Early mathematics

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  • Early childhood education has risen to the top of the national policy agenda with recognition that ensuring educational success and attainment must begin in the earliest years of schooling. There is now a substantial body of research to guide efforts to support young children’s learning. Over the past 15 years, great strides have been made in supporting young children’s literacy. This report summarizes the now substantial literature on learning and teaching mathematics for young children in hopes of catalyzing a similar effort in mathematics....

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  • Sincemany excellent treatises on the history ofmathemat- ics are available, there may seem little reason for writing still another. But most current works are severely techni- cal, written by mathematicians for other mathematicians or for historians of science. Despite the admirable schol- arship and often clear presentation of these works, they are not especially well adapted to the undergraduate classroom. (Perhaps the most notable exception is Howard Eves’s popular account, An Introduction to the History of Mathematics.

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  • Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!...

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  • The curriculum vitae of Alice Turner Schafer lists two specializations: abstract algebra (group theory) and women in mathematics. As early as her high school years Alice exhibited a love for mathematics and an interest in teaching as a career. As a mathematics educator she championed the full participation of women in mathematics.

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  • An early definition of mathematics in terms of logic was Benjamin Peirce's "the science that draws necessary conclusions" (1870).[24] In the Principia Mathematica, Bertrand Russell and Alfred North Whitehead advanced the philosophical program known as logicism, and attempted to prove that all mathematical concepts, statements, and principles can be defined and proven entirely in terms of symbolic logic. A logicist definition of mathematics is Russell's "All Mathematics is Symbolic Logic" (1903)

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  • Here are my online notes for my Calculus I course that I teach here at Lamar University. Despite the fact that these are my “class notes” they should be accessible to anyone wanting to learn Calculus I or needing a refresher in some of the early topics in calculus. I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from an Algebra or Trig class or contained in other sections of the notes.

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  • This work gives an overview of core topics in the “investment” side of finance, stressing the quantitative aspects of the subject. The presentation is at a moderately sophisticated level that would be appropriate for masters or early doctoral students in economics, engineering, finance, and mathematics. It would also be suitable for advanced and well motivated undergraduates-provided they are adequately prepared in math, probability, and statistics.

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  • Summary. In summary, we need to first describe the core mathematics that should be covered in, say, grades K - 7. This turns out to be far less than the content that is typically required by state standards in this country. It is consistent in all the programs in successful foreign countries that the number of topics covered in the early grades is far less than is covered here. But these are the key topics, and since they are covered to far greater depth than is the case here, those foreign students have a much more solid and dependable base, which makes it far more likely that...

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  • In 1991, David Gale and Raphael Robinson, building on explorations carried out by Michael Somos in the 1980s, introduced a three-parameter family of rational recurrence relations, each of which (with suitable initial conditions) appeared to give rise to a sequence of integers, even though a priori the recurrence might produce non-integral rational numbers. Throughout the '90s, proofs of integrality were known only for individual special cases. In the early '00s, Sergey Fomin and Andrei Zelevinsky proved Gale and Robinson's integrality conjecture.

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  • It is beneficial to decide on a target journal during the very early stages of writing an article, rather than first preparing an article and then considering where to send it. Analyse potential journals and choose one. Write your article with your target journal in mind. This is useful because different journals have different perceptions of science as well as differing opinions on how articles ought to be written. By writing directly for your target journal, you will ensure the right type of approach and speed up your writing process. If you wish to be even wiser, you may also...

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  • These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate, first years graduate level, which by author has taught for several years. These many axcellent good text in Differential Geometry bye very few have an early introduction to differential forms and their applications to Physisc

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  • From John Glenn s mission to orbit Earth to the International Space Station program, space food research has met the challenge of providing food that tastes good and travels well in space. To better understand this process, we can look back through history. Explorers have always had to face the problem of how to carry enough food for their journeys. Whether those explorers are onboard a sailing ship or on the Space Shuttle, adequate storage space has been a problem.

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  • In 1961, Baker, Gammel and Wills conjectured that for functions f meromorphic in the unit ball, a subsequence of its diagonal Pad´ approximants e converges uniformly in compact subsets of the ball omitting poles of f . There is also apparently a cruder version of the conjecture due to Pad´ himself, going e back to the early twentieth century. We show here that for carefully chosen q on the unit circle, the Rogers-Ramanujan continued fraction 1+ qz| q 2 z| q 3 z| + + + ··· |1 |1 |1 provides a counterexample to the conjecture. We also highlight some...

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  • By means of the Hardy-Littlewood method, we apply a new mean value theorem for exponential sums to confirm the truth, over the rational numbers, of the Hasse principle for pairs of diagonal cubic forms in thirteen or more variables. 1. Introduction Early work of Lewis [14] and Birch [3], [4], now almost a half-century old, shows that pairs of quite general homogeneous cubic equations possess non-trivial integral solutions whenever the dimension of the corresponding intersection is suitably large (modern refinements have reduced this permissible affine dimension to 826; see [13]). ...

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  • In the previous sub-section we have described the evolution of yields and interest rate spreads in 2002 using weekly data. If the information revealed by policy events is processed efficiently in capital markets, it may nevertheless be necessary to look at higher frequencies to detect any impact of fiscal policy events. In this section we therefore focus more carefully on specific events using daily data. As an illustration, we select two periods for a closer look.

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  • Capitalism and socialism have not existed forever. Capitalism came into widespread existence in the mid-1700s; socialism came into existence in the early 1900s. Before capitalism and socialism other forms of economic systems existed: Feudalism dominated the Western world from about the 8th to the 15th century.

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  • As the workshop summarized in this volume demonstrated, the research base about learning in early childhood is expanding and has great potential to contrib- ute to a broader set of national policy goals focused on making sure that all children enter kindergarten ready to learn. With this important research base in mind, the National Research Council’s Center for Education (CFE) convened a workshop to focus on early learning in mathematics and science.

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  • Taken as a whole, the German cinema is both more and less than the sum of its films. When one thinks of individual titles, quite a few, especially from the 1920s and early 1930s, have entered the canon, have become cultural icons the world over. Yet in these very same classics, the brilliant and the dark sides of their genius appear not only close together but inextricable. If we think of The Golem, The Cabinet of Dr Caligari, Nosferatu and Dr Mabuse: these are titles which by themselves evoke the spirit of an age, conjuring up...

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  • In 1991, David Gale and Raphael Robinson, building on explorations carried out by Michael Somos in the 1980s, introduced a three-parameter family of rational recurrence relations, each of which (with suitable initial conditions) appeared to give rise to a sequence of integers, even though a priori the recurrence might produce non-integral rational numbers. Throughout the '90s, proofs of integrality were known only for individual special cases. In the early '00s, Sergey Fomin and Andrei Zelevinsky proved Gale and Robinson's integrality conjecture.

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  • The direction of science is often driven by methodological progress, and the topic of this book is no exception. I remember sitting with a visitor on the terrace of a hotel overlooking Lake Constance in the early 1970s. We were discussing the gravimetric method of measuring total lipids in zooplankton. A few years later, as a visitor in Clyde E. Goulden’s lab, I was greatly impressed by the ability of an instrument called an Iatroscan to discriminate and quantify specific lipid classes (e.g., triacylglycerols, polar lipids, wax esters).

    pdf395p phoebe75 01-02-2013 23 4   Download

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