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.

    Boundless works with subject matter experts to select the best open educational resources available on the web, review the content for quality, and create introductory, college-level textbooks designed to meet the study needs of university students.<br><br>This textbook covers:<br><br><b>Human Anatomy and Physiology Introduction</b> -- Anatomy and Physiology Overview, Life, Homeostasis, Anatomical Terms, Clinical Cases<br><br><b>General Chemistry</b> -- Matter and Energy, Element Properties: Atomic structure, Chemical Bonds, Chemical Reactions, Inorganic Compounds, Organic Compounds<br><br><b>Cellular Structure and Function</b> -- the study of cells, Cell membranes and the fluid mosaic model, Transport across membranes, How reception works in cell signaling, Nucleus and Ribosomes, Organelles, The Cytoskeleton, External cellular components, Cell division: process and importance, The cell cycle, Transcription and translation, RNA processing, Translation to a polypeptide, Transcription, Apoptosis signals an orderly cell death<br><br><b>Tissues</b> -- Epithelial Tissue, Cell Junctions, Clinical Cases, Tissue Repair, Tissue Development, Cancer, Connective Tissue, Membranes, Nervous Tissue<br><br><b>The Integumentary System</b> -- The Skin, Accessory Structures of the Skin, Functions of the Integumentary System, Wound Healing, Integumentary System Development, Skin Disorders, Imbalances, Diseases, and Clinical Cases<br><br><b>Skeletal Tissue</b> -- Cartilage, Bone Classification, Bone Formation, Bone and Calcium, Bone Development, Bone Diseases, Disorders, Imbalances, and Clinical Cases<br><br><b>The Skeletal System</b> -- Overview of the Musculoskeletal system, Divisions of the Skeletal System, The Axial Skeleton, Skull, Hyoid Bone, Vertebral Column, Thorax, Clinical Cases of the Axial Skeleton, The Appendicular Skeleton, The Pectoral (Shoulder) Girdle, Upper Limb, The Pelvic (Hip) Girdle, Lower Limb, Skeletal System Development, Clinical Cases of the Appendicular Skeleton<br><br><b>Joints</b> -- Classification of Joints, Synovial Joints, Joint Development, Clinical Cases<br><br><b>Muscle Tissue</b> -- Overview of Muscle Tissue, Skeletal Muscle, Control of Muscle Tension, Muscle Metabolism, Exercise and Skeletal Muscle Tissue, Smooth Muscle, Clinical Cases: Muscle Disorders, Development of Muscle<br><br><b>The Muscular System</b> -- Overview of the Muscular System, Head And Neck Muscles, Trunk Muscles, Muscles of the Upper Limb, Muscles of the Lower Limb, Clinical Cases and Muscular System Disorders<br><br><b>Nervous Tissue</b> -- Overview of the Nervous System, Neuroglia, Neurons, Collections of Nervous Tissue, Neurophysiology<br><br><b>Central Nervous System (CNS)</b> -- The Brain, Consciousness, Sleep, Language, and Memory, Protection of the Brain, Parts of The Brain Stem, The Cerebellum, The Diencephalon, Cerebral Cortex (or Cerebral Hemispheres), Functional Systems of the Cerebral Cortex, Development of the CNS, Brain Disorders and Clinical Cases, The Spinal Cord, Spinal Cord Anatomy, Disorders and Clinical Cases of the Spinal Cord<br><br><b>Peripheral Nervous System (PNS)</b> -- Sensation, Sensory Receptors, Somatosensory System, Nerves, Cranial Nerves, Spinal Nerves, Distribution of Spinal Nerves, Motor Activity, Motor Pathways, Reflexes, Pain, Development of the Nervous System, Disorders of Spinal Nerves and Clinical Cases<br><br><b>Autonomic Nervous System (ANS)</b> -- Autonomic Nervous System, ANS Anatomy, Physiology of ANS,

    What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.This sixtieth anniversary edition includes not only the original text but also an introduction by Harold Kuhn, an afterword by Ariel Rubinstein, and reviews and articles on the book that appeared at the time of its original publication in the New York Times, tthe American Economic Review, and a variety of other publications. Together, these writings provide readers a matchless opportunity to more fully appreciate a work whose influence will yet resound for generations to come.

