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.

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    This connectedness is found in many incarnations: in the rapid growth of the Internet, in the ease with which global communication takes place, and in the ability of news and information as well as epidemics and financial crises to spread with surprising speed and intensity. These are phenomena that involve networks, incentives, and the aggregate behavior of groups of people; they are based on the links that connect us and the ways in which our decisions can have subtle consequences for others. This introductory undergraduate textbook takes an interdisciplinary look at economics, sociology, computing and information science, and applied mathematics to understand networks and behavior. It describes the emerging field of study that is growing at the interface of these areas, addressing fundamental questions about how the social, economic, and technological worlds are connected.

    Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.

    

    Following on the success of the first six editions of the series, this work introduces theoretical and pedagogical innovations in statics, dynamics, and mechanics of materials education.

    Intuitive Biostatistics covers all the topics typically found in an introductory statistics text, but with the emphasis on confidence intervals rather than P values, making it easier for students to understand both. Additionally, it introduces a broad range of topics left out of most other introductory texts but used frequently in biomedical publications, including survival curves. multiple comparisons, sensitivity and specificity of lab tests, Bayesian thinking, lod scores, and logistic, proportional hazards and nonlinear regression. By emphasizing interpretation rather than calculation, this text provides a clear and virtually painless introduction to statistical principles for those students who will need to use statistics constantly in their work. In addition, its practical approach enables readers to understand the statistical results published in biological and medical journals.

    But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place."Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct--including the revelation that ants can actually count how many steps they've taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. "Here's Looking at Euclid "is a rare gem that brings the beauty of math to life.

    Features exceptionally clear explanations and descriptions, step-by-step examples, more than 50 practical applications, over 2000 easy-to-challenging practice problems, and comprehensive coverage of essentials. PSpice, OrCAd version 9.2 Lite Edition, Multisims 2001 version of Electronics Workbench, and MathCad software references and examples are used throughout. Computer programs (C++, BASIC and PSpice) are printed in color, as they run, at the point in the book where they are discussed. Current and Voltage. Resistance. Ohm's Law, Power, and Energy. Series Circuits. Parallel Circuits. Series-Parallel Networks. Methods of Analysis & Selected Topics. Network Theorems. Capacitors. Magnetic Circuits. Inductors. Sinusodial Alternating Waveforms. The Basic Elements and Phasors. Series and Parallel ac Circuits. Series-Parallel ac Networks. Methods of Analysis and Related Topics. Network Theorems (ac). Power (ac). Resonance. Transformers. Polyphase Systems. Decibels, Filters, and Bode Points. Pulse Waveforms and the R-C Response. Nonsinusodial Circuits. System Analysis: An Introduction. For those working in electronic technology.

    Theory has been provided in points between each chapter for clarifying relevant basic concepts. The book consist four parts algebra and trigonometry, fundamentals of analysis, geometry and vector algebra and the problems and questions set during oral examinations. Each chapter consist topic wise problems. Sample examples are provided after each text for understanding the topic well. The fourth part "oral examination problems and question" includes samples suggested by the higher schools for the help of students. Answers and hints are given at the end of the book for understanding the concept well. About the Book: Problems in Mathematics with Hints and Solutions Contents: Preface Part 1. Algebra, Trigonometry and Elementary Functions Problems on Integers. Criteria for Divisibility Real Number, Transformation of Algebraic Expressions Mathematical Induction. Elements of Combinatorics. BinomialTheorem Equations and Inequalities of the First and the SecondDegree Equations of Higher Degrees, Rational Inequalities Irrational Equations and Inequalities Systems of Equations and Inequalities The Domain of Definition and the Range of a Function Exponential and Logarithmic Equations and Inequalities Transformations of Trigonometric Expressions. InverseTrigonometric Functions Solutions of Trigonometric Equations, Inequalities and Systemsof Equations Progressions Solutions of Problems on Derivation of Equations Complex Numbers Part 2. Fundamentals of Mathematical Analysis Sequences and Their Limits. An Infinitely Decreasing GeometricProgression. Limits of Functions The Derivative. Investigating the Behaviors of Functions withthe Aid of the Derivative Graphs of Functions The Antiderivative. The Integral. The Area of a CurvilinearTrapezoid Part 3. Geometry and Vector Algebra Vector Algebra Plane Geometry. Problems on Proof Plane Geometry. Construction Problems Plane Geometry. C

    In 1935, aged 22, he developed the mathematical theory upon which all subsequent stored-program digital computers are modeled.At the outbreak of hostilities with Germany in September 1939, he joined the Government Codebreaking team at Bletchley Park, Buckinghamshire and played a crucial role in deciphering Engima, the code used by the German armed forces to protect their radio communications. Turing's work on the versionof Enigma used by the German navy was vital to the battle for supremacy in the North Atlantic. He also contributed to the attack on the cyphers known as Fish, which were used by the German High Command for the encryption of signals during the latter part of the war. His contribution helped toshorten the war in Europe by an estimated two years.After the war, his theoretical work led to the development of Britain's first computers at the National Physical Laboratory and the Royal Society Computing Machine Laboratory at Manchester University.Turing was also a founding father of modern cognitive science, theorizing that the cortex at birth is an unorganized machine which through training becomes organized into a universal machine or something like it. He went on to develop the use of computers to model biological growth, launchingthe discipline now referred to as Artificial Life.The papers in this book are the key works for understanding Turing's phenomenal contribution across all these fields. The collection includes Turing's declassified wartime Treatise on the Enigma; letters from Turing to Churchill and to codebreakers; lectures, papers, and broadcasts which opened upthe concept of AI and its implications; and the paper which formed the genesis of the investigation of Artifical Life.

    

    The book includes full discussions of many problems of current interest which are not treated in any extant book, and all these matters are considered with perception and understanding."—S. Chandrasekhar "A tour de force: lucid, straightforward, mathematically rigorous, exacting in the analysis of the theory in its physical aspect."—L. P. Hughston, Times Higher Education Supplement"Truly excellent. . . . A sophisticated text of manageable size that will probably be read by every student of relativity, astrophysics, and field theory for years to come."—James W. York, Physics Today

    This book provides an introduction to the field of solid state physics for undergraduate students in physics, chemistry, engineering, and materials science.

    Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory.All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points.The Second Edition features: * Chapters reorganized to improve teaching * 200 new problems * New material on source coding, portfolio theory, and feedback capacity * Updated referencesNow current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications.