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In Pursuit of the Traveling Salesman

In Pursuit of the Traveling Salesman Author William Cook
ISBN-10 9780691152707
Release 2012
Pages 228
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Covers the history, applications, theory, and computation of the traveling salesman problem right up to state-of-the-art solution machinery.

The Traveling Salesman Problem

The Traveling Salesman Problem Author David L. Applegate
ISBN-10 9781400841103
Release 2011-09-19
Pages 608
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This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple enough: given a set of cities and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience. The authors of this book are the same pioneers who for nearly two decades have led the investigation into the traveling salesman problem. They have derived solutions to almost eighty-six thousand cities, yet a general solution to the problem has yet to be discovered. Here they describe the method and computer code they used to solve a broad range of large-scale problems, and along the way they demonstrate the interplay of applied mathematics with increasingly powerful computing platforms. They also give the fascinating history of the problem--how it developed, and why it continues to intrigue us.

The Golden Ticket

The Golden Ticket Author Lance Fortnow
ISBN-10 9781400846610
Release 2013-03-27
Pages 192
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The P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.

X and the City

X and the City Author John A. Adam
ISBN-10 9781400841691
Release 2012-05-27
Pages 336
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X and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? Can you predict whether a traffic light will stay green long enough for you to cross the intersection? And what is the likelihood that your city will be hit by an asteroid? Every math problem and equation in this book tells a story and examples are explained throughout in an informal and witty style. The level of mathematics ranges from precalculus through calculus to some differential equations, and any reader with knowledge of elementary calculus will be able to follow the materials with ease. There are also some more challenging problems sprinkled in for the more advanced reader. Filled with interesting and unusual observations about how cities work, X and the City shows how mathematics undergirds and plays an important part in the metropolitan landscape.

Graph Theory 1736 1936

Graph Theory  1736 1936 Author Norman Biggs
ISBN-10 0198539169
Release 1976
Pages 239
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First published in 1976, this book has been widely acclaimed both for its significant contribution to the history of mathematics and for the way that it brings the subject alive. Building on a set of original writings from some of the founders of graph theory, the book traces the historical development of the subject through a linking commentary. The relevant underlying mathematics is also explained, providing an original introduction to the subject for students. From reviews: 'The book...serves as an excellent examplein fact, as a modelof a new approach to one aspect of mathematics, when mathematics is considered as a living, vital and developing tradition.' (Edward A. Maziark in Isis) 'Biggs, Lloyd and Wilson's unusual and remarkable book traces the evolution and development of graph theory...Conceived in a very original manner and obviously written with devotion and a very great amount of painstaking historical research, it contains an exceptionally fine collection of source material, and to a graph theorist it is a treasure chest of fascinating historical information and curiosities with rich food for thought.' (Gabriel Dirac in Centaurus) 'The lucidity, grace and wit of the writing makes this book a pleasure to read and re-read.' (S. H. Hollingdale in Bulletin of the Institute of Mathematics and its Applications)

The Great Mathematical Problems

The Great Mathematical Problems Author Ian Stewart
ISBN-10 9781847653512
Release 2013-03-07
Pages 340
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There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincar Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

Combinatorial Optimization

Combinatorial Optimization Author Christos H. Papadimitriou
ISBN-10 9780486320137
Release 2013-04-26
Pages 528
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This graduate-level text considers the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; local search heuristics for NP-complete problems, more. 1982 edition.

Professor Stewart s Hoard of Mathematical Treasures

Professor Stewart s Hoard of Mathematical Treasures Author Ian Stewart
ISBN-10 9780465021376
Release 2010-04-27
Pages 352
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Opening another drawer in his Cabinet of Curiosities, renowned mathematics professor Ian Stewart presents a new medley of games, paradoxes, and riddles in Professor Stewart's Hoard of Mathematical Treasures. With wit and aplomb, Stewart mingles casual puzzles with grander forays into ancient and modern mathematical thought. Amongst a host of arcane and astonishing facts about every kind of number from irrational and imaginary to complex and cuneiform, we learn: – How to organize chaos – How matter balances anti-matter – How to turn a sphere inside out (without creasing it) – How to calculate pi by observing the stars – ...and why you can't comb a hairy ball. Along the way Stewart offers the reader tantalizing glimpses of the mathematics underlying life and the universe. Mind-stretching, enlightening, and endlessly amusing, Professor Stewart's Hoard of Mathematical Treasures will stimulate, delight, and enthrall.

50 Visions of Mathematics

50 Visions of Mathematics Author Dara O Briain
ISBN-10 9780198701811
Release 2014-05
Pages 198
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Relax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. This book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain.

The Logician and the Engineer

The Logician and the Engineer Author Paul J. Nahin
ISBN-10 9780691151007
Release 2013
Pages 228
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Examines how mathematician and philosopher George Boole and electrical engineer Claude Shannon became the fathers of the information age by advancing Boolean logic, and looks at the influence of other factors, including the Turing machine.

Algorithmic Puzzles

Algorithmic Puzzles Author Anany Levitin
ISBN-10 9780199740444
Release 2011-10-14
Pages 257
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Algorithmic puzzles are puzzles involving well-defined procedures for solving problems. This book will provide an enjoyable and accessible introduction to algorithmic puzzles that will develop the reader's algorithmic thinking. The first part of this book is a tutorial on algorithm design strategies and analysis techniques. Algorithm design strategies — exhaustive search, backtracking, divide-and-conquer and a few others — are general approaches to designing step-by-step instructions for solving problems. Analysis techniques are methods for investigating such procedures to answer questions about the ultimate result of the procedure or how many steps are executed before the procedure stops. The discussion is an elementary level, with puzzle examples, and requires neither programming nor mathematics beyond a secondary school level. Thus, the tutorial provides a gentle and entertaining introduction to main ideas in high-level algorithmic problem solving. The second and main part of the book contains 150 puzzles, from centuries-old classics to newcomers often asked during job interviews at computing, engineering, and financial companies. The puzzles are divided into three groups by their difficulty levels. The first fifty puzzles in the Easier Puzzles section require only middle school mathematics. The sixty puzzle of average difficulty and forty harder puzzles require just high school mathematics plus a few topics such as binary numbers and simple recurrences, which are reviewed in the tutorial. All the puzzles are provided with hints, detailed solutions, and brief comments. The comments deal with the puzzle origins and design or analysis techniques used in the solution. The book should be of interest to puzzle lovers, students and teachers of algorithm courses, and persons expecting to be given puzzles during job interviews.

Deterministic Operations Research

Deterministic Operations Research Author David J. Rader
ISBN-10 9781118627358
Release 2013-06-07
Pages 632
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Uniquely blends mathematical theory and algorithm design for understanding and modeling real-world problems Optimization modeling and algorithms are key components to problem-solving across various fields of research, from operations research and mathematics to computer science and engineering. Addressing the importance of the algorithm design process. Deterministic Operations Research focuses on the design of solution methods for both continuous and discrete linear optimization problems. The result is a clear-cut resource for understanding three cornerstones of deterministic operations research: modeling real-world problems as linear optimization problem; designing the necessary algorithms to solve these problems; and using mathematical theory to justify algorithmic development. Treating real-world examples as mathematical problems, the author begins with an introduction to operations research and optimization modeling that includes applications form sports scheduling an the airline industry. Subsequent chapters discuss algorithm design for continuous linear optimization problems, covering topics such as convexity. Farkas’ Lemma, and the study of polyhedral before culminating in a discussion of the Simplex Method. The book also addresses linear programming duality theory and its use in algorithm design as well as the Dual Simplex Method. Dantzig-Wolfe decomposition, and a primal-dual interior point algorithm. The final chapters present network optimization and integer programming problems, highlighting various specialized topics including label-correcting algorithms for the shortest path problem, preprocessing and probing in integer programming, lifting of valid inequalities, and branch and cut algorithms. Concepts and approaches are introduced by outlining examples that demonstrate and motivate theoretical concepts. The accessible presentation of advanced ideas makes core aspects easy to understand and encourages readers to understand how to think about the problem, not just what to think. Relevant historical summaries can be found throughout the book, and each chapter is designed as the continuation of the “story” of how to both model and solve optimization problems by using the specific problems-linear and integer programs-as guides. The book’s various examples are accompanied by the appropriate models and calculations, and a related Web site features these models along with Maple™ and MATLAB® content for the discussed calculations. Thoroughly class-tested to ensure a straightforward, hands-on approach, Deterministic Operations Research is an excellent book for operations research of linear optimization courses at the upper-undergraduate and graduate levels. It also serves as an insightful reference for individuals working in the fields of mathematics, engineering, computer science, and operations research who use and design algorithms to solve problem in their everyday work.

Magical Mathematics

Magical Mathematics Author Persi Diaconis
ISBN-10 9780691151649
Release 2011-10-23
Pages 244
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Magical Mathematics reveals the secrets of fun-to-perform card tricks—and the profound mathematical ideas behind them—that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today’s mathematical knowledge. Diaconis and Graham tell the stories—and reveal the best tricks—of the eccentric and brilliant inventors of mathematical magic. The book exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card Monte, traces the history of mathematical magic back to the oldest mathematical trick—and much more.

