A Course In Arithmetic

Author : J-P. Serre
Publisher : Springer Science & Business Media
Page : 126 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468498844

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A Course in Arithmetic by J-P. Serre Pdf

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 : Unknown
Page : 115 pages
File Size : 41,6 Mb
Release : 1973
Category : Analytic functions
ISBN : 3540900403

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A Course in Arithmetic by Jean-Pierre Serre Pdf

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 : Thomas A. Garrity
Publisher : 清华大学出版社有限公司
Page : 380 pages
File Size : 55,7 Mb
Release : 2004
Category : Mathematics
ISBN : 7302090858

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All the Mathematics You Missed by Thomas A. Garrity Pdf

Author : Fred Diamond,Jerry Shurman
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 54,5 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387272269

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A First Course in Modular Forms by Fred Diamond,Jerry Shurman Pdf

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 : Susan Jo Russell,Deborah Schifter,Virginia Bastable
Publisher : Heinemann Educational Books
Page : 0 pages
File Size : 45,9 Mb
Release : 2011
Category : Education
ISBN : 0325041911

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Connecting Arithmetic to Algebra by Susan Jo Russell,Deborah Schifter,Virginia Bastable Pdf

"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
Page : 267 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642514470

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Introduction to Modular Forms by Serge Lang Pdf

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 : Charles Hutton
Publisher : Unknown
Page : 492 pages
File Size : 46,9 Mb
Release : 1836
Category : Mathematics
ISBN : OXFORD:590517365

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A Course of Mathematics by Charles Hutton Pdf

Author : Norman T. Hamilton,Joseph Landin
Publisher : Courier Dover Publications
Page : 288 pages
File Size : 46,7 Mb
Release : 2018-05-16
Category : Mathematics
ISBN : 9780486830476

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Set Theory: The Structure of Arithmetic by Norman T. Hamilton,Joseph Landin Pdf

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 : Ann Faber,Gale Edgerton,Paul Karanevich
Publisher : Rowman & Littlefield
Page : 254 pages
File Size : 45,5 Mb
Release : 1985
Category : Mathematics
ISBN : 091267508X

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A Brief Course in Arithmetic by Ann Faber,Gale Edgerton,Paul Karanevich Pdf

A useful study tool and guide for anyone interesting in sharpening their arithmetic skills.

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
Page : 238 pages
File Size : 50,8 Mb
Release : 2018-07-30
Category : Electronic
ISBN : 1724572636

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Discrete Mathematics by Oscar Levin Pdf

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.

Author : Katherine Loop
Publisher : Master Books
Page : 0 pages
File Size : 48,8 Mb
Release : 2016-09-02
Category : Electronic
ISBN : 0890519145

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Principles of Mathematics Book 1 Set by Katherine Loop Pdf

Katherine Loop has done the remarkable! She has written a solid math course with a truly Biblical worldview. This course goes way beyond the same old Christian math course that teaches math with a few Scriptures sprinkled in and maybe some church-based word problems. This course truly transforms the way we see math. Katherine makes the argument that math is not a neutral subject as most have come to believe. She carefully lays the foundation of how math points to our Creator, the God of the Bible. The nature of God, His Creation, and even the Gospel itself is seen through the study of math. Katherine does a marvelous job of revealing His Glory in this one-of-a-kind math course. Katherine Loop's Principles of Mathematics Biblical Worldview Curriculum is a first of its kind. It takes math to a whole new level students and parents are going to love. It is a guaranteed faith grower!

Author : Fernando Q. Gouvea
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 53,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662222782

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p-adic Numbers by Fernando Q. Gouvea Pdf

p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.

Author : Marius Overholt
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 42,6 Mb
Release : 2014-12-30
Category : Mathematics
ISBN : 9781470417062

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A Course in Analytic Number Theory by Marius Overholt Pdf

This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem. The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader. The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.

Author : Eric Lehman,F. Thomson Leighton,Albert R. Meyer
Publisher : Unknown
Page : 988 pages
File Size : 41,9 Mb
Release : 2017-03-08
Category : Business & Economics
ISBN : 9888407066

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Mathematics for Computer Science by Eric Lehman,F. Thomson Leighton,Albert R. Meyer Pdf

This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 50,8 Mb
Release : 2012-09-05
Category : Mathematics
ISBN : 9781441985927

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A Course in Number Theory and Cryptography by Neal Koblitz Pdf

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.