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Tips for simplifying tricky basic math and pre-algebra operationsWhether you’re a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you’ll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.Explanations and practical examples that mirror today’s teaching methodsRelevant cultural vernacular and referencesStandard For Dummiesmaterials that match the current standard and designBasic Math & Pre-Algebra For Dummies takes the intimidation out of tricky operations and helps you get ready for algebra!
This book contains 500 problems that range over a wide spectrum of mathematics and of levels of difficulty. Some are simple mathematical puzzlers while others are serious problems at the Olympiad level. Students of all levels of interest and ability will be entertained by the book. For many problems, more than one solution is supplied so that students can compare the elegance and efficiency of different mathematical approaches. A special mathematical toolchest summarizes the results and techniques needed by competition-level students.
In this sweeping book, applied mathematician and popular author David Orrell questions the promises and pitfalls of associating beauty with truth, showing how ideas of mathematical elegance have inspired—and have sometimes misled—scientists attempting to understand nature.Orrell shows how the ancient Greeks constructed a concept of the world based on musical harmony; later thinkers replaced this model with a program, based on Newton’s “rational mechanics,” to reduce the universe to a few simple equations.
Neal Koblitz is a co-inventor of one of the two most popular forms of encryption and digital signature, and his autobiographical memoirs are collected in this volume.
While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren’t available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.
Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.
From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.
Was Plato a Pythagorean? Plato’s students and earliest critics thought so, but scholars since the nineteenth century have been more skeptical. With this probing study, Phillip Sidney Horky argues that a specific type of Pythagorean philosophy, called "mathematical" Pythagoreanism, exercised a decisive influence on fundamental aspects of Plato’s philosophy. The progenitor of mathematical Pythagoreanism was the infamous Pythagorean heretic and political revolutionary Hippasus of Metapontum, a student of Pythagoras who is credited with experiments in harmonics that led to innovations in mathematics.
G. H. Hardy was one of this century’s finest mathematical thinkers, renowned among his contemporaries as a ‘real mathematician … the purest of the pure’. He was also, as C. P. Snow recounts in his Foreword, ‘unorthodox, eccentric, radical, ready to talk about anything’. This ‘apology’, written in 1940, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James’s notebooks as ‘the best account of what it was like to be a creative artist’.
John D. Barrow’s Pi in the Sky is a profound — and profoundly different — exploration of the world of mathematics: where it comes from, what it is, and where it’s going to take us if we follow it to the limit in our search for the ultimate meaning of the universe. Barrow begins by investigating whether math is a purely human invention inspired by our practical needs. Or is it something inherent in nature waiting to be discovered?
In answering these questions, Barrow provides a bridge between the usually irreconcilable worlds of mathematics and theology.
Drawing on a wealth of archival material, including personal correspondence and diaries, Robert Leonard tells the fascinating story of the creation of game theory by Hungarian Jewish mathematician John von Neumann and Austrian economist Oskar Morgenstern. Game theory first emerged amid discussions of the psychology and mathematics of chess in Germany and fin-de-siècle Austro-Hungary. In the 1930s, on the cusp of anti-Semitism and political upheaval, it was developed by von Neumann into an ambitious theory of social organization.
One of the leading historians in the mathematics field, Victor Katz provides a world view of mathematics, balancing ancient, early modern, and modern history.
From one of the foremost interpreters for lay readers of the history and meaning of mathematics: a stimulating account of the origins of mathematical thought and the development of numerical theory. It probes the work of Pythagoras, Galileo, Berkeley, Einstein, and others, exploring how "number magic" has influenced religion, philosophy, science, and mathematics
Consulting and collecting numbers has been a feature of human affairs since antiquity-from the pyramids to tax collection to head counts for military service-but not until the Scientific Revolution in the seventeenth century did social numbers such as births, deaths and marriages begin to be analysed. The Triumph of Numbers explores how numbers have come to assume a leading role in science, in the operations and structure of government, in the analysis of society, in marketing and in many other aspects of daily life.
In the 1940s and 50s, when the newly minted Jet Propulsion Laboratory needed quick-thinking mathematicians to calculate velocities and plot trajectories, they didn’t turn to male graduates. Rather, they recruited an elite group of young women who, with only pencil, paper, and mathematical prowess, transformed rocket design, helped bring about the first American satellites, and made the exploration of the solar system possible.For the first time, Rise of the Rocket Girls tells the stories of these women–known as "human computers"–who broke the boundaries of both gender and science.
Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann Hypothesis, which remains to be one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann Hypothesis. Students with minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes.
This volume is a result of mathematicians, cognitive scientists, mathematics educators, and classroom teachers combining their efforts to help address issues of importance to classroom instruction in mathematics. In so doing, the contributors provide a general introduction to fundamental ideas in cognitive science, plus an overview of cognitive theory and its direct implications for mathematics education. A practical, no-nonsense attempt to bring recent research within reach for practicing teachers, this book also raises many issues for cognitive researchers to consider.
From the medicine we take, the treatments we receive, the aptitude and psychometric tests given by employers, the cars we drive, the clothes we wear to even the beer we drink, statistics have given shape to the world we inhabit. For the media, statistics are routinely ‘damning’, ‘horrifying’, or, occasionally, ‘encouraging’. Yet, for all their ubiquity, most of us really don’t know what to make of statistics. Exploring the history, mathematics, philosophy and practical use of statistics, Eileen Magnello – accompanied by Bill Mayblin’s intelligent graphic illustration – traces the rise of statistics from the ancient Babylonians, Egyptians and Chinese, to the censuses of Romans and the Greeks, and the modern emergence of the term itself in Europe.
Two fundamental theories are commonly debated in the study of random processes: the Bachelier Wiener model of Brownian motion, which has been the subject of many books, and the Poisson process. While nearly every book mentions the Poisson process, most hurry past to more general point processes or to Markov chains. This comparative neglect is ill judged, and stems from a lack of perception of the real importance of the Poisson process. This distortion partly comes about from a restriction to one dimension, while the theory becomes more natural in more general contexts.
Das Buch lotet diese "obskure" Konstante aus. Die Reise beginnt mit Logarithmen und der harmonischen Reihe. Es folgen Zeta-Funktionen und Eulers wunderbare Identitat, Bernoulli-Zahlen, Madelungsche Konstanten, Fettfinger in Worterbuchern, elende mathematische Wurmer und Jeeps in der Wuste. Harmonien in der Geometrie, in der Musik und bei Primzahlen!
The main focus of this book is on the interconnection of two unorthodox scientific ideas, the varying-gravity hypothesis and the expanding-earth hypothesis. As such, it provides a fascinating insight into a nearly forgotten chapter in both the history of cosmology and the history of the earth sciences.The hypothesis that the force of gravity decreases over cosmic time was first proposed by Paul Dirac in 1937. In this book the author examines in detail the historical development of Dirac’s hypothesis and its consequences for the structure and history of the earth, the most important of which was that the earth must have been smaller in the past.
The title doesn’t lie. Mathematician Georges Ifrah’s masterpiece, The Universal History of Numbers, is a wonderfully comprehensive overview of numbers and counting spanning all the inhabited continents as far back in time as records will allow us to look. Beyond the ancient Babylonians, Sumerians, and Indians, Ifrah takes us farther south into Africa to examine an early decimal counting system and into ancient Mexico to reconstruct what we can of the Mayan calendar and numerical system. The 27 chapters are chiefly organized by culture, though there are some cross-cultural overviews of topics like letters and numbers.T
This is a history of the use of Bayes theoremfrom its discovery by Thomas Bayes to the rise of the statistical competitors in the first part of the twentieth century. The book focuses particularly on the development of one of the fundamental aspects of Bayesian statistics, and in this new edition readers will find new sections on contributors to the theory. In addition, this edition includes amplified discussion of relevant work.
What is mathematics about? Is there a mathematical universe glimpsed by a mathematical intuition? Or is mathematics an arbitrary game of symbols, with no inherent meaning, that somehow finds application to life on earth? Robert Knapp holds, on the contrary, that mathematics is about the world. His book develops and applies its alternative viewpoint, first, to elementary geometry and the number system and, then, to more advanced topics, such as topology and group representations. Its theme is that mathematics, however abstract, arises from and is shaped by requirements of indirect measurement.
At a summer tea party in Cambridge, England, a lady states that tea poured into milk tastes differently than that of milk poured into tea. Her notion is shouted down by the scientific minds of the group. But one guest, by the name Ronald Aylmer Fisher, proposes to scientifically test the lady’s hypothesis. In this book, readers encounter not only Ronald Fisher’s theories (and their repercussions), but the ideas of dozens of men and women whose revolutionary work affects our everyday lives.
Drawing primarily from historical examples, this book explains the tremendous role that numbers and, in particular, mathematics play in all aspects of our civilization and culture. The lively style and illustrative examples will engage the reader who wants to understand the many ways in which mathematics enables science, technology, art, music, politics, and rational foundations of human thought. Each chapter focuses on the influence of mathematics in a specific field and on a specific historical figure, such as "Pythagoras: Numbers and Symbol"; "Bach: Numbers and Music"; "Descartes: Numbers and Space.&
Showing 1–24 of 26 results