Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.

    Essentially, you make an initial guess, and then get more data to improve it. Bayes Theorem, or Bayes Rule, has a ton of real world applications, from estimating your risk of a heart attack to making recommendations on Netflix But It Isn't That Complicated This book is a short introduction to Bayes Theorem. It is only 15 pages long, and is intended to show you how Bayes Theorem works as quickly as possible. The examples are intentionally kept simple to focus solely on Bayes Theorem without requiring that the reader know complicated probability distributions. If you want to learn the basics of Bayes Theorem as quickly as possible, with some easy to duplicate examples, this is a good book for you.

    This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

    It moves beyond a mere study of algorithms without sacrificing the rigor that faculty desire. As in every edition, Winston reinforces the book's successful features and coverage with the most recent developments in the field. The Student Suite CD-ROM, which now accompanies every new copy of the text, contains the latest versions of commercial software for optimization, simulation, and decision analysis.

    Readers will find an enlightening history of the vacuum: how the efforts to make a better vacuum led to the discovery of the electron; the ideas of Newton, Mach, and Einstein on the nature of space and time; the mysterious aether and how Einstein did away with it; and the latest ideas that the vacuum is filled with the Higgs field. The story ranges from the absolute zero of temperature and the seething vacuum of virtual particles and anti-particles that fills space, to the extreme heat and energy of the early universe. About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    This is a new view of mathematics, not the one we learned at school but a comprehensive guide to the patterns that recur through the universe and underlie human affairs. A Beginner's Guide to Constructing, the Universe shows you: Why cans, pizza, and manhole covers are round.Why one and two weren't considered numbers by the ancient Greeks.Why squares show up so often in goddess art and board games.What property makes the spiral the most widespread shape in nature, from embryos and hair curls to hurricanes and galaxies. How the human body shares the design of a bean plant and the solar system. How a snowflake is like Stonehenge, and a beehive like a calendar. How our ten fingers hold the secrets of both a lobster a cathedral, and much more.

    It covers areas such as fundamentals, logic, counting, relations and digraphs, trees, topics in graph theory, languages and finite-state machines, and groups and coding.

    The tipping point, Mirbat, South Oman, 19 July 1972 is one of the least-known yet most crucial battles of modern times. If the SAS had been defeated at Mirbat, the Russian and Chinese plan for a communist foothold in the Middle East would have succeeded, with catastrophic consequences for the oil-hungry West. OPERATION STORM is a page-turning account of courage and resilience. Mirbat was a battle fought and won by nine SAS soldiers and a similar number of brave local people - some as young as ten years old - outnumbered by at least twenty-five to one. Roger Cole, one of the SAS soldiers who took part, and writer Richard Belfield have interviewed every SAS survivor who fought in the battle from the beginning to the end - the first time every single one of them has revealed their experience. OPERATION STORM is a classic story of bravery against impossible odds, minute by minute, bullet by bullet.

    While pure mathematics is mostly interested in abstract structures, applied mathematics sits at the interface between this abstract world and the world inwhich we live. This area of mathematics takes its nourishment from society and science and, in turn, provides a unified way to understand problems arising in diverse fields.This Very Short Introduction presents a compact yet comprehensive view of the field of applied mathematics, and explores its relationships with (pure) mathematics, science, and engineering. Explaining the nature of applied mathematics, Alain Goriely discusses its early achievements in physics andengineering, and its development as a separate field after World War II. Using historical examples, current applications, and challenges, Goriely illustrates the particular role that mathematics plays in the modern sciences today and its far-reaching potential.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

    A rapturous guide through five major Ice Age sites” (Archaeology).   The cave art of France’s Dordogne region is world-famous for the mythology and beauty of its remarkable drawings and paintings. These ancient images of lively bison, horses, and mammoths, as well as symbols of all kinds, are fascinating touchstones in the development of human culture, demonstrating how far humankind has come and reminding us of the ties that bind us across the ages.   Over more than twenty-five years of teaching and research, Christine Desdemaines-Hugon has become an unrivaled expert in the cave art and artists of the Dordogne region. In Stepping-Stones she combines her expertise in both art and archaeology to convey an intimate understanding of the “cave experience.” Her keen insights communicate not only the incomparable artistic value of these works but also the near-spiritual impact of viewing them for oneself.   Focusing on five fascinating sites, including the famed Font de Gaume and others that still remain open to the public, this book reveals striking similarities between art forms of the Paleolithic and works of modern artists and gives us a unique pathway toward understanding the culture of the Dordogne Paleolithic peoples and how it still touches our lives today.   “Her vivid descriptions help readers visualize the Cro-Magnon man or woman painting the beautiful bison, horses, mammoths, and other symbols. [A] fine reading experience.” —Library Journal

    Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge--from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool--the general principle--from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    The book has been designed to offer maximal accessibility to the widest range of students (not only those majoring in philosophy) and assumes no formal training in elementary symbolic logic. It offers a comprehensive course covering all basic definitions of induction and probability, and considers such topics as decision theory, Bayesianism, frequency ideas, and the philosophical problem of induction. The key features of the book are: * A lively and vigorous prose style* Lucid and systematic organization and presentation of the ideas* Many practical applications* A rich supply of exercises drawing on examples from such fields as psychology, ecology, economics, bioethics, engineering, and political science* Numerous brief historical accounts of how fundamental ideas of probability and induction developed.* A full bibliography of further reading Although designed primarily for courses in philosophy, the book could certainly be read and enjoyed by those in the social sciences (particularly psychology, economics, political science and sociology) or medical sciences such as epidemiology seeking a reader-friendly account of the basic ideas of probability and induction. Ian Hacking is University Professor, University of Toronto. He is Fellow of the Royal Society of Canada, Fellow of the British Academy, and Fellow of the American Academy of Arts and Sciences. he is author of many books including five previous books with Cambridge (The Logic of Statistical Inference, Why Does Language Matter to Philosophy?, The Emergence of Probability, Representing and Intervening, and The Taming of Chance).

    Despite this, he has remained inaccessible to most modern readers, indisputably great but undeniably remote. In this witty, engaging, and often moving examination of Newton's life, David Berlinski recovers the man behind the mathematical breakthroughs. The story carries the reader from Newton's unremarkable childhood to his awkward undergraduate days at Cambridge through the astonishing year in which, working alone, he laid the foundation for his system of the world, his Principia Mathematica, and to the subsequent monumental feuds that poisoned his soul and wearied his supporters. An edifying appreciation of Newton's greatest accomplishment, Newton's Gift is also a touching celebration of a transcendent man.

    Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.