Taking Sudoku Seriously
Taking Sudoku Seriously

Author: Jason Rosenhouse

Publisher: Oxford University Press

Published: 2012-01-19

Total Pages: 227

ISBN-13: 0199913153

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Packed with more than a hundred color illustrations and a wide variety of puzzles and brainteasers, Taking Sudoku Seriously uses this popular craze as the starting point for a fun-filled introduction to higher mathematics. How many Sudoku solution squares are there? What shapes other than three-by-three blocks can serve as acceptable Sudoku regions? What is the fewest number of starting clues a sound Sudoku puzzle can have? Does solving Sudoku require mathematics? Jason Rosenhouse and Laura Taalman show that answering these questions opens the door to a wealth of interesting mathematics. Indeed, they show that Sudoku puzzles and their variants are a gateway into mathematical thinking generally. Among many topics, the authors look at the notion of a Latin square--an object of long-standing interest to mathematicians--of which Sudoku squares are a special case; discuss how one finds interesting Sudoku puzzles; explore the connections between Sudoku, graph theory, and polynomials; and consider Sudoku extremes, including puzzles with the maximal number of vacant regions, with the minimal number of starting clues, and numerous others. The book concludes with a gallery of novel Sudoku variations--just pure solving fun! Most of the puzzles are original to this volume, and all solutions to the puzzles appear in the back of the book or in the text itself. A math book and a puzzle book, Taking Sudoku Seriously will change the way readers look at Sudoku and mathematics, serving both as an introduction to mathematics for puzzle fans and as an exploration of the intricacies of Sudoku for mathematics buffs.

Introductory Combinatorics
Introductory Combinatorics

Author: Kenneth P. Bogart

Publisher: Harcourt Brace College Publishers

Published: 1990

Total Pages: 648

ISBN-13:

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Introductory, Combinatorics, Third Edition is designed for introductory courses in combinatorics, or more generally, discrete mathematics. The author, Kenneth Bogart, has chosen core material of value to students in a wide variety of disciplines: mathematics, computer science, statistics, operations research, physical sciences, and behavioral sciences. The rapid growth in the breadth and depth of the field of combinatorics in the last several decades, first in graph theory and designs and more recently in enumeration and ordered sets, has led to a recognition of combinatorics as a field with which the aspiring mathematician should become familiar. This long-overdue new edition of a popular set presents a broad comprehensive survey of modern combinatorics which is important to the various scientific fields of study.

The Algorithm Design Manual
The Algorithm Design Manual

Author: Steven S Skiena

Publisher: Springer Science & Business Media

Published: 2009-04-05

Total Pages: 742

ISBN-13: 1848000707

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This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency. Expanding on the first edition, the book now serves as the primary textbook of choice for algorithm design courses while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students. The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Techniques, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, Resources, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations and an extensive bibliography. NEW to the second edition: • Doubles the tutorial material and exercises over the first edition • Provides full online support for lecturers, and a completely updated and improved website component with lecture slides, audio and video • Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them • Includes several NEW "war stories" relating experiences from real-world applications • Provides up-to-date links leading to the very best algorithm implementations available in C, C++, and Java

Sage for Undergraduates
Sage for Undergraduates

Author: Gregory V. Bard

Publisher: American Mathematical Soc.

Published: 2015-02-16

Total Pages: 378

ISBN-13: 1470411113

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As the open-source and free competitor to expensive software like MapleTM, Mathematica®, Magma, and MATLAB®, Sage offers anyone with access to a web browser the ability to use cutting-edge mathematical software and display his or her results for others, often with stunning graphics. This book is a gentle introduction to Sage for undergraduate students toward the end of Calculus II (single-variable integral calculus) or higher-level course work such as Multivariate Calculus, Differential Equations, Linear Algebra, or Math Modeling. The book assumes no background in computer science, but the reader who finishes the book will have learned about half of a first semester Computer Science I course, including large parts of the Python programming language. The audience of the book is not only math majors, but also physics, engineering, finance, statistics, chemistry, and computer science majors.

Algorithms and Data Structures
Algorithms and Data Structures

Author: Kurt Mehlhorn

Publisher: Springer Science & Business Media

Published: 2008-05-27

Total Pages: 300

ISBN-13: 3540779787

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Algorithms are at the heart of every nontrivial computer application, and algorithmics is a modern and active area of computer science. Every computer scientist and every professional programmer should know about the basic algorithmic toolbox: structures that allow efficient organization and retrieval of data, frequently used algorithms, and basic techniques for modeling, understanding and solving algorithmic problems. This book is a concise introduction addressed to students and professionals familiar with programming and basic mathematical language. Individual chapters cover arrays and linked lists, hash tables and associative arrays, sorting and selection, priority queues, sorted sequences, graph representation, graph traversal, shortest paths, minimum spanning trees, and optimization. The algorithms are presented in a modern way, with explicitly formulated invariants, and comment on recent trends such as algorithm engineering, memory hierarchies, algorithm libraries and certifying algorithms. The authors use pictures, words and high-level pseudocode to explain the algorithms, and then they present more detail on efficient implementations using real programming languages like C++ and Java. The authors have extensive experience teaching these subjects to undergraduates and graduates, and they offer a clear presentation, with examples, pictures, informal explanations, exercises, and some linkage to the real world. Most chapters have the same basic structure: a motivation for the problem, comments on the most important applications, and then simple solutions presented as informally as possible and as formally as necessary. For the more advanced issues, this approach leads to a more mathematical treatment, including some theorems and proofs. Finally, each chapter concludes with a section on further findings, providing views on the state of research, generalizations and advanced solutions.

