Download or read book The Rationale of Calculating Numbers written by Henry Clarke and published by . This book was released on 1794 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Rationale of Circulating Numbers written by Henry Clarke and published by . This book was released on 1777 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Rationale of Circulating Numbers With the Investigations of All the Rules and Peculiar Processes Used in That Part of Decimal Arithmetic 1777 written by Henry Clarke and published by . This book was released on 2009-05 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.
Download or read book Visual Complex Analysis written by Tristan Needham and published by Oxford University Press. This book was released on 1997 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Download or read book The Number Sense How the Mind Creates Mathematics written by Stanislas Dehaene Research Affiliate Institut National de la Sante et de la Recherche Medicale and published by Oxford University Press, USA. This book was released on 1997-11-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of how the human brain performs mathematical calculations is far from complete. But in recent years there have been many exciting scientific discoveries, some aided by new imaging techniques--which allow us for the first time to watch the living mind at work--and others by ingenious experiments conducted by researchers all over the world. There are still perplexing mysteries--how, for instance, do idiot savants perform almost miraculous mathematical feats?--but the picture is growing steadily clearer. In The Number Sense, Stanislas Dehaene offers general readers a first look at these recent stunning discoveries, in an enlightening exploration of the mathematical mind. Dehaene, a mathematician turned cognitive neuropsychologist, begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and he describes ingenious experiments that show that human infants also have a rudimentary number sense (American scientist Karen Wynn, for instance, using just a few Mickey Mouse toys and a small puppet theater, proved that five-month-old infants already have the ability to add and subtract). Further, Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain. But how then did the brain leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics, and in a marvelous chapter he traces the history of numbers, from early times when people indicated a number by pointing to a part of their body (even today, in many societies in New Guinea, the word for six is "wrist"), to early abstract numbers such as Roman numerals (chosen for the ease with which they could be carved into wooden sticks), to modern numbers. On our way, we also discover many fascinating facts: for example, because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. Dehaene also explores the unique abilities of idiot savants and mathematical geniuses, asking what might explain their special mathematical talent. And we meet people whose minute brain lesions render their mathematical ability useless--one man, in fact, who is certain that two and two is three. Using modern imaging techniques (PET scans and MRI), Dehaene reveals exactly where in the brain numerical calculation takes place. But perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in mathematics or the mind. Dehaene argues, for instance, that many of the difficulties that children face when learning math, and which may turn into a full-blown adult "innumeracy," stem from the architecture of our primate brain, which has not evolved for the purpose of doing mathematics. He also shows why the human brain does not work like a computer, and that the physical world is not based on mathematics--rather, mathematics evolved to explain the physical world the way that the eye evolved to provide sight. A truly fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.
Download or read book An Introduction to Mathematical Reasoning written by Peter J. Eccles and published by Cambridge University Press. This book was released on 1997-12-11 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. Over 250 problems include questions to interest and challenge the most able student as well as plenty of routine exercises to help familiarize the reader with the basic ideas.
Download or read book Numbers written by John Tabak and published by Infobase Publishing. This book was released on 2014-05-14 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a survey of the history and evolution of the use of numbers and numerical quantities by different civilizations around the world.
Download or read book Pharmaceutical Calculations written by Mitchell J. Stoklosa and published by . This book was released on 1986 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reasoned Mathematics for Quick Mental Calculation written by Manuel Carsini and published by Independently Published. This book was released on 2018-12-27 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has always accompanied man in his life, and accompanies him even more so today, not only every time an arithmetic calculation is needed, but also in consideration of the manifestations of the surrounding nature, which often use well-defined mathematical schemes to form and develop.Quick mental calculation algorithms are useful tools to simplify some calculations using "mathematical tricks," "shortcuts," which are based both on simple reasoning and application of basic properties of arithmetic, and on more or less complex methodologies to speed up the execution of the calculations avoiding being forced to execute them on sheets of paper.By way of example, calculating the square of the number 63 in mind can be quite easy by simply calculating the square of 60 and summing the fixed number 9 and six times the number 60, i.e. simply calculating the sum 3600+360+9, obtaining, in this way, the result 3969. Nothing, therefore, that cannot be calculated quickly in mind, even without a particular mental training.Another typical, very significant example is the fast mental calculation of the square of the numbers ending in the number 5, such as the number 85; well, the result will be simply equal to the concatenation of the multiplication between the number that precedes the number 5 and its following number and the fixed number 25, that is it will be equal to 8x9 concatenated with 25, that is equal to 7225.This small guide deals with cases such as those just exposed and aims to provide the reader with many simple and detailed examples of application of quick mental calculations, focusing attention, in particular, on the squares of numbers and on the multiplication of numbers. Along with mental training techniques, you can thus have an extra gear that, if nothing else, is a starting point to get closer to the magnificent world of mathematics starting from useful and partly fun concepts of simple understanding.In this situation, Vedic math, of which one often hears about, is very useful for making very fast multiplications, in mind, between particular numbers and it is for this reason that, sometimes, maybe a little improperly, one talks about the magic of mathematics or mental tricks for calculation.