Effective Programming

Effective Programming Author Jeff Atwood
ISBN-10 147830054X
Release 2012-07-04
Pages 278
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ABOUT THE BOOK Jeff Atwood began the Coding Horror blog in 2004, and is convinced that it changed his life. He needed a way to keep track of software development over time - whatever he was thinking about or working on. He researched subjects he found interesting, then documented his research with a public blog post, which he could easily find and refer to later. Over time, increasing numbers of blog visitors found the posts helpful, relevant and interesting. Now, approximately 100,000 readers visit the blog per day and nearly as many comment and interact on the site. Effective Programming: More Than Writing Code is your one-stop shop for all things programming. Jeff writes with humor and understanding, allowing for both seasoned programmers and newbies to appreciate the depth of his research. From such posts as "The Programmer's Bill of Rights" and "Why Cant Programmers... Program?" to "Working With the Chaos Monkey," this book introduces the importance of writing responsible code, the logistics involved, and how people should view it more as a lifestyle than a career. TABLE OF CONTENTS - Introduction - The Art of Getting Shit Done - Principles of Good Programming - Hiring Programmers the Right Way - Getting Your Team to Work Together - The Batcave: Effective Workspaces for Programmers - Designing With the User in Mind - Security Basics: Protecting Your Users' Data - Testing Your Code, So it Doesn't Suck More Than it Has To - Building, Managing and Benefiting from a Community - Marketing Weasels and How Not to Be One - Keeping Your Priorities Straight EXCERPT FROM THE BOOK As a software developer, you are your own worst enemy. The sooner you realize that, the better off you'll be.I know you have the best of intentions. We all do. We're software developers; we love writing code. It's what we do. We never met a problem we couldn't solve with some duct tape, a jury-rigged coat hanger and a pinch of code. But Wil Shipley argues that we should rein in our natural tendencies to write lots of code: The fundamental nature of coding is that our task, as programmers, is to recognize that every decision we make is a trade-off. To be a master programmer is to understand the nature of these trade-offs, and be conscious of them in everything we write.In coding, you have many dimensions in which you can rate code: Brevity of codeFeaturefulnessSpeed of executionTime spent codingRobustnessFlexibility Now, remember, these dimensions are all in opposition to one another. You can spend three days writing a routine which is really beautiful and fast, so you've gotten two of your dimensions up, but you've spent three days, so the "time spent coding" dimension is way down.So, when is this worth it? How do we make these decisions? The answer turns out to be very sane, very simple, and also the one nobody, ever, listens to: Start with brevity. Increase the other dimensions as required by testing. I couldn't agree more. I've given similar advice when I exhorted developers to Code Smaller. And I'm not talking about a reductio ad absurdum contest where we use up all the clever tricks in our books to make the code fit into less physical space. I'm talking about practical, sensible strategies to reduce the volume of code an individual programmer has to read to understand how a program works. Here's a trivial little example of what I'm talking about: if (s == String.Empty)if (s == "") It seems obvious to me that the latter case is... the book to read more!

Who s 1

Who s  1 Author Amy N. Langville
ISBN-10 9781400841677
Release 2012-02-26
Pages 272
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A website's ranking on Google can spell the difference between success and failure for a new business. NCAA football ratings determine which schools get to play for the big money in postseason bowl games. Product ratings influence everything from the clothes we wear to the movies we select on Netflix. Ratings and rankings are everywhere, but how exactly do they work? Who's #1? offers an engaging and accessible account of how scientific rating and ranking methods are created and applied to a variety of uses. Amy Langville and Carl Meyer provide the first comprehensive overview of the mathematical algorithms and methods used to rate and rank sports teams, political candidates, products, Web pages, and more. In a series of interesting asides, Langville and Meyer provide fascinating insights into the ingenious contributions of many of the field's pioneers. They survey and compare the different methods employed today, showing why their strengths and weaknesses depend on the underlying goal, and explaining why and when a given method should be considered. Langville and Meyer also describe what can and can't be expected from the most widely used systems. The science of rating and ranking touches virtually every facet of our lives, and now you don't need to be an expert to understand how it really works. Who's #1? is the definitive introduction to the subject. It features easy-to-understand examples and interesting trivia and historical facts, and much of the required mathematics is included.

Category Theory

Category Theory Author Steve Awodey
ISBN-10 9780191612558
Release 2010-06-17
Pages 328
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Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists! This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.

Math Girls

Math Girls Author Hiroshi Yuki
ISBN-10 9780983951308
Release 2011
Pages 288
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"Combining mathematical rigor with light romance, Math Girls is a unique introduction to advanced mathematics, delivered through the eyes of three students as they learn to deal with problems seldom found in textbooks."--Front flap.