A Course In Arithmetic

Author : J-P. Serre
Publisher : Springer Science & Business Media
ISBN 13 : 1468498843
Total Pages : 126 pages
Book Rating : 4.44/5 ( download)

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Download or read book A Course in Arithmetic written by J-P. Serre and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.-J. Sansuc (Chapters I-IV) and J.-P. Ramis and G. Ruget (Chapters VI-VII). They were very useful to me; I extend here my gratitude to their authors.

Author : Jean-Pierre Serre
Publisher :
ISBN 13 : 9783540900405
Total Pages : 115 pages
Book Rating : 4.03/5 ( download)

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Download or read book A Course in Arithmetic written by Jean-Pierre Serre and published by . This book was released on 1973 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: Serre's A Course in Arithmetic is a concentrated, modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms. The first edition was very well accepted and is now one of the leading introductory texts on the advanced undergraduate or beginning graduate level.From the reviews: ..." The book is carefully written - in particular very much self-contained. As was the intention of the author, it is easily accessible to graduate or even undergraduate students, yet even the advanced mathematician will enjoy reading it. The last chapter, more difficult for the beginner, is an introduction to contemporary problems." American Scientist

Author : Fred Diamond
Publisher : Springer Science & Business Media
ISBN 13 : 0387272267
Total Pages : 450 pages
Book Rating : 4.69/5 ( download)

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Download or read book A First Course in Modular Forms written by Fred Diamond and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.

Author : Norman T. Hamilton
Publisher : Courier Dover Publications
ISBN 13 : 0486830470
Total Pages : 288 pages
Book Rating : 4.76/5 ( download)

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Download or read book Set Theory: The Structure of Arithmetic written by Norman T. Hamilton and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.

Author : Thomas A. Garrity
Publisher : 清华大学出版社有限公司
ISBN 13 : 9787302090854
Total Pages : 380 pages
Book Rating : 4.58/5 ( download)

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Download or read book All the Mathematics You Missed written by Thomas A. Garrity and published by 清华大学出版社有限公司. This book was released on 2004 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jiri Herman
Publisher : Springer Science & Business Media
ISBN 13 : 1475739257
Total Pages : 402 pages
Book Rating : 4.51/5 ( download)

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Download or read book Counting and Configurations written by Jiri Herman and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.

Author : Susan Jo Russell
Publisher : Heinemann Educational Books
ISBN 13 : 9780325041919
Total Pages : 0 pages
Book Rating : 4.11/5 ( download)

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Download or read book Connecting Arithmetic to Algebra written by Susan Jo Russell and published by Heinemann Educational Books. This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "To truly engage in mathematics is to become curious and intrigued about regularities and patterns, then describe and explain them. A focus on the behavior of the operations allows students starting in the familiar territory of number and computation to progress to true engagement in the discipline of mathematics." -Susan Jo Russell, Deborah Schifter, and Virginia Bastable Algebra readiness: it's a topic of concern that seems to pervade every school district. How can we better prepare elementary students for algebra? More importantly, how can we help all children, not just those who excel in math, become ready for later instruction? The answer lies not in additional content, but in developing a way of thinking about the mathematics that underlies both arithmetic and algebra. Connecting Arithmetic to Algebra invites readers to learn about a crucial component of algebraic thinking: investigating the behavior of the operations. Nationally-known math educators Susan Jo Russell, Deborah Schifter, and Virginia Bastable and a group of collaborating teachers describe how elementary teachers can shape their instruction so that students learn to: *notice and describe consistencies across problems *articulate generalizations about the behavior of the operations *develop mathematical arguments based on representations to explain why such generalizations are or are not true. Through such work, students become familiar with properties and general rules that underlie computational strategies-including those that form the basis of strategies used in algebra-strengthening their understanding of grade-level content and at the same time preparing them for future studies. Each chapter is illustrated by lively episodes drawn from the classrooms of collaborating teachers in a wide range of settings. These provide examples of posing problems, engaging students in productive discussion, using representations to develop mathematical arguments, and supporting both students with a wide range of learning profiles. Staff Developers: Available online, the Course Facilitator's Guide provides math leaders with tools and resources for implementing a Connecting Arithmetic to Algebra workshop or preservice course. For information on the PD course offered through Mount Holyoke College, download the flyer.

Author : Serge Lang
Publisher : Springer Science & Business Media
ISBN 13 : 3642514472
Total Pages : 267 pages
Book Rating : 4.70/5 ( download)

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Download or read book Introduction to Modular Forms written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book gives a thorough introduction to several theories that are fundamental to research on modular forms. Most of the material, despite its importance, had previously been unavailable in textbook form. Complete and readable proofs are given... In conclusion, this book is a welcome addition to the literature for the growing number of students and mathematicians in other fields who want to understand the recent developments in the theory of modular forms." #Mathematical Reviews# "This book will certainly be indispensable to all those wishing to get an up-to-date initiation to the theory of modular forms." #Publicationes Mathematicae#

Author : Edwin Weiss
Publisher : Courier Corporation
ISBN 13 : 048615436X
Total Pages : 308 pages
Book Rating : 4.67/5 ( download)

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Download or read book Algebraic Number Theory written by Edwin Weiss and published by Courier Corporation. This book was released on 2012-01-27 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
ISBN 13 : 1441985921
Total Pages : 245 pages
Book Rating : 4.27/5 ( download)

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Download or read book A Course in Number Theory and Cryptography written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2012-09-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.