Download or read book Teaching and Learning About Whole Numbers in Primary School written by Terezinha Nunes and published by Springer. This book was released on 2016-08-29 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished – the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbers meaningful in the classroom and contrast the outcomes of these diverse aspects of teaching. The book identifies themes and trends in empirical research on the teaching and learning of whole numbers since the launch of the major journals in mathematics education research in the 1970s. It documents a shift in focus in the teaching of arithmetic from research about teaching written algorithms to teaching arithmetic in ways that result in flexible approaches to calculation. The analysis of studies on quantitative reasoning reveals classifications of problem types that are related to different cognitive demands and rates of success in both additive and multiplicative reasoning. Three different approaches to quantitative reasoning education illustrate current thinking on teaching problem solving: teaching reasoning before arithmetic, schema-based instruction, and the use of pre-designed diagrams. The book also includes a summary of contemporary approaches to the description of the knowledge of numbers and arithmetic that teachers need to be effective teachers of these aspects of mathematics in primary school. The concluding section includes a brief summary of the major themes addressed and the challenges for the future. The new theoretical framework presented offers researchers in mathematics education novel insights into the differences between empirical studies in this domain. At the same time the description of the two meanings of numbers helps teachers distinguish between the different aims of teaching about numbers supported by diverse methods used in primary school. The framework is a valuable tool for comparing the different methods and identifying the various assumptions about teaching and learning.
Download or read book The rationale of arithmetical teaching exemplified written by John Blain and published by . This book was released on 1857 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numbers Rational and Irrational written by Ivan Niven and published by . This book was released on 1961 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-study guide on the classification of numbers and the standards used to determine whether a number is rational or irrational.
Download or read book Notes on the Principles of Pure and Applied Calculation written by James Challis and published by . This book was released on 1869 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantitative Reasoning written by Eric Zaslow and published by Cambridge University Press. This book was released on 2020-01-16 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is college worth the cost? Should I worry about arsenic in my rice? Can we recycle pollution? Real questions of personal finance, public health, and social policy require sober, data-driven analyses. This unique text provides students with the tools of quantitative reasoning to answer such questions. The text models how to clarify the question, recognize and avoid bias, isolate relevant factors, gather data, and construct numerical analyses for interpretation. Themes and techniques are repeated across chapters, with a progression in mathematical sophistication over the course of the book, which helps the student get comfortable with the process of thinking in numbers. This textbook includes references to source materials and suggested further reading, making it user-friendly for motivated undergraduate students. The many detailed problems and worked solutions in the text and extensive appendices help the reader learn mathematical areas such as algebra, functions, graphs, and probability. End-of-chapter problem material provides practice for students, and suggested projects are provided with each chapter. A solutions manual is available online for instructors.
Download or read book T hoku Mathematical Journal written by and published by . This book was released on 1921 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Systems written by Anthony Kay and published by CRC Press. This book was released on 2021-09-15 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs. The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The author’s motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems. Features Approachable for students who have not yet studied mathematics beyond school Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof Draws attention to connections with other areas of mathematics Plenty of exercises for students, both straightforward problems and more in-depth investigations Introduces many concepts that are required in more advanced topics in mathematics.
