In the past forty years an entirely new paradigm has developed regarding the contact population of the New World. Proponents of this new theory argue that the American Indian population in 1492 was ten, even twenty, times greater than previous estimates. In Numbers From Nowhere David Henige argues that the data on which these high counts are based are meager and often demonstrably wrong. Drawing on a wide variety of primary and secondary sources, Henige illustrates the use and abuse of numerical data throughout history. He shows that extrapolation of numbers is entirely subjective, however masked it may be by arithmetic, and he questions what constitutes valid evidence in historical and scientific scholarship.

This handbook focuses on some important topics from Number Theory and Discrete Mathematics. These include the sum of divisors function with the many old and new issues on Perfect numbers; Euler's totient and its many facets; the Möbius function along with its generalizations, extensions, and applications; the arithmetic functions related to the divisors or the digits of a number; the Stirling, Bell, Bernoulli, Euler and Eulerian numbers, with connections to various fields of pure or applied mathematics. Each chapter is a survey and can be viewed as an encyclopedia of the considered field, underlining the interconnections of Number Theory with Combinatorics, Numerical mathematics, Algebra, or Probability Theory. This reference work will be useful to specialists in number theory and discrete mathematics as well as mathematicians or scientists who need access to some of these results in other fields of research.

These volumes provide an authoritative reference resource on leadership issues specific to women and gender, with a focus on positive aspects and opportunities for leadership in various domains.

From the Preface to the first edition (1906): "A few of the most modern books on the Theory of Functions devote some pages to the establishment of certain results belonging to our subject, and required for the special purposes in hand... But we may fairly claim that the present work is the first attempt at a systematic exposition of the subject as a whole."

This book is based on two new nominalistic theses: first, that material things (houses, cats, people, symphonies, and also hair, milk, red, and love) are recurrent types, and second, that things are ontologically incomplete. Using these ideas, simple solutions are offered to a plethora of questions in ontology, philosophy of mind, and aesthetics.

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) is intimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas of mathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals. In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectual exercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite. 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, and enthusiasm to make interesting and challenging topics highly readable.

Uncover the mysteries that lie within your calculator This remarkable book explores the simple internal calculatorprocesses—algorithms and programs—that tell us, forexample, that the cosine of 56? is 0.5591929035. Using carefullyconstructed diagrams and figures, the author effectivelydemonstrates how calculator keys compute powers, roots, logarithms,and trigonometry functions, while also providing insights intosimple programming, the conversion between decimal and binarynumeration, and perhaps most importantly, the structure of ournumeration systems. Many people believe that the processes thatdrive calculators demand advanced mathematical concepts; however,this book proves that a minimal understanding of algebra andgeometry is all that is needed to follow the step-by-stepexplanations of how scientific calculators work. Inside Your Calculator: From Simple Programs to SignificantInsights is a complete and multifaceted exercise in criticalthinking. This book features: A detailed explanation of how to use a graphics calculator andprogram basic functions A discussion of the history of mathematics when appropriate,which provides a foundation for further learning Fundamental mathematical lessons and interesting applications ofpre-calculus mathematics A thorough review of the fundamentals of programming, algebra,and geometry needed to gain insight into why the algorithms workand how the results are meaningful in our lives While the simultaneous use of a calculator is not needed to gaininsight into how the algorithms work, those who do have aprogrammable graphics calculator can experiment with the programspresented in the book. These programs may be used on TI-84 andTI-83 calculators, and additional information for other TexasInstruments calculators as well as the Casio FX series is availableon the book's related web site. As a result of over fifty years of award-winning teachingexperience in both high school and college classrooms, Dr. Risinganticipates and answers potential questions from readers, and hesuccessfully brings this subject alive in an illuminating andentertaining way. This book is therefore not only ideal forundergraduate mathematics majors as either a primary orsupplemental text, but it also appeals to anyone with an interestin mathematics and its ideas. View Dr. Rising's book presentation: atitle="http://www.youtube.com/watch?v=aqadHbc2YOA"href="http://www.youtube.com/watch?v=aqadHbc2YOA"http://www.youtube.com/watch?v=aqadHbc2YOA/a