The Theory Of Arithmetic PDF Download
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Author | : Norman T. Hamilton |
Publisher | : Courier Dover Publications |
Total Pages | : 289 |
Release | : 2018-05-16 |
Genre | : Mathematics |
ISBN | : 0486830470 |
Download Set Theory: The Structure of Arithmetic Book in PDF, ePub and Kindle
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 | : Harold M. Edwards |
Publisher | : American Mathematical Soc. |
Total Pages | : 228 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9780821844397 |
Download Higher Arithmetic Book in PDF, ePub and Kindle
Among the topics featured in this textbook are: congruences; the fundamental theorem of arithmetic; exponentiation and orders; primality testing; the RSA cipher system; polynomials; modules of hypernumbers; signatures of equivalence classes; and the theory of binary quadratic forms. The book contains exercises with answers.
Author | : Oystein Ore |
Publisher | : Courier Corporation |
Total Pages | : 404 |
Release | : 2012-07-06 |
Genre | : Mathematics |
ISBN | : 0486136434 |
Download Number Theory and Its History Book in PDF, ePub and Kindle
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
Author | : Álvaro Lozano-Robledo |
Publisher | : American Mathematical Soc. |
Total Pages | : 488 |
Release | : 2019-03-21 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 147045016X |
Download Number Theory and Geometry: An Introduction to Arithmetic Geometry Book in PDF, ePub and Kindle
Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.
Author | : John A. Peterson |
Publisher | : |
Total Pages | : 360 |
Release | : 1967 |
Genre | : Arithmetic |
ISBN | : |
Download Theory of Arithmetic Book in PDF, ePub and Kindle
Author | : J-P. Serre |
Publisher | : Springer Science & Business Media |
Total Pages | : 126 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468498843 |
Download A Course in Arithmetic Book in PDF, ePub and Kindle
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 | : H. Davenport |
Publisher | : Cambridge University Press |
Total Pages | : 248 |
Release | : 1999-12-09 |
Genre | : Mathematics |
ISBN | : 9780521634465 |
Download The Higher Arithmetic Book in PDF, ePub and Kindle
Seventh edition of a classic elementary number theory book.
Author | : Lawrence M Graves |
Publisher | : Courier Corporation |
Total Pages | : 361 |
Release | : 2012-01-27 |
Genre | : Mathematics |
ISBN | : 0486158136 |
Download The Theory of Functions of Real Variables Book in PDF, ePub and Kindle
This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.
Author | : Gorō Shimura |
Publisher | : Princeton University Press |
Total Pages | : 292 |
Release | : 1971-08-21 |
Genre | : Mathematics |
ISBN | : 9780691080925 |
Download Introduction to the Arithmetic Theory of Automorphic Functions Book in PDF, ePub and Kindle
The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.
Author | : Steven H. Weintraub |
Publisher | : American Mathematical Soc. |
Total Pages | : 226 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821832220 |
Download Representation Theory of Finite Groups: Algebra and Arithmetic Book in PDF, ePub and Kindle
``We explore widely in the valley of ordinary representations, and we take the reader over the mountain pass leading to the valley of modular representations, to a point from which (s)he can survey this valley, but we do not attempt to widely explore it. We hope the reader will be sufficiently fascinated by the scenery to further explore both valleys on his/her own.'' --from the Preface Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, representation theory has been one of the great tools in the study and classification of finite groups. There are some beautiful results that come from representation theory: Frobenius's Theorem, Burnside's Theorem, Artin's Theorem, Brauer's Theorem--all of which are covered in this textbook. Some seem uninspiring at first, but prove to be quite useful. Others are clearly deep from the outset. And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers. The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group. The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference.