Problems With A Point Exploring Math And Computer Science
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Problems With A Point Exploring Math And Computer Science
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Author : William Gasarch
language : en
Publisher: World Scientific
Release Date : 2018-12-26
Problems With A Point Exploring Math And Computer Science written by William Gasarch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-26 with Young Adult Nonfiction categories.
'Points, questions, stories, and occasional rants introduce the 24 chapters of this engaging volume. With a focus on mathematics and peppered with a scattering of computer science settings, the entries range from lightly humorous to curiously thought-provoking. Each chapter includes sections and sub-sections that illustrate and supplement the point at hand. Most topics are self-contained within each chapter, and a solid high school mathematics background is all that is needed to enjoy the discussions. There certainly is much to enjoy here.'CHOICEEver notice how people sometimes use math words inaccurately? Or how sometimes you instinctively know a math statement is false (or not known)?Each chapter of this book makes a point like those above and then illustrates the point by doing some real mathematics through step-by-step mathematical techniques.This book gives readers valuable information about how mathematics and theoretical computer science work, while teaching them some actual mathematics and computer science through examples and exercises. Much of the mathematics could be understood by a bright high school student. The points made can be understood by anyone with an interest in math, from the bright high school student to a Field's medal winner.
Problems With A Point
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Author : William I. Gasarch
language : en
Publisher: World Scientific Publishing Company
Release Date : 2019
Problems With A Point written by William I. Gasarch and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with General semantics categories.
Ever notice how people sometimes use math words inaccurately? Or how sometimes you instinctively know a math statement is false (or not known)? Each chapter of this book makes a point like those above and then illustrates the point by doing some real mathematics through step-by-step mathematical techniques. This book gives readers valuable information about how mathematics and theoretical computer science work, while teaching them some actual mathematics and computer science through examples and exercises. Much of the mathematics could be understood by a bright high school student. The points made can be understood by anyone with an interest in math, from the bright high school student to a Field's medal winner.
Mathematical Muffin Morsels Nobody Wants A Small Piece
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Author : William Gasarch
language : en
Publisher: World Scientific
Release Date : 2020-05-28
Mathematical Muffin Morsels Nobody Wants A Small Piece written by William Gasarch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-28 with Mathematics categories.
Suppose you have five muffins that you want to divide and give to Alice, Bob, and Carol. You want each of them to get 5/3. You could cut each muffin into 1/3-1/3-1/3 and give each student five 1/3-sized pieces. But Alice objects! She has large hands! She wants everyone to have pieces larger than 1/3.Is there a way to divide five muffins for three students so that everyone gets 5/3, and all pieces are larger than 1/3? Spoiler alert: Yes! In fact, there is a division where the smallest piece is 5/12. Is there a better division? Spoiler alert: No.In this book we consider THE MUFFIN PROBLEM: what is the best way to divide up m muffins for s students so that everyone gets m/s muffins, with the smallest pieces maximized. We look at both procedures for the problem and proofs that these procedures are optimal.This problem takes us through much mathematics of interest, for example, combinatorics and optimization theory. However, the math is elementary enough for an advanced high school student.
An Introduction To Mathematical Modeling
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Author : Edward A. Bender
language : en
Publisher: Courier Corporation
Release Date : 2000-03-06
An Introduction To Mathematical Modeling written by Edward A. Bender and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-06 with Mathematics categories.
Accessible text features over 100 reality-based examples pulled from the science, engineering and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.
Mathematics And Computation
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Author : Avi Wigderson
language : en
Publisher: Princeton University Press
Release Date : 2019-10-29
Mathematics And Computation written by Avi Wigderson 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 2019-10-29 with Computers categories.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
What Can Be Computed
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Author : John MacCormick
language : en
Publisher: Princeton University Press
Release Date : 2018-05-01
What Can Be Computed written by John MacCormick 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 2018-05-01 with Computers categories.
An accessible and rigorous textbook for introducing undergraduates to computer science theory What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference. The book covers the standard topics in the theory of computation, including Turing machines and finite automata, universal computation, nondeterminism, Turing and Karp reductions, undecidability, time-complexity classes such as P and NP, and NP-completeness, including the Cook-Levin Theorem. But the book also provides a broader view of computer science and its historical development, with discussions of Turing's original 1936 computing machines, the connections between undecidability and Gödel's incompleteness theorem, and Karp's famous set of twenty-one NP-complete problems. Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book's examples and other content allow readers to view demonstrations of—and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation. An accessible and rigorous introduction to the essential fundamentals of computer science theory, written specifically for undergraduates taking introduction to the theory of computation Features a practical, interactive approach using real computer programs (Python in the text, with forthcoming Java alternatives online) to enhance motivation and understanding Gives equal emphasis to computability and complexity Includes special topics that demonstrate the profound nature of key ideas in the theory of computation Lecture slides and Python programs are available at whatcanbecomputed.com
A Programmer S Introduction To Mathematics
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Author : Jeremy Kun
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-11-27
A Programmer S Introduction To Mathematics written by Jeremy Kun and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-27 with Computer science categories.
A Programmer's Introduction to Mathematics uses your familiarity with ideas from programming and software to teach mathematics. You'll learn about the central objects and theorems of mathematics, including graphs, calculus, linear algebra, eigenvalues, optimization, and more. You'll also be immersed in the often unspoken cultural attitudes of mathematics, learning both how to read and write proofs while understanding why mathematics is the way it is. Between each technical chapter is an essay describing a different aspect of mathematical culture, and discussions of the insights and meta-insights that constitute mathematical intuition. As you learn, we'll use new mathematical ideas to create wondrous programs, from cryptographic schemes to neural networks to hyperbolic tessellations. Each chapter also contains a set of exercises that have you actively explore mathematical topics on your own. In short, this book will teach you to engage with mathematics. A Programmer's Introduction to Mathematics is written by Jeremy Kun, who has been writing about math and programming for 8 years on his blog "Math Intersect Programming." As of 2018, he works in datacenter optimization at Google.
Problems In Applied Mathematics
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Author : Murray S. Klamkin
language : en
Publisher: SIAM
Release Date : 1990-01-01
Problems In Applied Mathematics written by Murray S. Klamkin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
People in all walks of life--and perhaps mathematicians especially--delight in working on problems for the sheer pleasure of meeting a challenge. The problem section of SIAM Review has always provided such a challenge for mathematicians. The section was started to offer classroom instructors and their students as well as other interested problemists, a set of problems--solved or unsolved-- illustrating various applications of mathematics. In many cases the unsolved problems were eventually solved. Problems in Applied Mathematics is a compilation of 380 of SIAM Review's most interesting problems dating back to the journal's inception in 1959. The problems are classified into 22 broad categories including Series, Special Functions, Integrals, Polynomials, Probability, Combinatorics, Matrices and Determinants, Optimization, Inequalities, Ordinary Differential Equations, Boundary Value Problems, Asymptotics and Approximations, Mechanics, Graph Theory, and Geometry.
Lessons In Enumerative Combinatorics
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Author : Ömer Eğecioğlu
language : en
Publisher: Springer Nature
Release Date : 2021-05-13
Lessons In Enumerative Combinatorics written by Ömer Eğecioğlu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-13 with Mathematics categories.
This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science. Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications. Lessons in Enumerative Combinatorics captures the authors' distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate, or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed; familiarity with linear algebra will enhance the study of certain chapters.
Concrete Mathematics
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Author : Ronald L. Graham
language : zh-CN
Publisher:
Release Date : 2020
Concrete Mathematics written by Ronald L. Graham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Computer science categories.