The Beauty of Mathematics in Computer Science PDF Download

Author: Jun Wu
Publisher: CRC Press
ISBN: 1351689118
Category : Business & Economics
Languages : en
Pages : 288

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Book Description
The Beauty of Mathematics in Computer Science explains the mathematical fundamentals of information technology products and services we use every day, from Google Web Search to GPS Navigation, and from speech recognition to CDMA mobile services. The book was published in Chinese in 2011 and has sold more than 600,000 copies. Readers were surprised to find that many daily-used IT technologies were so tightly tied to mathematical principles. For example, the automatic classification of news articles uses the cosine law taught in high school. The book covers many topics related to computer applications and applied mathematics including: Natural language processing Speech recognition and machine translation Statistical language modeling Quantitive measurement of information Graph theory and web crawler Pagerank for web search Matrix operation and document classification Mathematical background of big data Neural networks and Google’s deep learning Jun Wu was a staff research scientist in Google who invented Google’s Chinese, Japanese, and Korean Web Search Algorithms and was responsible for many Google machine learning projects. He wrote official blogs introducing Google technologies behind its products in very simple languages for Chinese Internet users from 2006-2010. The blogs had more than 2 million followers. Wu received PhD in computer science from Johns Hopkins University and has been working on speech recognition and natural language processing for more than 20 years. He was one of the earliest engineers of Google, managed many products of the company, and was awarded 19 US patents during his 10-year tenure there. Wu became a full-time VC investor and co-founded Amino Capital in Palo Alto in 2014 and is the author of eight books.

Author:
Publisher:
ISBN: 9814472573
Category :
Languages : en
Pages :

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Author: Arindama Singh
Publisher: Springer Science & Business Media
ISBN: 1848824971
Category : Computers
Languages : en
Pages : 422

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Book Description
The foundation of computer science is built upon the following questions: What is an algorithm? What can be computed and what cannot be computed? What does it mean for a function to be computable? How does computational power depend upon programming constructs? Which algorithms can be considered feasible? For more than 70 years, computer scientists are searching for answers to such qu- tions. Their ingenious techniques used in answering these questions form the theory of computation. Theory of computation deals with the most fundamental ideas of computer s- ence in an abstract but easily understood form. The notions and techniques employed are widely spread across various topics and are found in almost every branch of c- puter science. It has thus become more than a necessity to revisit the foundation, learn the techniques, and apply them with con?dence. Overview and Goals This book is about this solid, beautiful, and pervasive foundation of computer s- ence. It introduces the fundamental notions, models, techniques, and results that form the basic paradigms of computing. It gives an introduction to the concepts and mathematics that computer scientists of our day use to model, to argue about, and to predict the behavior of algorithms and computation. The topics chosen here have shown remarkable persistence over the years and are very much in current use.

Author: W.H.J. Feijen
Publisher: Springer Science & Business Media
ISBN: 1461244765
Category : Computers
Languages : en
Pages : 474

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Book Description
More than anything else, this book is a tribute to Edsger W. Dijkstra, on the occasion of his sixtieth birthday, by just a few of those fortunate enough to be influenced by him and his work and to be called his friend or relation, his master, colleague, or pupil. This book contains fifty-four technical contributions in different areas of endeavor, although many of them deal with an area of particular concern to Dijkstra: programming. Each contribution is relatively short and could be digested in one sitting. Together, they form a nice cross section of the discipline of programming at the beginning of the nineties. While many know of Dijkstra's technical contributions, they may not be aware of his ultimate goal, the mastery of complexity in mathematics and computing science. He has forcefully argued that beauty and elegance are essential to this mastery. The title of this book, chosen to reflect his ultimate goal, comes from a sentence in an article of his on some beautiful arguments using mathematical induction: "... when we recognize the battle against chaos, mess, and unmastered complexity as one of computing sci- ence's major callings, we must admit that 'Beauty Is Our Business'."

Author: Mark C. Chu-Carroll
Publisher: Pragmatic Bookshelf
ISBN: 168050360X
Category : Computers
Languages : en
Pages : 269

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Book Description
Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you. Why do Roman numerals persist? How do we know that some infinities are larger than others? And how can we know for certain a program will ever finish? In this fast-paced tour of modern and not-so-modern math, computer scientist Mark Chu-Carroll explores some of the greatest breakthroughs and disappointments of more than two thousand years of mathematical thought. There is joy and beauty in mathematics, and in more than two dozen essays drawn from his popular "Good Math" blog, you'll find concepts, proofs, and examples that are often surprising, counterintuitive, or just plain weird. Mark begins his journey with the basics of numbers, with an entertaining trip through the integers and the natural, rational, irrational, and transcendental numbers. The voyage continues with a look at some of the oddest numbers in mathematics, including zero, the golden ratio, imaginary numbers, Roman numerals, and Egyptian and continuing fractions. After a deep dive into modern logic, including an introduction to linear logic and the logic-savvy Prolog language, the trip concludes with a tour of modern set theory and the advances and paradoxes of modern mechanical computing. If your high school or college math courses left you grasping for the inner meaning behind the numbers, Mark's book will both entertain and enlighten you.

