The Unity Of Mathematics

Author : Kelvin Sung,Gregory Smith
Publisher : Apress
Page : 414 pages
File Size : 47,6 Mb
Release : 2019-12-05
Category : Computers
ISBN : 9781484254431

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Basic Math for Game Development with Unity 3D by Kelvin Sung,Gregory Smith Pdf

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 developmentApply mathematical concepts to modern video game functionality, such as spherical and box collidersImplement 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

Author : Ezra Brown,Richard K. Guy
Publisher : American Mathematical Soc.
Page : 353 pages
File Size : 55,5 Mb
Release : 2021-04-05
Category : Education
ISBN : 9781470465094

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The Unity of Combinatorics by Ezra Brown,Richard K. Guy Pdf

Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable. Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”

Author : Birkhauser Verlag AG
Publisher : Unknown
Page : 128 pages
File Size : 50,7 Mb
Release : 2005
Category : Electronic
ISBN : 3764340762

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The Unity of Mathematics by Birkhauser Verlag AG Pdf

Author : Peter Hilton,Jean Pedersen
Publisher : Cambridge University Press
Page : 128 pages
File Size : 40,9 Mb
Release : 2010-07-22
Category : Mathematics
ISBN : 9781139489072

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A Mathematical Tapestry by Peter Hilton,Jean Pedersen Pdf

This easy-to-read 2010 book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paper-folding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain hands-on experience constructing these models and to discover for themselves the patterns and relationships they unearth.

Author : Pavel Etingof,Vladimir S. Retakh,I. M. Singer
Publisher : Springer Science & Business Media
Page : 646 pages
File Size : 50,9 Mb
Release : 2007-05-31
Category : Mathematics
ISBN : 9780817644673

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The Unity of Mathematics by Pavel Etingof,Vladimir S. Retakh,I. M. Singer Pdf

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

Author : Dan Romik
Publisher : Cambridge University Press
Page : 366 pages
File Size : 54,5 Mb
Release : 2015-02-02
Category : Mathematics
ISBN : 9781107075832

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The Surprising Mathematics of Longest Increasing Subsequences by Dan Romik Pdf

In a surprising sequence of developments, the longest increasing subsequence problem, originally mentioned as merely a curious example in a 1961 paper, has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model. The detailed and playful study of these connections makes this book suitable as a starting point for a wider exploration of elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians. The specific topics covered are the Vershik-Kerov-Logan-Shepp limit shape theorem, the Baik-Deift-Johansson theorem, the Tracy-Widom distribution, and the corner growth process. This exciting body of work, encompassing important advances in probability and combinatorics over the last forty years, is made accessible to a general graduate-level audience for the first time in a highly polished presentation.

Author : Cathy O'Neil
Publisher : Crown Publishing Group (NY)
Page : 274 pages
File Size : 53,7 Mb
Release : 2016
Category : Business & Economics
ISBN : 9780553418811

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Weapons of Math Destruction by Cathy O'Neil Pdf

"A former Wall Street quantitative analyst sounds an alarm on mathematical modeling, a pervasive new force in society that threatens to undermine democracy and widen inequality,"--NoveList.

Author : Peter Lynch
Publisher : Gill & Macmillan Ltd
Page : 328 pages
File Size : 51,9 Mb
Release : 2016-10-14
Category : Mathematics
ISBN : 9780717169566

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That's Maths by Peter Lynch Pdf

From atom bombs to rebounding slinkies, open your eyes to the mathematical magic in the everyday. Mathematics isn't just for academics and scientists, a fact meteorologist and blogger Peter Lynch has spent the past several years proving through his Irish Times newspaper column and blog, That's Maths.Here, he shows how maths is all around us, with chapters on the beautiful equations behind designing a good concert venue, predicting the stock market and modelling the atom bomb, as well as playful meditations on everything from coin-stacking to cartography. If you left school thinking maths was boring, think again!

Author : D. B. Fuks,Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 42,9 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821843161

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Mathematical Omnibus by D. B. Fuks,Serge Tabachnikov Pdf

The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

Author : James McKee,Chris Smyth
Publisher : Springer Nature
Page : 444 pages
File Size : 53,6 Mb
Release : 2021-12-08
Category : Mathematics
ISBN : 9783030800314

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Around the Unit Circle by James McKee,Chris Smyth Pdf

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.

Author : Ronald L. Graham,Donald E. Knuth,Oren Patashnik
Publisher : Addison-Wesley Professional
Page : 811 pages
File Size : 44,8 Mb
Release : 1994-02-28
Category : Computers
ISBN : 9780134389981

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Concrete Mathematics by Ronald L. Graham,Donald E. Knuth,Oren Patashnik Pdf

This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: Sums Recurrences Integer functions Elementary number theory Binomial coefficients Generating functions Discrete probability Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.

Author : Paris Buttfield-Addison,Jon Manning,Tim Nugent
Publisher : O'Reilly Media
Page : 408 pages
File Size : 45,5 Mb
Release : 2019-03-13
Category : Computers
ISBN : 9781491999127

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Unity Game Development Cookbook by Paris Buttfield-Addison,Jon Manning,Tim Nugent Pdf

Find out how to use the Unity Game Engine to its fullest for both 3D and 2D game development—from the basics to the hottest new tricks in virtual reality. With this unique cookbook, you’ll get started in two ways: First, you’ll learn about the Unity game engine by following very brief exercises that teach specific features of the software Second, this tutorial-oriented guide provides a collection of snippets that solve common gameplay problems, like determining if a player has completed a lap in a race Using our cookbook format, we pinpoint the problem, set out the solution, and discuss how to solve your problem in the best and most straightforward way possible so you can move onto the next step in the project. Unity Game Development Cookbook is ideal for beginning to intermediate Unity developers. Beginners will get a broad immersion into the Unity development environment, while intermediate developers will learn how to apply the foundational Unity skills they have to solve real game development problems.

Author : Theokritos Kouremenos
Publisher : Franz Steiner Verlag Wiesbaden GmbH
Page : 141 pages
File Size : 54,8 Mb
Release : 2015
Category : Mathematics
ISBN : 3515110763

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The Unity of Mathematics in Plato's Republic by Theokritos Kouremenos Pdf

In his Republic Plato considers grasping the unity of mathematics as the ultimate goal of the mathematical studies in which the future philosopher-rulers must engage before they turn to philosophy. How the unity of mathematics is supposed to be understood is not explained, however. This book argues that Plato conceives of the unity of mathematics in terms of the mutually benefiting links between its branches, just as he conceives of the unity of the state outlined in the Republic in terms of the common benefit for all citizens. Evidence for this view is provided by a discussion of his conception of astronomy as a propedeutic to philosophy, which can be best understood as hinting at a historically possible link between fourth-century-BC astronomy and solid geometry. The monograph also includes a detailed discussion of two well-known stories about Plato: not only he motivated Greek mathematicians to solve a difficult problem in solid geometry with his interpretation of a Delphic oracle given to the inhabitants of the island of Delos but he also posed the question which led to the development of the astronomical theory of homocentric spheres. It is argued that these stories are best understood as fictional episodes in Plato's life, constructed from passages in his works.

Author : Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour
Publisher : Springer Nature
Page : 493 pages
File Size : 50,7 Mb
Release : 2021-02-09
Category : Philosophy
ISBN : 9783030536541

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Mathematics, Logic, and their Philosophies by Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour Pdf

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

Author : Philip J. Davis
Publisher : Unknown
Page : 149 pages
File Size : 52,5 Mb
Release : 2015
Category : MATHEMATICS
ISBN : 147042570X

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Unity and Disunity and Other Mathematical Essays by Philip J. Davis Pdf