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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 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.



Mathematics for Operations Research

Mathematics for Operations Research Author W. H. Marlow
ISBN-10 9780486677231
Release 1993
Pages 483
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Practical and applications-oriented, this text explains effective procedures for performing mathematical tasks that arise in many fields, including operations research, engineering, systems sciences, statistics, and economics. Most of the examples and many of the 1,300 problems illustrate techniques, and nearly all of the tables display reference material for procedures. 1978 edition.



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)



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.



Viewpoints

Viewpoints Author Marc Frantz
ISBN-10 140083905X
Release 2011-07-05
Pages 248
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An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students. Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists--who include mathematicians and scientists--examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery. Classroom-tested activities and problem solving Accessible problems that move beyond regular art school curriculum Multiple solutions of varying difficulty and applicability Appropriate for students of all mathematics and art levels Original and exclusive essays by contemporary artists Forthcoming: Instructor's manual (available only to teachers)



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 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.



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.



Loving and Hating Mathematics

Loving and Hating Mathematics Author Reuben Hersh
ISBN-10 1400836115
Release 2010-12-13
Pages 432
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Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math. This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.



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.



Number Words and Number Symbols

Number Words and Number Symbols Author Karl Menninger
ISBN-10 9780486319773
Release 2013-04-10
Pages 512
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Classic study discusses number sequence and number language, then explores written numerals and computations in a wide range of cultures. 282 illustrations. "Superior narrative ability." — Library Journal.



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... ...buy the book to read more!



Model Building in Mathematical Programming

Model Building in Mathematical Programming Author H. Paul Williams
ISBN-10 9781118506189
Release 2013-01-18
Pages 432
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The 5th edition of Model Building in Mathematical Programming discusses the general principles of model building in mathematical programming and demonstrates how they can be applied by using several simplified but practical problems from widely different contexts. Suggested formulations and solutions are given together with some computational experience to give the reader a feel for the computational difficulty of solving that particular type of model. Furthermore, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations. By emphasizing the importance of the building and interpreting of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject. In this article, H.P. Williams explains his original motivation and objectives in writing the book, how it has been modified and updated over the years, what is new in this edition and why it has maintained its relevance and popularity over the years: http://www.statisticsviews.com/details/feature/4566481/Model-Building-in-Mathematical-Programming-published-in-fifth-edition.html



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.