The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for shastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.This book is being published in two volumes. This second volume develops shastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time.Masters level students and researchers in mathematical finance and financial engineering will find this book useful.Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.

    Fully revised to meet the needs of the wide range of students beginning engineering courses, this edition has an extended Foundation section including new chapters on graphs, trigonometry, binomial series and functions and a CD-ROM

    This text provides a simple and straightforward introduction to econometrics for the beginner. The book is designed to help students understand econometric techniques through extensive examples, careful explanations, and a wide variety of problem material. In each of the editions, I have tried to incorporate major developments in the field in an intuitive and informative way without resort to matrix algebra, calculus, or statistics beyond the introductory level. The fourth edition continues that tradition.

    

    This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes.Understand even the basics of Einstein's amazing theory and the world will never seem the same again. ContentsPrefaceIntroduction1 Foundation mathematics2 Newtonian mechanics3 Special relativity4 Introducing the manifold5 Scalars, vectors, one-forms and tensors6 More on curvature7 General relativity8 The Newtonian limit9 The Schwarzschild metric10 Schwarzschild black holes11 Cosmology12 Gravitational wavesAppendix: The Riemann curvature tensorBibliographyAcknowledgementsJanuary 2019. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

    A number of the key figures in the new edition are revised to provide a more inviting and informative treatment. The figures are broken into component parts with supporting commentary so that they can more readily see the key ideas. Material from The Flying Circus is incorporated into the chapter opener puzzlers, sample problems, examples and end-of-chapter problems to make the subject more engaging. Checkpoints enable them to check their understanding of a question with some reasoning based on the narrative or sample problem they just read. Sample Problems also demonstrate how engineers can solve problems with reasoned solutions.

    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!

    

    This gorgeous book features clear, entertaining, and enlightening commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties.  With its lush format and layflat dimensions that closely approximate the golden ratio, this is the ultimate coffee table book for math enthusiasts, architects, designers, and fans of sacred geometry.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

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

    Reveals mathematics' great power as an alternative language for understanding things and explores such concepts as logic as a computing tool, digital versus analog processes and communication as information transmission.

    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.

    I'm here to tell you it is not. In fact, fundamental poker math is very easy to learn. More importantly, it can yield you a lot more profits at the poker table. Without using simple math at the poker table, you are simply playing a guessing game. Use Simple Math at the Poker Table and Increase You Winnings In this book I will teach you how to use simple arithmetic at the poker table to gain a huge skill advantage over your opponents that will allow you to win more and lose less. Poker players that don't use math are simply guessing and you'll learn to no longer guess and know the right mathematical move at the poker table. These simple mathematical concepts I will be teaching you will drastically help improve your poker game and allow you to make the most profitable decisions at the poker. Contents and Overview First you will be introduced to some fundamental overarching poker concepts that apply to poker mathematics. Then we will begin our journey into poker mathematics where you will learn about probabilities and odds, pot odds and implied odds, pot equity, and expected value. You will then learn how to quickly estimate your equity at the poker table using the Rule of 2 & 4. Moreover, you'll learn the steps involved in determining if calling with a drawing hand is profitable or not. We will also cover how to size your bets with the best hand and teach you how often bluffs and hero calls need to work to be profitable. Lastly, we will show you how to perform EV calculations and better understand card combinations. Effectively Understand and Utilize Essential Poker Math Develop a keen understanding of Probability and Odds Learn to quickly calculate Pot Odds & Implied Odds at the poker table Effectively use Pot Equity & The Rule of 2 & 4 to Determine the correct poker play Understand how to use Expected Value (EV) both on and off the table to analyze your plays Learn the important math behind Bluffs & Hero Calls to give you a skill advantage over your opponent Learn Card Combinations to further enhance your card reading abilities And Many More Amazing Topics… What You Will Get out of This Book Suitable for both beginning and experienced poker players alike you'll learn many essential fundamental poker mathematical concepts that will help you drastically improve your poker game. After reading this book, you will have mastered fundamental No Limit Holdem mathematics. You will have gained a huge skill advantage over your opponents and you will be able to quickly and effectively use math at the poker table to make are always the most profitable move. Most importantly, you will become a much better and profitable poker player! So what are you waiting for? Purchase this book today to start learning how to advance your poker game with simple poker math! Alton Hardin is the founder of MicroGrinder.com, a free micro stakes poker website that is dedicated to helping micro stakes poker players improve their poker game by offering a wide array of free and low-cost resources including poker courses, poker t

    The Times called it elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf and The Philadelphia Inquirer praised it as absolutely scintillating. In this delightful new book, Robert Kaplan, writing together with his wife Ellen Kaplan, once again takes us on a witty, literate, and accessible tour of the world of mathematics. Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved that infinity can come in different sizes, the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics. The Kaplans guide us through the Republic of Numbers, where we meet both its upstanding citizens and more shadowy dwellers; and we travel across the plane of geometry into the unlikely realm where parallel lines meet. Along the way, deft character studies of great mathematicians (and equally colorful lesser ones) illustrate the opposed yet intertwined modes of mathematical thinking: the intutionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it. Less than All, wrote William Blake, cannot satisfy Man. The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination.