The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    

    

    

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

    When hearing those words just a couple of years back, people used to say: It’s a scam, financial bubble IThere is no point in investing, the price is too low INo country will ever recognize cryptocurrency IIt’s an obvious pyramid scheme IIt’s a sort of amusement for nerds IIt's not serious, it will collapse in a couple of years. Until recently, cryptocurrency had been viewed as a sort of amusement for a handful of the chosen who bought and sold something and believed that a new currency would make a hit one day! You surely were also among those people who did not take Bitcoin and cryptocurrency seriously, but the current events gag even the biggest skeptics. Current Bitcoin price is 6,644$* The price of the most popular cryptocurrency repeatedly breaks all the unthinkable records. Capitalization is about $120 billion World recognition The world's largest economies – India and Japan – recognized Bitcoin as the official currency. The US authorities recognized cryptocurrency as the asset. And this is just the beginning. Mining on an industrial scale The cryptocurrency market is extremely fast-changing, and it is almost impossible to monitor the situation and make the right decisions on your own. Most people have no proper experience, time and money for that. My book gives basic yet quite extensive information for those people who do not chase a rainbow but want to build a long-term profitable business in one of the cryptocurrency areas: from mining to investing. So, this book is not about: Illegal ways of making money Praising cryptocurrency and urging you to invest in it to the last penny Fraud techniques and making a fast buck Boring and pointless theory Ways to earn millions without investments and risks This book will help you get to learn the following: Which way of making money in cryptocurrency market suits you best. Where should you start if you have just $500. What information about cryptocurrency the experts withhold (Take the rose-colored glasses off!). How to elaborate a personal strategy, set up your own cryptocurrency business and earn your first $3,000-10,000 as early as 2018. I can also guarantee that you: Puzzle out the main present-day currency trend even if you are clueless about economics, finance and technology. Understand whether you really want to invest in cryptocurrency (perhaps, this type of business doesn’t suit you at all and you will save your time) Get to learn how to check the risks and not to invest in the first available currency Having considered my experience, protect yourself from possible failures and pouring money down the drain which will inevitably happen if you go it blind.

    

    This is type of problems asked at the JEE (IIT). The purpose of this book is to show students how to handle such problems and give them sufficient practice in solving problems of this type, thus building their confidence. The main features of this book are:Each chapter begins with a summary of facts, formulate and working techniques. Trick, tips and techniques have been clearly marked with the icon.A large number of problems have been solved and explained in each chapter.The exercises contain short-answer, long-answer and objective type questions.Multiple-choice questions in which more than one option may be correct have also been given.Time-bound tests at the end of each chapter will help students practise answering questions in a given time.The book also includes integrated tests, bases on all the chapters.A chapter containing miscellaneous problems has been given at the end of the book. This will help students gain confidence in solving problems without prior knowledge of the chapter(s) to which the problems belong.Table of ContentsAlgebraProgressions, Related Inequalities and SeriesDeterminants and Cramer's RuleEquations, Inequations and ExpressionsComplex NumbersPermutation and CombinationBinomial Theorem for Positive Integral IndexPrinciple of Mathematical Induction (PMI)Infinite SeriesMatricesTrigonometryCircular Functions, IdentitiesSolution of EquationsInverse Circular FunctionsTrigonometrical Inequalities and InequationsLogarithmProperties of TriangleHeights and DistancesCoordinate GeometryCoordinates and Straight LinesPairs of Straight Lines and Transformation of AxesCirclesParabolaEllipse and HyperbolaCalculusFunctionDifferentiationLimit, Indeterminate FormContinuity, Differentiability and Graph of FunctionApplication of dy/dxMaxima and MinimaMonotonic Function and Lagrange's TheoremIndefinite In

    Fully stocked with solved problemsN950 of themNit shows you how to solve problems that may not have been fully explained in class. Plus you ge"

    

    Whereas Caesar Triumphant covers Caesar's invasion of the Isle of Wa, now known as Japan, Caesar Ascending is set in 44 BC and tells the story of his planned invasion of Parthia, and includes the characters of the internationally bestselling Marching With Caesar series, featuring Titus Pullus. Determined not to repeat the mistakes made by Caesar's friend and fellow Triumvir Marcus Licinius Crassus, the Dictator has trained his Legions in tactics specifically designed to thwart the famed Parthian cataphracts and horse archers, but as Caesar and his army learns, the Parthians have been working on their own surprises, all in an attempt to destroy another Roman army and send a message to Rome that they are not the only world power.

    This is one of the most power-packed prosperity books around. Anyone can attract more money using simple metaphysical and mind power techniques, but advanced money attractors have a deeper grasp of the subtler spiritual truths underlying the money-manifesting process. You can attract a lot more money than you ever have before, and this book will give you the knowledge you need to be able to do it just as naturally as you now breathe.In fact, this life-changing little book will teach you that the money you want is actually here now, that it is a part of you, and that you already have it. Within these covers resides an astounding power, which will become increasingly apparent to you over time and with subsequent readings, and spurred on by this power, you can begin to turn your financial dreams into reality. Table of Contents: Secret One......: You Already Have ItSecret Two......: It Is Not Separate from YouSecret Three...: It Is Not in Your FutureSecret Four.....: It Is Right for You to Have ItSecret Five......: You Are Worthy of Having ItSecret Six........: A Higher You Wants ItSecret Seven...: Inspiration Beats PlanningSecret Eight.....: Be a Person Who Has ItSecret Nine......: Cooperate with the UniverseSecret Ten.......: Spread the Good AroundAttracting more money, manifesting wealth, creating a life of prosperity, abundance, and affluence—these are things anyone can accomplish, but relatively few do. The difference between the haves and the have nots? It’s a mental difference. It all starts in the mind, with the power of thought. This book will teach you how to think in a way that will raise you to glorious new heights of success, achievement, and financial freedom.

     In fact, it may even be bigger than the Internet. It is such a profound paradigm shift in the technology of money that even experts on the topic are still trying to wrap their heads around it. Pandora's box has been opened and there is no going back. Bitcoin will forever transform society and its implications are beyond what we can even currently imagine. Bitcoin can be hard to grasp at first – and if someone has tried to explain it to you and you feel like you still don't get it, don't worry. This book will take you by the hand and explain to you in the simplest terms, using analogies, metaphors and illustrations what the essence of Bitcoin is and why you must pay attention to the revolution that is about to take place. In Bitcoin for Beginners you will find out: How the Bitcoin Technology works The difference between Bitcoin and Blockchain How mining works How to make money with Bitcoin The top myths about Bitcoin How Bitcoin will take over the world How to buy and sell Bitcoin What forks are And much more! DON'T HESITATE. TO START ON A JOURNEY THAT COULD DEEPLY TRANSFORM HOW YOU RELATE TO THE CONCEPT OF MONEY, SCROLL UP AND CLICK THE "BUY" BUTTON NOW!

    Topics covered in the book include linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and much more!The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems.This book can serve as a complete Algebra I course, and also includes many concepts covered in Algebra II. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of algebra will find this book an instrumental part of their mathematics libraries.656About the author: Richard Rusczyk is a co-author of Art of Problem Solving, Volumes 1 and 2, the author of Art of Problem Solving's Introduction to Geometry. He was a national MATHCOUNTS participant, a USA Math Olympiad winner, and is currently director of the USA Mathematical Talent Search.

    Whether you want to retire as soon as possible or are looking forward to continuing to work in some form for as long as you can, Retirement 101 guides you through each step as you approach this important milestone. From how to save for the day when you stop—or scale back—working to smart investment strategies to the best states to retire in to how to calculate your benefits, Retirement 101 helps you create a retirement plan to accomplish your goals, whatever they are.