The Sourcebook for Teaching Science, Grades 6-12
The Sourcebook for Teaching Science, Grades 6-12

Author: Norman Herr

Publisher: John Wiley & Sons

Published: 2008-08-11

Total Pages: 614

ISBN-13: 0787972983

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The Sourcebook for Teaching Science is a unique, comprehensive resource designed to give middle and high school science teachers a wealth of information that will enhance any science curriculum. Filled with innovative tools, dynamic activities, and practical lesson plans that are grounded in theory, research, and national standards, the book offers both new and experienced science teachers powerful strategies and original ideas that will enhance the teaching of physics, chemistry, biology, and the earth and space sciences.

Constraint Solving and Planning with Picat
Constraint Solving and Planning with Picat

Author: Neng-Fa Zhou

Publisher: Springer

Published: 2015-11-07

Total Pages: 155

ISBN-13: 3319258834

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This book introduces a new logic-based multi-paradigm programming language that integrates logic programming, functional programming, dynamic programming with tabling, and scripting, for use in solving combinatorial search problems, including CP, SAT, and MIP (mixed integer programming) based solver modules, and a module for planning that is implemented using tabling. The book is useful for undergraduate and graduate students, researchers, and practitioners.

Security, Privacy and Reliability in Computer Communications and Networks
Security, Privacy and Reliability in Computer Communications and Networks

Author: Kewei Sha

Publisher: River Publishers

Published: 2016-11-30

Total Pages: 446

ISBN-13: 8793379897

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Future communication networks aim to build an intelligent and efficient living environment by connecting a variety of heterogeneous networks to fulfill complicated tasks. These communication networks bring significant challenges in building secure and reliable communication networks to address the numerous threat and privacy concerns. New research technologies are essential to preserve privacy, prevent attacks, and achieve the requisite reliability. Security, Privacy and Reliability in Computer Communications and Networks studies and presents recent advances reflecting the state-of-the-art research achievements in novel cryptographic algorithm design, intrusion detection, privacy preserving techniques and reliable routing protocols. Technical topics discussed in the book include: Vulnerabilities and Intrusion DetectionCryptographic Algorithms and EvaluationPrivacy Reliable Routing Protocols This book is ideal for personnel in computer communication and networking industries as well as academic staff and collegial, master, Ph.D. students in computer science, computer engineering, cyber security, information insurance and telecommunication systems.

Pattern-Based Constraint Satisfaction and Logic Puzzles (Second Edition)
Pattern-Based Constraint Satisfaction and Logic Puzzles (Second Edition)

Author: Denis Berthier

Publisher:

Published: 2015-07-11

Total Pages: 568

ISBN-13: 9781326350642

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""Pattern-Based Constraint Satisfaction and Logic Puzzles (Second Edition)"" develops a pure logic, pattern-based perspective of solving the finite Constraint Satisfaction Problem (CSP), with emphasis on finding the ""simplest"" solution. Different ways of reasoning with the constraints are formalised by various families of ""resolution rules,"" each of them carrying its own notion of simplicity. A large part of the book illustrates the power of the approach by applying it to various popular logic puzzles. It provides a unified view of how to model and solve them, even though they involve very different types of constraints: obvious symmetric ones in Sudoku, non-symmetric but transitive ones in Futoshiki, topological and geometric ones in Map colouring, Numbrix and Hidato, non-binary arithmetic ones in Kakuro and both non-binary and non-local ones in Slitherlink. It also shows that the most familiar techniques for these puzzles can be understood as mere application-specific presentations of the general rules.

The Tower of Hanoi – Myths and Maths
The Tower of Hanoi – Myths and Maths

Author: Andreas M. Hinz

Publisher: Springer Science & Business Media

Published: 2013-01-31

Total Pages: 340

ISBN-13: 3034802374

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This is the first comprehensive monograph on the mathematical theory of the solitaire game “The Tower of Hanoi” which was invented in the 19th century by the French number theorist Édouard Lucas. The book comprises a survey of the historical development from the game’s predecessors up to recent research in mathematics and applications in computer science and psychology. Apart from long-standing myths it contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs, including also unpublished material. The main objects of research today are the so-called Hanoi graphs and the related Sierpiński graphs. Acknowledging the great popularity of the topic in computer science, algorithms and their correctness proofs form an essential part of the book. In view of the most important practical applications of the Tower of Hanoi and its variants, namely in physics, network theory, and cognitive (neuro)psychology, other related structures and puzzles like, e.g., the “Tower of London”, are addressed. Numerous captivating integer sequences arise along the way, but also many open questions impose themselves. Central among these is the famed Frame-Stewart conjecture. Despite many attempts to decide it and large-scale numerical experiments supporting its truth, it remains unsettled after more than 70 years and thus demonstrates the timeliness of the topic. Enriched with elaborate illustrations, connections to other puzzles and challenges for the reader in the form of (solved) exercises as well as problems for further exploration, this book is enjoyable reading for students, educators, game enthusiasts and researchers alike.