Haskell emerged in the last decade as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvellous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures.This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others.

    The presentation develops physical insight by stressing the microscopic content of the theory.

    

    Topics covered in the book include linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and much more!The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems.This book can serve as a complete Algebra I course, and also includes many concepts covered in Algebra II. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of algebra will find this book an instrumental part of their mathematics libraries.656About the author: Richard Rusczyk is a co-author of Art of Problem Solving, Volumes 1 and 2, the author of Art of Problem Solving's Introduction to Geometry. He was a national MATHCOUNTS participant, a USA Math Olympiad winner, and is currently director of the USA Mathematical Talent Search.

    Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science.

    Written By Two Of Today'S Most Respected Computer Science Educators, Nell Dale And John Lewis, The Text Provides A Broad Overview Of The Many Aspects Of The Discipline From A Generic View Point. Separate Program Language Chapters Are Available As Bundle Items For Those Instructors Who Would Like To Explore A Particular Programming Language With Their Students. The Many Layers Of Computing Are Thoroughly Explained Beginning With The Information Layer, Working Through The Hardware, Programming, Operating Systems, Application, And Communication Layers, And Ending With A Discussion On The Limitations Of Computing. Perfect For Introductory Computing And Computer Science Courses, Computer Science Illuminated, Third Edition's Thorough Presentation Of Computing Systems Provides Computer Science Majors With A Solid Foundation For Further Study, And Offers Non-Majors A Comprehensive And Complete Introduction To Computing.

    In this richly illustrated book, accessible examples are used to show how information theory can be understood in terms of everyday games like '20 Questions', and the simple MatLab programs provided give hands-on experience of information theory in action. Written in a tutorial style, with a comprehensive glossary, this text represents an ideal primer for novices who wish to become familiar with the basic principles of information theory.Download chapter 1 from http://jim-stone.staff.shef.ac.uk/Boo...

    Covering various the materials needed by students in engineering, science, and mathematics, this calculus text makes effective use of computing technology, graphics, and applications. It presents at least two technology projects in each chapter.

    This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

    Collected here to keep your wits sharp, The Best Brain Teasers of All Time features the cleverest brain teasers from around the world and throughout history.The Best Brain Teasers of All Time gives you hours of fun-filled entertainment with brain teasers that develop your problem-solving skills in math, logic, and wordplay. Organized as an integrated challenge, these brain teasers build in momentum as they increase in difficulty from classic nursery rhymes to the riddle of the sphinx.The Best Brain Teasers of All Time puts your mind to the test with: 125 Brain Teasers that require no special skills to solve. Plus, each question comes with an optional clue in case you get stumped and a handy answer key in the back to test yourself or play with friends Brain Teasers for Every Level that cater to beginners and advanced masterminds alike, with brain teasers organized by level of difficulty to improve your skills as you move forward Hints of History that provide fun facts and background information for every brain teaser Get ready to sharpen your wit with every “aha” moment. The Best Brain Teasers of All Time is a go-to source for timeless fun and mind-blowing challenges.

    More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you:  Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved.

    This edition contains NEW tables on Properties of Ionic Liquids, Solubilities of Hydrocarbons in Sea Water, Solubility of Organic Compounds in Superheated Water, and Nutritive Value of Foods. It also updates many tables including Critical Constants, Heats of Vaporization, Aqueous Solubility of Organic Compounds, Vapor Pressure of Mercury, Scientific Abbreviations and Symbols, and Bond Dissociation Energies. The 88th Edition also presents a new Foreword written by Dr. Harold Kroto, a 1996 Nobel Laureate in Chemistry.

    In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets.In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

    Plethora of Solved examples help the students know the variety of problems & Procedure to solve them. Plenty of practice problems facilitate testing their understanding of the subject. Key Features: Covers the syllabus of all the four papers of Engineering Mathematics Detailed coverage of topics with lot of solved examples rendering clear understanding to the students. Engineering Applications of Integral Calculus, Ordinary Differential Equations of First and Higher Order, & Partial Differential Equations illustrate the use of these methods. Chapters on preliminary topics like Analytical Solid Geometry Matrices and Determinants Sequence and Series Complex Numbers Vector Algebra Differential and Integral Calculus Extensive coverage of Probability and Statistics (5 chapters). Covers the syllabus of all the four papers of Engineering Mathematics Engineering Applications of Integral Calculus, Ordinary Differential Equations of First and Higher Order, & Partial Differential Equations illustrate the use of these methods. Extensive coverage of ?Probability and Statistics (5 chapters) Table of Content: PART I PRELIMI NARIES Chapter 1 Vector Algebra , Theory of Equations ,Complex Numbers PART II DIFFERENTIAL AND INTEGRAL CALCULUS

    But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them.Hidden symmetries were first discovered nearly two hundred years ago by French mathematician �variste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination.The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.