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Rational number theory in the 20th century : from PNT to FLT
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ISBN: 9780857295323 0857295322 Year: 2012 Publisher: London : Springer,

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The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan. These methods were the driving force behind new advances in prime and additive number theory.  At the same time, Hecke’s resuscitation of modular forms started a whole new body of research  which culminated in the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and students in number theory, however the presentation of main results without technicalities and proofs will make this accessible to anyone with an interest in the area. Detailed references and a vast bibliography offer an excellent starting point for readers who wish to delve into specific topics.

Number story : from counting to cryptography
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ISBN: 1281179094 9786611179090 1848000014 9781848000001 1848000006 9781848000018 Year: 2008 Publisher: London : Copernicus Books,

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Numbers have fascinated people for centuries. They are familiar to everyone, forming a central pillar of our understanding of the world, yet the number system was not presented to us "gift-wrapped" but, rather, was developed over millennia. Today, despite all this development, it remains true that a child may ask a question about numbers that no one can answer. Many unsolved problems surrounding number matters appear as quirky oddities of little account while others are holding up fundamental progress in mainstream mathematics. Peter Higgins distills centuries of work into one delightful narrative that celebrates the mystery of numbers and explains how different kinds of numbers arose and why they are useful. Full of historical snippets and interesting examples, the book ranges from simple number puzzles and magic tricks, to showing how ideas about numbers relate to real-world problems, such as: How are our bank account details kept secure when shopping over the internet? What are the chances of winning at Russian roulette; or of being dealt a flush in a poker hand? This fascinating book will inspire and entertain readers across a range of abilities. Easy material is blended with more challenging ideas about infinity and complex numbers, and a final chapter "For Connoisseurs" works through some of the particular claims and examples in the book in mathematical language for those who appreciate a complete explanation. As our understanding of numbers continues to evolve, this book invites us to rediscover the mystery and beauty of numbers and reminds us that the story of numbers is a tale with a long way to run...


Book
Algebraic Geometry over the Complex Numbers
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ISBN: 9781461418092 9781461418085 Year: 2012 Publisher: Boston MA Springer US

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This textbook is a strong addition to existing introductory literature on algebraic geometry. The author's treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and related fields. Unique features of this textbook: - Contains a rapid introduction to complex algebraic geometry - Includes background material on topology, manifold theory and sheaf theory - Analytic and algebraic approaches are developed somewhat in parallel The presentation is easy going, elementary, and well illustrated with examples. Algebraic Geometry over the Complex Numbers  is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory.

World atlas of biodiversity : earth's living resources in the 21st century
Authors: --- --- ---
ISBN: 0520236688 Year: 2002 Publisher: Berkeley Cambridge : University of California press,


Multi
Price Indexes in Time and Space : Methods and Practice
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ISBN: 9783790821406 9783790821413 9783790828146 9783790821390 Year: 2010 Publisher: Heidelberg Physica-Verlag HD

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This book deals with the currently most relevant topics in price index numbers theory and practice. The problem of the harmonization of Consumer Price Indexes (CPIs) and the time-space integration of baskets is analyzed at the EU-zone level, with methodological and practical proposals on how to proceed for an overall treatment of the matter. Another issue is comparisons between Purchasing Power Parities (PPPs) and CPIs. Likewise, the construction of sub-indexes for households, economic and social groups is investigated, in order to obtain specific inflation measurement instruments. The book provides evidence from the most updated databases. Among the other issues treated in this book are spatial comparisons of price levels through PPPs and the international comparisons of macroeconomic aggregates, a re-consideration of index numbers theory, the measurement of production in non-market services, deflation problems, and price indexes in financial markets.

Cohomology of Number Fields
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ISBN: 3540378898 9783540378891 354037888X 9783540378884 Year: 2008 Volume: 323 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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The second edition is a corrected and extended version of the first. It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. The first part provides algebraic background: cohomology of profinite groups, duality groups, free products, and homotopy theory of modules, with new sections on spectral sequences and on Tate cohomology of profinite groups. The second part deals with Galois groups of local and global fields: Tate duality, structure of absolute Galois groups of local fields, extensions with restricted ramificatio


Book
Sets, Logic and Maths for Computing
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ISBN: 9781447125006 9781447124993 Year: 2012 Publisher: London Springer London

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This easy-to-follow textbook introduces the mathematical language, knowledge and problem-solving skills that undergraduate students need to enter the world of computer and information sciences. The language is in part qualitative, with concepts such as set, relation, function and recursion/induction; but it is also partly quantitative, with principles of counting and finite probability. Entwined with both are the fundamental notions of logic and their use for representation and proof. In ten chapters on these topics, the book guides the student through essential concepts and techniques. The extensively revised second edition provides further clarification of matters that typically give rise to difficulty in the classroom and restructures the chapters on logic to emphasize the role of consequence relations and higher-level rules, as well as including more exercises and solutions. Topics and features: Teaches finite mathematics as a language for thinking, as much as knowledge and skills to be acquired Uses an intuitive approach with a focus on examples for all general concepts Brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction Balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives Includes highlight boxes that raise common queries and clear away confusions Provides numerous exercises, with selected solutions, to test and deepen the reader's understanding This clearly-written text/reference is a must-read for first-year undergraduate students of computing. Assuming only minimal mathematical background, it is ideal for both the classroom and independent study. Dr. David Makinson is a Visiting Professor in the Department of Philosophy, Logic and Scientific Method at the London School of Economics, UK.

Surveys in number theory
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ISBN: 9780387785103 0387785094 9780387785097 9786612037801 1282037803 0387785108 Year: 2008 Publisher: New York ; London : Springer,

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Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt). All of the surveys were outgrowths of featured talks given during the Special Year in Number Theory and Combinatorics at the University of Florida, Gainesville, 2004-2005, and describe major progress on a broad range of topics. This volume is intended for mathematicians and graduate students interested in number theory and related areas.


Book
The map of my life
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ISBN: 9780387797151 0387797149 9780387797144 1441927247 9786611954420 128195442X 0387797157 Year: 2008 Publisher: New York : Springer,

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In this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days. He describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a post-war university system that was seriously deficient, and his life as a mature mathematician in Princeton and in the international academic community. Every page of this memoir contains personal observations and striking stories. Such luminaries as Chevalley, Oppenheimer, Siegel, and Weil figure prominently in its anecdotes. Goro Shimura is Professor Emeritus of Mathematics at Princeton University. In 1996, he received the Leroy P. Steele Prize for Lifetime Achievement from the American Mathematical Society. He is the author of Elementary Dirichlet Series and Modular Forms (Springer 2007), Arithmeticity in the Theory of Automorphic Forms (AMS 2000), and Introduction to the Arithmetic Theory of Automorphic Functions (Princeton University Press 1971).


Book
The 1-2-3 of Modular Forms : Lectures at a Summer School in Nordfjordeid, Norway
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ISBN: 9783540741190 3540741194 Year: 2008 Publisher: Berlin : Springer,

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ThisbookgrewoutoflecturesgivenatthesummerschoolonModularForms and their Applications  at the Sophus Lie Conference center in Nordfjordeid in June 2004. This center, set beautifully in the fjords of the west coast of Norway, has been the site of annual summer schools in algebra and algebraic geometry since 1996. The schools are a joint e?ort between the universities in Bergen, Oslo, Tromsø and Trondheim. They are primarily aimed at graduate students in Norway, but also attract a large number of students from other parts of the world. The theme varies among central topics in contemporary mathematics, but the format is the same: three leading experts give indep- dentbutconnectedseriesoflectures,andgiveexercisesthatthestudentswork on in evening sessions. In 2004 the organizing committee consisted of Stein Arild Strømme (Bergen), Geir Ellingsrud and Kristian Ranestad (Oslo) and Alexei Rudakov (Trondheim). We wanted to have a summer school that introduced the s- dents both to the beauty of modular forms and to their varied applications in other areas of mathematics, and were very fortunate to have Don Zagier, Jan Bruinier and Gerard van der Geer give the lectures. The lectures were organizedin three series that are re?ected in the title of this book both by their numbering and their content. The ?rst series treats the classical one-variabletheory and some of its many applications in number theory, algebraic geometry and mathematical physics. Thesecondseries,whichhasamoregeometric?avor,givesanintroduction tothetheoryofHilbertmodularformsintwovariablesandtoHilbertmodular surfaces. In particular, it discusses Borcherds products and some geometric and arithmetic applications.

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