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"Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research.The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis.Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms.Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity.Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject."

Mathematics --- Inventions --- History. --- Mathematical models. --- Creative ability in technology --- Prior art (Patent law) --- Research, Industrial --- Math --- Science --- mathematical ideas --- development of numbers --- development number systems --- negative numbers --- irrationals numbers --- complex numbers

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This book answers the question of how exactly property price indexes should be constructed. The formation and collapse of property bubbles has had a profound impact on the economic administration of many nations. The property price bubble that began around the mid-1980s in Japan has been called the 20th century's biggest bubble. In its aftermath, the country faced a period of long-term economic stagnation dubbed the "lost decade." Sweden and the United States have also faced collapses of property bubbles in the 20th and early 21st centuries, respectively. It has been pointed out that the "information gap" that existed between policy-making authorities and the property (including housing) and financial markets was a problem. In 2009, the IMF proposed the creation of a housing price index to the G20 in order to fill this information gap, and the proposal was adopted. Furthermore, in 2011, it was suggested that the next economic crisis would be caused by a bubble in commercial property prices, and it was decided to create a commercial property index as well. This book provides practical examples of how the theory of property price indexes can be applied to the issues of property as a non-homogenous good and a technological and environmental change. W. Erwin Diewert is a Professor in the Vancouver School of Economics at the University of British Columbia. Kiyohiko G. Nishimura is a Professor at the National Graduate Institute for Policy Studies (GRIPS) and Professor Emeritus and Distinguished Project Research Fellow of the Center for Advanced Research in Finance at the University of Tokyo. Chihiro Shimizu is a Senior Fellow Professor of the Center for Spatial Information Science, the University of Tokyo, and Professor of Nihon University. Tsutomu Watanabe is a Professor in the Faculty of Economics at the University of Tokyo.

Price indexes. --- Price indices --- Index numbers (Economics) --- Macroeconomics. --- Macroeconomics/Monetary Economics//Financial Economics. --- Economics

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This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.

Galois cohomology. --- Galois theory --- Homology theory --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra

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This textbook covers a wide array of topics in analytic and multiplicative number theory, suitable for graduate level courses. Extensively revised and extended, this Advanced Edition takes a deeper dive into the subject, with the elementary topics of the previous edition making way for a fuller treatment of more advanced topics. The core themes of the distribution of prime numbers, arithmetic functions, lattice points, exponential sums and number fields now contain many more details and additional topics. In addition to covering a range of classical and standard results, some recent work on a variety of topics is discussed in the book, including arithmetic functions of several variables, bounded gaps between prime numbers à la Yitang Zhang, Mordell's method for exponential sums over finite fields, the resonance method for the Riemann zeta function, the Hooley divisor function, and many others. Throughout the book, the emphasis is on explicit results. Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exercises, all with solutions, it is now an even better guide for independent study.

Number theory. --- Mathematics. --- Number Theory. --- Mathematics, general. --- Math --- Science --- Number study --- Numbers, Theory of --- Algebra

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Ulysses has been read obsessively for a century. What if instead of focusing on the words to understand the structure, design, and history of Joyce’s masterpiece, we pay attention to the numbers?Taking a computational approach, Ulysses by Numbers lets us see the novel’s basic building blocks in a significantly new light—words, paragraphs, pages, and characters, as well as the original print run and the dates marking the beginning and end of its composition. Numbers provide access into Joyce’s creative process, enhanced by graphs, diagrams, timelines, and maps, and they also give us a startling new perspective on the proportions that continue to structure, organize, and pace the reading experience. Numbers are there to help us navigate the history of Ulysses from its earliest material beginnings, and they offer a concrete basis upon which we can explore the big questions about its length, style, origins, readership, and design.An innovative computational reading on both a micro and macro level, Ulysses by Numbers is a timely intervention into debates about the use and abuse of quantitative methods in literary analysis. Eric Bulson demonstrates how reading by numbers can bring us closer to the words of Ulysses, helping us rediscover a novel we thought we already knew.

Criticism, Textual --- Literature --- Symbolism of numbers in literature. --- Data processing. --- Research --- Methodology. --- Joyce, James, --- Literary style