Author: Alexey Stakhov
Publisher: World Scientific
ISBN: 9812775838
Category : Mathematics
Languages : en
Pages : 745

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Book Description
Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."

Author: David D Thornburg
Publisher:
ISBN: 9781955604031
Category :
Languages : en
Pages : 0

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Book Description
This is a book about discovery-the discoveries each of us can make when finding beauty in geometric patterns, beauty in mathematics, and beauty in computer programming. This is also a guide for teaching children to program computers in uniquely powerful ways. It is easy to see how one might find beauty in geometric patterns; this beauty forms the foundation of nature and art. We are continually entranced by geometric form-the symmetry of a butterfly's wings, the spiral of a snail's shell, the facets of a crystal-and each of these natural occurrences is perceived as having beauty associated with it. The hands of people have produced geometric art since marks were first made on cave walls or stones were first fashioned into tools. From the Pyramids and the Parthenon to the finest gold-link chain, the beauty of geometric form is clearly present for all who care to find it. Underlying the geometric pattern that we experience with our eyes lies a more subtle pattern of mathematical beauty, which is experienced intellectually-a collection of unifying principles that govern the arrangement and shapes of objects, both natural and crafted. Computer programming offers a bridge between the worlds of nature, design, and intellect. The computer today can be a tool for discovery and creative expression. It can be as malleable as a piece of clay and as powerful as the very ideas it helps to express. You do not have to be good at math or accept the passive ways computers are often used in classrooms. Thornburg's approach is eye-opening. The programming language used in this book is Lynx, a cloud-based implementation of Logo that can be used on any device with a web browser. A free trial version is available, while licenses for student and classroom use are quite affordable. Lynx was created by LCSI, developer of Logo learning environments for four decades. It is quite similar to MicroWorlds EX and a great next language for kids who have used Scratch. The Logo programming language was designed for learning and its various dialects have been used by millions of learners for more than half a century. With Logo, students experience powerful ideas, solve problems, and create while engaging in conversation with the computer. Although coding is often thought of in vocational terms, Logo programming lies squarely in the grand traditions of the liberal arts and progressive education. Lynx is easily one of the most powerful and user-friendly computer languages ever implemented on a personal computer. It has an extraordinarily powerful graphics environment (whose characteristics will be amply illustrated in this book); it can be used with very little formal instruction; and it can be extended by the user as desired. The power of Lynx must be experienced to be believed. Many people who are familiar with other languages embrace Lynx as being among the best computer languages they have seen. As you work with Lynx yourself, you may see why the enthusiasm for this language is so great.[Gs2]

Author: K Tahir Shah
Publisher: World Scientific
ISBN: 9814555452
Category :
Languages : en
Pages : 218

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Book Description
This book contains some invited lectures on subjects as diverse as document preparation systems, fractals, number theory, graph colouring and neural networks.

Author: Cristopher Moore
Publisher: OUP Oxford
ISBN: 0191552763
Category : Science
Languages : en
Pages : 1004

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Book Description
Computational complexity is one of the most beautiful fields of modern mathematics, and it is increasingly relevant to other sciences ranging from physics to biology. But this beauty is often buried underneath layers of unnecessary formalism, and exciting recent results like interactive proofs, phase transitions, and quantum computing are usually considered too advanced for the typical student. This book bridges these gaps by explaining the deep ideas of theoretical computer science in a clear and enjoyable fashion, making them accessible to non-computer scientists and to computer scientists who finally want to appreciate their field from a new point of view. The authors start with a lucid and playful explanation of the P vs. NP problem, explaining why it is so fundamental, and so hard to resolve. They then lead the reader through the complexity of mazes and games; optimization in theory and practice; randomized algorithms, interactive proofs, and pseudorandomness; Markov chains and phase transitions; and the outer reaches of quantum computing. At every turn, they use a minimum of formalism, providing explanations that are both deep and accessible. The book is intended for graduate and undergraduate students, scientists from other areas who have long wanted to understand this subject, and experts who want to fall in love with this field all over again.

Author: Peter Hilton
Publisher: Cambridge University Press
ISBN: 1139489070
Category : Mathematics
Languages : en
Pages :

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Book Description
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.