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Author: J-P. Serre Publisher: Springer Science & Business Media ISBN: 1468498843 Category : Mathematics Languages : en Pages : 126
Book Description
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: J-P. Serre Publisher: Springer Science & Business Media ISBN: 1468498843 Category : Mathematics Languages : en Pages : 126
Book Description
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: F. W. Bardwell Publisher: Forgotten Books ISBN: 9780267630158 Category : Mathematics Languages : en Pages : 390
Book Description
Excerpt from Course in Arithmetic, Vol. 1 of 3: A Treatise in Three Parts, Complete in One Volume IN presenting to the public a new treatise op Arithmetic, it is proper to call attention to the features which distinguish it from others, and to the need of. Radical changes in the traditional precepts retained in the text-books in current use. First, it is intended to present, in the compass of a single volume, a complete treatise, and, indeed, all that the average pupil needs to study on the subject from first to last. It is supposed the pupil has previously acquired those first elementary notions of numbers, such as may be best taught orally, and, indeed, should be learned before he is prepared to use a book for systematic study. Secondly, the subject-matter is arranged in three parts logically distinct, in each of which the pupil gives his attention to a Specific object, complete in itself. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: F. W. Bardwell Publisher: Forgotten Books ISBN: 9781330130544 Category : Mathematics Languages : en Pages : 391
Book Description
Excerpt from Course in Arithmetic, Vol. 1 of 3: A Treatise in Three Parts, Complete in One Volume About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Fred Diamond Publisher: Springer Science & Business Media ISBN: 0387272267 Category : Mathematics Languages : en Pages : 462
Book Description
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: McGraw-Hill Education Publisher: McGraw-Hill Education ISBN: 9780076691005 Category : Mathematics Languages : en Pages : 528
Book Description
The Glencoe Math Student Edition is an interactive text that engages students and assist with learning and organization. It personalizes the learning experience for every student. The write-in text, 3-hole punched, perfed pages allow students to organize while they are learning.
Author: Marius Overholt Publisher: American Mathematical Soc. ISBN: 1470417065 Category : Mathematics Languages : en Pages : 394
Book Description
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: Charles Hutton Publisher: Forgotten Books ISBN: 9780366501694 Category : Mathematics Languages : en Pages : 378
Book Description
Excerpt from A Course of Mathematics, Vol. 1 of 3: Composed for the Use of the Royal Military Academy, by Order of His Lordship the Master General of the Ordnance Though the several parts of this course of mathematics are ranged in the order naturally required by such elements, yet students may omit any of the particulars that may be thought the least necessary to their several purposes; or they may study and learn various parts in a difi'erent order from their present arrangement in the book, at the discretion of the tutor. So, for instance, all the notes at the foot of the pages may be omitted, as well as many of the rules particularly the 1st or Common Rule for the Cube Root, p. 85, may well be omitted, being more tedious than useful. Also the chap ters on Surds and Infinite Series, in the Algebra: or these might be learned after Simple Equations. Also Compound Interest and Annuities at the end of the Algebra. Also any part of the Geometry, in vol. 1; any of the branches in vol. 2, at the discretion of the preceptor. And, in any of the parts, he may omit some of the examples, or hemay give more than are printed in the book; or he may very pro fitably vary or change them, by altering the numbers oc casionally.-as to the quantity of writing; the author. Would recommend, that the student copy out into his fair book no more than the chief rules which he is directed to learn of by rote, with the work of one example only to each rule, set down at full length omitting to set down the work of all the other examples, how many soever he may be directed to work out upon his slate or waste paper.-in short, a great deal of the business, as to the quantity and order and manner. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: William Fulton Publisher: Springer Science & Business Media ISBN: 9780387974958 Category : Mathematics Languages : en Pages : 616
Book Description
Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.
Author: Jason Batterson Publisher: ISBN: 9781934124307 Category : Languages : en Pages :
Book Description
Beast Academy Guide 2A and its companion Practice 2A (sold separately) are the first part in the planned four-part series for 2nd grade mathematics. Book 2A includes chapters on place value, comparing, and addition.
Author: J-P. Serre
Author: J-P. Serre
Author: F. W. Bardwell
Author: F. W. Bardwell
Author: Fred Diamond
Author: McGraw-Hill Education
Author: Marius Overholt
Author: Charles Hutton
Author: 
Author: William Fulton
Author: Jason Batterson