Page : 0 pages
File Size : 50,6 Mb
Release : 1994
Category : Algebra
ISBN : 0883850001
There is a long tradition of geometric questions requiring algebra for their answers. The oldest go back to the Greeks, such as "Can we construct a square with the same area as that of a given disk?" many of which were not resolved until mathematicians concluded that [lowercase Greek]Pi is transcendental. There are many questions that appear to focus on geometry, but which require algebra to solve. This book looks at the algebra used to solve tiling and related problems. One purpose of the text is to bring abstract algebra ideas down to earth by applying them in geometric settings. The text is intended for undergraduate and graduate students with at least a semester of algebra, and experienced mathematicians. For both beginners and experts, there are questions that have not yet been answered, which have been labeled "Problems" to distinguish them from the exercises.
Author : Sherman K. Stein,Sandor Szabo
Publisher : Mathematical Association of America (MAA)
Page : 222 pages
File Size : 43,6 Mb
Release : 2014-05-10
Category : MATHEMATICS
ISBN : 1614440247
A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.
Author : Sherman K. Stein,Sándor Szabó
Publisher : American Mathematical Soc.
Page : 207 pages
File Size : 53,8 Mb
Release : 1993-12-31
Category : Electronic
ISBN : 9781470451110
Algebra and Tiling is accessible to undergraduate mathematics majors, as most of the tools necessary to read the book are found in standard upper division algebra courses, but teachers, researchers, and professional mathematicians will find the book equally appealing. Beginners will find the exercises and the appendices especially useful. The unsolved problems will challenge both beginners and experts. The book could serve as the basis of an undergraduate or graduate seminar or a source of applications to enrich an algebra or geometry course.
Author : Chuanming Zong
Publisher : Cambridge University Press
Page : 196 pages
File Size : 51,5 Mb
Release : 2006-02-02
Category : Mathematics
ISBN : 0521855357
Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory.
Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1928 pages
File Size : 55,9 Mb
Release : 2017-11-22
Category : Computers
ISBN : 9781498711425
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Author : Csaba D. Toth,Joseph O'Rourke,Jacob E. Goodman
Publisher : CRC Press
Page : 1557 pages
File Size : 41,9 Mb
Release : 2004-04-13
Category : Mathematics
ISBN : 9781420035315
While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies
Author : Peter Brass,William O. J. Moser,János Pach
Publisher : Springer Science & Business Media
Page : 507 pages
File Size : 51,5 Mb
Release : 2006-06-19
Category : Mathematics
ISBN : 9780387238159
This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.
Author : Moshe Lewenstein,Gabriel Valiente
Publisher : Springer
Page : 425 pages
File Size : 43,8 Mb
Release : 2006-07-01
Category : Computers
ISBN : 9783540354611
This book constitutes the refereed proceedings of the 17th Annual Symposium on Combinatorial Pattern Matching, CPM 2006, held in Barcelona, Spain, July 2006. The book presents 33 revised full papers together with 3 invited talks, organized in topical sections on data structures, indexing data structures, probabilistic and algebraic techniques, applications in molecular biology, string matching, data compression, and dynamic programming.
Author : J.M. Aarts
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 43,5 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9780387782416
This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook. The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry while at the same time giving the student tools that will be useful in other courses.
Author : Henk W. Broer
Publisher : American Mathematical Soc.
Page : 163 pages
File Size : 48,6 Mb
Release : 2016-12-31
Category : Science
ISBN : 9780883851425
Near the Horizon starts out by considering several optical phenomena that can occur when the sun is near the horizon. One can sometimes see objects that are actually below the horizon. Sometimes there seems to be a dark strip in the middle of the solar disk. These are a result of the way that the atmosphere affects the geometry of light rays. Broer starts his book with the Fermat principle (rays of light take least-time paths) and deduces from it laws for refraction and reflection; by expressing these as conservation laws, he can handle both the case of inhomogeneous layers of air and the case of continuous variation in the refraction index. A surprising application is the brachistochrone problem, in which the path of fastest descent is determined by studying how a light ray would behave in a “flat earth” atmosphere whose refraction index is determined by the gravitational potential. This leads to a very interesting chapter on the cycloid and its properties. The final chapters move from the elementary theory to a more sophisticated version in which the Fermat Principle leads to a Riemannian metric whose geodesics are the paths of light rays. This gives us an optics which is geometric in a new sense, and serves as a nice demonstration of the physical applicability of Riemannian geometry.
Author : Sandor Szabo
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 55,5 Mb
Release : 2004-10-25
Category : Mathematics
ISBN : 3764371587
The main objective of this book is to give a systematic exposition of the main results and techniques of the factorization theory of abelian groups. The necessary background materials are presented along with some of the most important applications in geometry, combinatorics, coding theory, and number theory. A large part of the text is accessible to students, requiring only basic knowledge in group theory and algebra. Helpful exercises are provided in every chapter.
Author : Sandor Szabo,Arthur D. Sands
Publisher : CRC Press
Page : 282 pages
File Size : 50,9 Mb
Release : 2009-01-21
Category : Mathematics
ISBN : 9781420090475
Decomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups. Th
Author : Steven G. Krantz
Publisher : American Mathematical Soc.
Page : 357 pages
File Size : 54,6 Mb
Release : 2019-07-03
Category : Electronic
ISBN : 9781470451127
A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject. A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.
Author : Robert S. Wolf
Publisher : Cambridge University Press
Page : 424 pages
File Size : 43,9 Mb
Release : 2005-03-10
Category : Mathematics
ISBN : 0883850362
The foundations of mathematics include mathematical logic, set theory, recursion theory, model theory, and Gdel's incompleteness theorems. Professor Wolf provides here a guide that any interested reader with some post-calculus experience in mathematics can read, enjoy, and learn from. It could also serve as a textbook for courses in the foundations of mathematics, at the undergraduate or graduate level. The book is deliberately less structured and more user-friendly than standard texts on foundations, so will also be attractive to those outside the classroom environment wanting to learn about the subject.