    Readerswill find information on frequency distributions; mean, median, and mode; range, variance, and standard deviation;probability; and more.-Emphasizes Microsoft Excel for number-crunching and computationsDownload a sample chapter.

    Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical―that what is commonly called mathematics is simply later deductions from logical premises.His ideas have had a profound influence on twentieth-century work on logic and the foundations of mathematics.

    Requiring essentially no background apart from mathematical maturity, the book can be used as a reference for self-study for anyone interested in complexity, including physicists, mathematicians, and other scientists, as well as a textbook for a variety of courses and seminars. More than 300 exercises are included with a selected hint set.

     -Byte, September 1995 I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up. -Charles Long If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing. -Bill Gates It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers. -Jonathan Laventhol This first volume in the series begins with basic programming concepts and techniques, then focuses more particularly on information structures-the representation of information inside a computer, the structural relationships between data elements and how to deal with them efficiently. Elementary applications are given to simulation, numerical methods, symbolic computing, software and system design. Dozens of simple and important algorithms and techniques have been added to those of the previous edition. The section on mathematical preliminaries has been extensively revised to match present trends in research. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP), http: //msp.org

    The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    This popular Blueprints book has been refined and updated while keeping the concise, organized style and clinical high-yield content of previous editions. Features include USMLE-style questions and answers with full explanations; Key Points in every section; and a color-enhanced design that increases the usefulness of figures and tables.This edition's completely revised art program includes many additional illustrations. Each chapter in this edition ends with evidence-based references (journals) for students to do additional reading/research.

    This updated edition of Ross's classic bestseller provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries.This book now contains a new section on compound random variables that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions; a new section on hiddden Markov chains, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely sequence of states; and a simplified approach for analyzing nonhomogeneous Poisson processes. There are also additional results on queues relating to the conditional distribution of the number found by an M/M/1 arrival who spends a time t in the system; inspection paradox for M/M/1 queues; and M/G/1 queue with server breakdown. Furthermore, the book includes new examples and exercises, along with compulsory material for new Exam 3 of the Society of Actuaries.This book is essential reading for professionals and students in actuarial science, engineering, operations research, and other fields in applied probability.

    Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, intuitive visual representations of real-world examples are used to show how Bayes' rule is actually a form of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to gain an intuitive understanding of Bayesian analysis. As an aid to understanding, online computer code (in MatLab, Python and R) reproduces key numerical results and diagrams.Stone's book is renowned for its visually engaging style of presentation, which stems from teaching Bayes' rule to psychology students for over 10 years as a university lecturer.

    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.

    The algorithms you'll use most often as a programmer have already been discovered, tested, and proven. If you want to take a hard pass on Knuth's brilliant but impenetrable theories and the dense multi-page proofs you'll find in most textbooks, this is the book for you. This fully-illustrated and engaging guide makes it easy for you to learn how to use algorithms effectively in your own programs.Grokking Algorithms is a disarming take on a core computer science topic. In it, you'll learn how to apply common algorithms to the practical problems you face in day-to-day life as a programmer. You'll start with problems like sorting and searching. As you build up your skills in thinking algorithmically, you'll tackle more complex concerns such as data compression or artificial intelligence. Whether you're writing business software, video games, mobile apps, or system utilities, you'll learn algorithmic techniques for solving problems that you thought were out of your grasp. For example, you'll be able to:Write a spell checker using graph algorithmsUnderstand how data compression works using Huffman codingIdentify problems that take too long to solve with naive algorithms, and attack them with algorithms that give you an approximate answer insteadEach carefully-presented example includes helpful diagrams and fully-annotated code samples in Python. By the end of this book, you will know some of the most widely applicable algorithms as well as how and when to use them.

    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.

    Capturing the tone of students exchanging ideas among themselves, this unique guide also explains how calculus is taught, how to get the best teachers, what to study, and what is likely to be on exams—all the tricks of the trade that will make learning the material of first-semester calculus a piece of cake. Funny, irreverent, and flexible, How to Ace Calculus shows why learning calculus can be not only a mind-expanding experience but also fantastic fun.