The Unity Of Mathematics
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Basic Math For Game Development With Unity 3d
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Author : Kelvin Sung
language : en
Publisher: Apress
Release Date : 2019-12-05
Basic Math For Game Development With Unity 3d written by Kelvin Sung and has been published by Apress this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-05 with Computers categories.
Use Unity-based examples to understand fundamental mathematical concepts and see how they are applied when building modern video game functionality. You will gain the theoretical foundation you need, and you will know how to examine and modify an implementation. This book covers points in a 3D Cartesian coordinate system, and then discusses vectors and the details of dot and cross products. Basic mathematical foundations are illustrated through Unity-based example implementations. Also provided are examples showing how the concepts are applied when implementing video game functionality, such as collision support, motion simulations, autonomous behaviors, shadow approximations, and reflection off arbitrary walls. Throughout this book, you learn and examine the concepts and their applications in a game engine. What You Will Learn Understand the basic concepts of points and vectors and their applications in game development Apply mathematical concepts to modern video game functionality, such as spherical and box colliders Implement autonomous behaviors, including following way points, facing a target, chasing an object, etc. Who This Book is For Beginners, and those interested in the implementation of interactive games, who need a basic mathematical background or a refresher with modern examples
The Unity Of Mathematics
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Author : Pavel Etingof
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-31
The Unity Of Mathematics written by Pavel Etingof 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 2007-05-31 with Mathematics categories.
Tribute to the vision and legacy of Israel Moiseevich Gel'fand Written by leading mathematicians, these invited papers reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program
The Unity Of Mathematics
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Author : Birkhauser Verlag AG
language : en
Publisher:
Release Date : 2005
The Unity Of Mathematics written by Birkhauser Verlag AG and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Mathematics And The Natural Sciences
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Author : Francis Bailly
language : en
Publisher: World Scientific
Release Date : 2011
Mathematics And The Natural Sciences written by Francis Bailly and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
The book aims at the identification of the organising concepts of some physical and biological phenomena, by means of an analysis of the foundations of mathematics and of physics. This is done in the perspective of unifying phenomena, of bringing different conceptual universes into dialog. The analysis of the role of “order” and of symmetries in the foundations of mathematics is linked to the main invariants and principles, among which the geodesic principle (a consequence of symmetries), which govern and confer unity to the various physical theories. Moreover, we attempt to understand causal structures, a central element of physical intelligibility, in terms of symmetries and their breakings. The importance of the mathematical tool is also highlighted, enabling us to grasp the differences in the models for physics and biology which are proposed by continuous and discrete mathematics, such as computational simulations. A distinction between principles of (conceptual) construction and principles of proofs, both in physics and in mathematics, guides this part of the work.As for biology, being particularly difficult and not as thoroughly examined at a theoretical level, we propose a “unification by concepts”, an attempt which should always precede mathematisation. This constitutes an outline for unification also basing itself upon the highlighting of conceptual differences, of complex points of passage, of technical irreducibilities of one field to another. Indeed, a monist point of view such as ours should not make us blind: we, the living objects, are surely just big bags of molecules or, at least, this is our main metaphysical assumption. The point though is: which theory can help us to better understand these bags of molecules, as they are, indeed, rather “singular”, from the physical point of view. Technically, this singularity is expressed by the notion of “extended criticality”, a notion that logically extends the pointwise critical transitions in physics.
Mathematics Ideas And The Physical Real
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Author : Albert Lautman
language : en
Publisher: A&C Black
Release Date : 2011-06-02
Mathematics Ideas And The Physical Real written by Albert Lautman and has been published by A&C Black this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-02 with Philosophy categories.
Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.
The K Book
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Author : Charles A. Weibel
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-13
The K Book written by Charles A. Weibel 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 2013-06-13 with Mathematics categories.
Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr
Around The Unit Circle
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Author : James McKee
language : en
Publisher: Springer Nature
Release Date : 2021-12-08
Around The Unit Circle written by James McKee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-08 with Mathematics categories.
Mahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book. One way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure. All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions. Around the Unit Circle is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.
Linear Differential Equations And Group Theory From Riemann To Poincare
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Author : Jeremy Gray
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-21
Linear Differential Equations And Group Theory From Riemann To Poincare written by Jeremy Gray 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 2008-01-21 with Mathematics categories.
This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
Hajnal Andr Ka And Istv N N Meti On Unity Of Science
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Author : Judit Madarász
language : en
Publisher: Springer Nature
Release Date : 2021-05-31
Hajnal Andr Ka And Istv N N Meti On Unity Of Science written by Judit Madarász and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-31 with Philosophy categories.
This book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself.
The Argument Of Mathematics
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Author : Andrew Aberdein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-01
The Argument Of Mathematics written by Andrew Aberdein 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 2013-07-01 with Philosophy categories.
Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.