The Shape Of Algebra In The Mirrors Of Mathematics
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The Shape Of Algebra In The Mirrors Of Mathematics
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Author : Gabriel Katz
language : en
Publisher: World Scientific
Release Date : 2012
The Shape Of Algebra In The Mirrors Of Mathematics written by Gabriel Katz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
The Shape of Algebra is the authors' attempt to share their mathematical experiences with readers who have more than a passing interest in mathematics, but have only a traditional exposure to elementary algebra. Secondary school and college teachers and students who want to expand their horizons in the field will find a fresh presentation of familiar concepts and some unexpected results. This book serves as a text for an "appreciation" course in modern mathematics designed for non-mathematics majors or for first-year students who are considering the possibility of studying mathematics or related disciplines. It can also serve as a source of computer-supported activities that could supplement traditional courses in algebra, multivariable calculus, and complex variable. This book gives the reader a sense of the visual nature of mathematics. Mathematical experiments with universal mapping software VisuMatica, designed by Vladimir Nodel'man, form the very core of the book. Readers are encouraged to reproduce, play with, and expand on these experiments. Numerous problems are interspersed throughout the text to guide the reader. Our treatment of standard algebra is visual and computational. By introducing visual computational environments like VisuMatica, our book promotes this geometric approach to algebra and makes it accessible to readers a great deal earlier. The book will enable our readers to approach its content on three levels: the first one which requires only some fluency with elementary algebraic manipulations; the second one which also presumes familiarity with the notions of derivatives and tangent lines to plane curves, and the third one which uses some basic concepts of multivariable calculus. All three levels are clearly marked in the text, and will allow for a smooth reading and virtual experiments, regardless of the level that our readers will find comfortable.
Mathematics Studies Through Technology Precalculus Calculus And More
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Author : Vladimir Nodelman
language : en
Publisher: World Scientific
Release Date : 2024-12-16
Mathematics Studies Through Technology Precalculus Calculus And More written by Vladimir Nodelman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-16 with Mathematics categories.
This book caters to both prospective and current mathematics educators at the school and university levels, along with their students and anyone intrigued by the possibilities of integrating software into mathematics education.Mathematics, being a unified science, is best comprehended when its cohesive nature is emphasized and demonstrated to students. Educational software assumes a pivotal role in achieving this pedagogical goal.The book outlines the author's methodology in utilizing educational software for developing and applying computer models, grounded in a thorough analysis of the subject matter. This approach is vividly illustrated through examples employing a non-profit authoring program (VisuMatica) provided with the book, enabling users to:Through the guidance of this book, students will discover mathematics as clear, visible, friendly, and enjoyable.The author exemplifies this approach by focusing on the functional line of mathematics, spanning from school basics to advanced university courses in higher mathematics. Importantly, the assimilated ideas and techniques are readily applicable to teaching and learning other areas of mathematics.
The Best Writing On Mathematics 2012
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Author : Mircea Pitici
language : en
Publisher: Princeton University Press
Release Date : 2012-11-11
The Best Writing On Mathematics 2012 written by Mircea Pitici and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-11 with Mathematics categories.
The year's finest writing on mathematics from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
The Shape Of Algebra In The Mirrors Of Mathematics
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Author : Gabriel Katz
language : en
Publisher:
Release Date : 2010
The Shape Of Algebra In The Mirrors Of Mathematics written by Gabriel Katz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Electronic books categories.
Tropical Geometry And Mirror Symmetry
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Author : Mark Gross
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-01-20
Tropical Geometry And Mirror Symmetry written by Mark Gross and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-20 with Mathematics categories.
Tropical geometry provides an explanation for the remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and Siebert using log geometry to understand how the tropical world relates the A- and B-models in mirror symmetry. The text starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the mirror, B-model side, giving recent results of the author showing how tropical geometry can be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and Siebert for ``integral tropical manifolds.'' A complete version of the argument is given in two dimensions.
Doing Mathematics
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Author : Martin H. Krieger
language : en
Publisher: World Scientific
Release Date : 2003
Doing Mathematics written by Martin H. Krieger and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book discusses some ways of doing mathematical work and the subject matter that is being worked upon and created. It argues that the conventions we adopt, the subject areas we delimit, what we can prove and calculate about the physical world, and the analogies that work for mathematicians--all depend on mathematics, what will work out and what won't. And the mathematics, as it is done, is shaped and supported, or not, by convention, subject matter, calculation, and analogy. The causes studied include the central limit theorem of statistics, the sound of the shape of a drum, the connection between algebra and topology, the stability of matter, the Ising model, and the Langlands Program in number theory and representation theory. Contents: Convention: How Means and Variances are Entrenched as Statistics; Subject: The Fields of Topology; Appendix: The Two-Dimensional Ising Model of a Ferromagner; Calculation: Strategy, Structure, and Tactics in Applying Classical Analysis; Analogy; A Syzygy Between a research Program in Mathematics and a Research Program in Physics, Each of Which is Itself an Analogy; Mathematics in Concreto. Readership: Mathematicians, Physicists, philosophers and historians of science.
Maths All Week
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Author : June Loewenstein
language : en
Publisher: Nelson Thornes
Release Date : 2003
Maths All Week written by June Loewenstein and has been published by Nelson Thornes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Education categories.
This book will help you set up and run a successful and creative maths week or event in your school. It contains detailed advice on planning and suggestions for the evaluation of your maths week.
Mirrors And Reflections
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Author : Alexandre V. Borovik
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-07
Mirrors And Reflections written by Alexandre V. Borovik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-07 with Mathematics categories.
This graduate/advanced undergraduate textbook contains a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory; a large number of exercises at various levels of difficulty; some Euclidean geometry is included along with the theory of convex polyhedra; no prerequisites are necessary beyond the basic concepts of linear algebra and group theory; and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students.
Manifold Mirrors
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Author : Felipe Cucker
language : en
Publisher: Cambridge University Press
Release Date : 2013-04-25
Manifold Mirrors written by Felipe Cucker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-25 with Mathematics categories.
Most works of art, whether illustrative, musical or literary, are created subject to a set of constraints. In many (but not all) cases, these constraints have a mathematical nature, for example, the geometric transformations governing the canons of J. S. Bach, the various projection systems used in classical painting, the catalog of symmetries found in Islamic art, or the rules concerning poetic structure. This fascinating book describes geometric frameworks underlying this constraint-based creation. The author provides both a development in geometry and a description of how these frameworks fit the creative process within several art practices. He furthermore discusses the perceptual effects derived from the presence of particular geometric characteristics. The book began life as a liberal arts course and it is certainly suitable as a textbook. However, anyone interested in the power and ubiquity of mathematics will enjoy this revealing insight into the relationship between mathematics and the arts.
Abstracts Of Papers Presented To The American Mathematical Society
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Author : American Mathematical Society
language : en
Publisher:
Release Date : 2007
Abstracts Of Papers Presented To The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.