In A Brief History of Mathematical Thought, Luke Heaton explores how the language of mathematics has evolved over time, enabling new technologies and shaping the way people think. From stone-age rituals to algebra, calculus, and the concept of computation, Heaton shows the enormous influence of mathematics on science, philosophy and the broader human story. The book traces the fascinating history of mathematical practice, focusing on the impact of key conceptual innovations. Its structure of thirteen chapters split between four sections is dictated by a combination of historical and thematic considerations. In the first section, Heaton illuminates the fundamental concept of number. He begins with a speculative and rhetorical account of prehistoric rituals, before describing the practice of mathematics in Ancient Egypt, Babylon and Greece. He then examines the relationship between counting and the continuum of measurement, and explains how the rise of algebra has dramatically transformed our world. In the second section, he explores the origins of calculus and the conceptual shift that accompanied the birth of non-Euclidean geometries. In the third section, he examines the concept of the infinite and the fundamentals of formal logic. Finally, in section four, he considers the limits of formal proof, and the critical role of mathematics in our ongoing attempts to comprehend the world around us. The story of mathematics is fascinating in its own right, but Heaton does more than simply outline a history of mathematical ideas. More importantly, he shows clearly how the history and philosophy of maths provides an invaluable perspective on human nature.

    The book has been systematically revised throughout with most chapters entirely new to this edition. The second edition features substantial extra coverage of methodological issues, an additional chapter on the philosophical underpinnings of the study of politics and a simplified structure for the presentation of theories and approaches.

    In The Perfect Bet, mathematician and award-winning writer Adam Kucharski tells the astonishing story of how the experts have succeeded, revolutionizing mathematics and science in the process. The house can seem unbeatable. Kucharski shows us just why it isn't. Even better, he demonstrates how the search for the perfect bet has been crucial for the scientific pursuit of a better world.

    Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra.

    The material is arranged chronologically beginning with archaic origins and covers Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions done to the nineteenth century and present day. There are revised references and bibliographies and revised and expanded chapters on the nineteeth and twentieth centuries.

    Enjoy a thrilling intergalactic tour as Andrew Thomas redefines the force of gravity and introduces a brave new view of the universe!

    The chapters may be read independently of one another. But when read in order, they tell a more or less continuous story. We begin with some reflections about the legacy of Socrates and then go on to the existence of God, which is perhaps the most basic philosophical question of all because our answer to it influences how we will answer all the others. This leads naturally to a discussion of death and the soul, and then to more modern ideas about the nature of persons. The later chapters are about whether it is possible for us to have objective knowledge in either science or ethics. James Rachels, from the Preface Problems from Philosophy and The Truth About the World: Basic Readings in Philosophy are at once James Rachels' newest contributions to philosophy and his last. In these two books, Rachels found a culminating expression for his love of philosophy.

    We're all looking for new ways of thinking that can bring about real solutions to modern problems, from the pursuit of inner serenity to solving world conflicts. In Do You QuantumThink? author Dianne Collins shares her ingenious discovery that reveals a critical missing link to make sense of our changing times. Her discovery provides us with the understanding and methodology to rise above problems of today by laying the foundation for an entirely new way to think.Part science, part philosophy, part spirituality, Do You QuantumThink? draws on a wide spectrum of sources, from cutting edge innovations in the sciences to the insights of the world's greatest spiritual leaders. This book will make you laugh, free you from limiting ideas, and introduce you to the most advanced principles and practical methods for living. Do You QuantumThink? will rock your world in the best of ways as you experience one revelation after another.

    Highly recommended for graduate-level libraries.' ChoiceThis highly successful text, which first appeared in the year 1972 and has continued to be popular ever since, has now been brought up-to-date by incorporating the remarkable developments in the field of 'phase transitions and critical phenomena' that took place over the intervening years. This has been done by adding three new chapters (comprising over 150 pages and containing over 60 homework problems) which should enhance the usefulness of the book for both students and instructors. We trust that this classic text, which has been widely acclaimed for its clean derivations and clear explanations, will continue to provide further generations of students a sound training in the methods of statistical physics.

     Learn the essential concepts using concrete analogies and vivid diagrams, not mechanical definitions. Calculus isn't a set of rules, it's a specific, practical viewpoint we can apply to everyday thinking. Frustrated With Abstract, Mechanical Lessons? I was too. Despite years of classes, I didn't have a strong understanding of calculus concepts. Sure, I could follow mechanical steps, but I had no lasting intuition. The classes I've seen are too long, taught in the wrong order, and without solid visualizations. Here's how this course is different: 1) It gets to the point. A typical class plods along, saving concepts like Integrals until Week 8. I want to see what calculus can offer by Minute 8. Each compact, tightly-written lesson can be read in 15 minutes. 2) Concepts are taught in their natural order. Most classes begin with the theory of limits, a technical concept discovered 150 years after calculus was invented. That's like putting a new driver into a Formula-1 racecar on day 1. We can begin with the easy-to-grasp concepts discovered 2000 years ago. 3) It has vivid analogies and visualizations. Calculus is usually defined as the "study of change"... which sounds like history or geology. Instead of an abstract definition, we'll see calculus a step-by-step viewpoint to explore patterns. 4) It's written by a human, for humans. I'm not a haughty professor or strict schoolmarm. I'm a friend who saw a fun way to internalize some difficult ideas. This course is a chat over coffee, not a keep-your-butt-in-your-seat lecture. The goal is to help you grasp the Aha! moments behind calculus in hours, not a painful semester (or a decade, in my case). Join Thousands Of Happy Readers Here's a few samples of anonymous feedback as people went through the course. The material covers a variety of levels, whether you're looking for intuitive appreciation or the specifics of the rules. "I've done all of this stuff before, and I do understand calculus intuitively, but this was the most fun I've had going through this kind of thing. The informal writing and multitude of great analogies really helps this become an enjoyable read and the rest is simple after that - you make this seem easy, but at the same time, you aren't doing it for us…This is what math education is supposed to be like :)" "I have psychology and medicine background so I relate your ideas to my world. To me the most useful idea was what each circle production feels like. Rings are natural growth…Slices are automatable chunks and automation cheapens production… Boards in the shape on an Arch are psychologically most palatable for work (wind up, hard part, home stretch). Brilliant and kudos, from one INTP to another." "I like how you're introducing both derivatives and integrals at the same time - it's really helps with understanding the relationship between them. Also, I appreciate how you're coming from such a different angle than is traditionally taken - it's always interesting to see where you decide to go next." "That was breathtaking. Seriously, mail my air back please, I've grown used to it. Beautiful work, thank you. Lesson 15 was masterful. I am starting to feel calculus. "d/dx is good" (sorry, couldn't resist!)."

    Big and informative, "The New York Times Book of Mathematics" gathers more than 110 articles written from 1892 to 2010 that cover statistics, coincidences, chaos theory, famous problems, cryptography, computers, and many other topics. Edited by Pulitzer Prize finalist and senior "Times" writer Gina Kolata, and featuring renowned contributors such as James Gleick, William L. Laurence, Malcolm W. Browne, George Johnson, and John Markoff, it's a must-have for any math and science enthusiast!

    It is not a mere reorganization of the data into a new kind of library catalogue, nor another specualtive philosophy about the nature of man and language, but rather a rigorus explication of our intuitions about our language in terms of an overt axiom system, the theorems derivable from it, explicit results which may be compared with new data and other intuitions, all based plainly on an overt theory of the internal structure of languages; and it may well provide an opportunity for the application of explicity measures of simplicity to decide preference of one form over another form of grammar.