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The Theory Of Arithmetic
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Book Synopsis Set Theory: The Structure of Arithmetic by : Norman T. Hamilton
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.
Book Synopsis Higher Arithmetic by : Harold M. Edwards
Download or read book Higher Arithmetic written by Harold M. Edwards and published by American Mathematical Soc.. This book was released on 2008 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Number Theory and Geometry: An Introduction to Arithmetic Geometry by : Álvaro Lozano-Robledo
Download or read book Number Theory and Geometry: An Introduction to Arithmetic Geometry written by Álvaro Lozano-Robledo and published by American Mathematical Soc.. This book was released on 2019-03-21 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to the Arithmetic Theory of Automorphic Functions by : Gorō Shimura
Download or read book Introduction to the Arithmetic Theory of Automorphic Functions written by Gorō Shimura and published by Princeton University Press. This book was released on 1971-08-21 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Course in Arithmetic by : J-P. Serre
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.
Book Synopsis Representation Theory of Finite Groups: Algebra and Arithmetic by : Steven H. Weintraub
Download or read book Representation Theory of Finite Groups: Algebra and Arithmetic written by Steven H. Weintraub and published by American Mathematical Soc.. This book was released on 2003 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: ``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.
Book Synopsis An Adventurer's Guide to Number Theory by : Richard Friedberg
Download or read book An Adventurer's Guide to Number Theory written by Richard Friedberg and published by Courier Corporation. This book was released on 2012-07-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This witty introduction to number theory deals with the properties of numbers and numbers as abstract concepts. Topics include primes, divisibility, quadratic forms, and related theorems.
Book Synopsis Introduction to the Theory of Sets by : Joseph Breuer
Download or read book Introduction to the Theory of Sets written by Joseph Breuer and published by Courier Corporation. This book was released on 2012-08-09 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.
Book Synopsis Disquisitiones Arithmeticae by : Carl Friedrich Gauss
Download or read book Disquisitiones Arithmeticae written by Carl Friedrich Gauss and published by Springer. This book was released on 2018-02-07 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carl Friedrich Gauss’s textbook, Disquisitiones arithmeticae, published in 1801 (Latin), remains to this day a true masterpiece of mathematical examination. .
Book Synopsis Classical Theory of Arithmetic Functions by : R Sivaramakrishnan
Download or read book Classical Theory of Arithmetic Functions written by R Sivaramakrishnan and published by Routledge. This book was released on 2018-10-03 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on the classical theory of number-theoretic functions emphasizing algebraic and multiplicative techniques. It contains many structure theorems basic to the study of arithmetic functions, including several previously unpublished proofs. The author is head of the Dept. of Mathemati
Book Synopsis A Selection of Problems in the Theory of Numbers by : Waclaw Sierpinski
Download or read book A Selection of Problems in the Theory of Numbers written by Waclaw Sierpinski and published by Elsevier. This book was released on 2014-05-16 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Selection of Problems in the Theory of Numbers focuses on mathematical problems within the boundaries of geometry and arithmetic, including an introduction to prime numbers. This book discusses the conjecture of Goldbach; hypothesis of Gilbreath; decomposition of a natural number into prime factors; simple theorem of Fermat; and Lagrange's theorem. The decomposition of a prime number into the sum of two squares; quadratic residues; Mersenne numbers; solution of equations in prime numbers; and magic squares formed from prime numbers are also elaborated in this text. This publication is a good reference for students majoring in mathematics, specifically on arithmetic and geometry.
Book Synopsis A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z by : Paul Pollack
Download or read book A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z written by Paul Pollack and published by American Mathematical Soc.. This book was released on 2017-08-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
Book Synopsis The Theory of Arithmetic Functions by : Anthony A. Gioia
Download or read book The Theory of Arithmetic Functions written by Anthony A. Gioia and published by Springer. This book was released on 2006-11-15 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Building the Foundation: Whole Numbers in the Primary Grades by : Maria G. Bartolini Bussi
Download or read book Building the Foundation: Whole Numbers in the Primary Grades written by Maria G. Bartolini Bussi and published by Springer. This book was released on 2018-03-29 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This twenty-third ICMI Study addresses for the first time mathematics teaching and learning in the primary school (and pre-school) setting, while also taking international perspectives, socio-cultural diversity and institutional constraints into account. One of the main challenges of designing the first ICMI primary school study of this kind is the complex nature of mathematics at the early level. Accordingly, a focus area that is central to the discussion was chosen, together with a number of related questions. The broad area of Whole Number Arithmetic (WNA), including operations and relations and arithmetic word problems, forms the core content of all primary mathematics curricula. The study of this core content area is often regarded as foundational for later mathematics learning. However, the principles and main goals of instruction on the foundational concepts and skills in WNA are far from universally agreed upon, and practice varies substantially from country to country. As such, this study presents a meta-level analysis and synthesis of what is currently known about WNA, providing a useful base from which to gauge gaps and shortcomings, as well as an opportunity to learn from the practices of different countries and contexts.
Book Synopsis Number Theory - Modular Arithmetic by : Xing Zhou
Download or read book Number Theory - Modular Arithmetic written by Xing Zhou and published by Createspace Independent Publishing Platform. This book was released on 2017-03 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Remainder does not seem to be a big topic in school math. However, in competition math, it is. Almost every contest at middle school and high school level has remainder related problems. For example, in 2017 AMC 10B, out of total 25 problems, at least 3 are related to this topic: the 14th, 23rd, and 25th. Modular arithmetic is a branch in mathematics which studies remainders and tackles related problems. However, this important subject is not taught in schools. Consequently, many students rely on their intuition when attempting to solve such problems. This is clearly not the best situation. This book aims to provide a complete coverage of this topic at the level which is suitable for middle school and high school students. Contents will include both theoretical knowledge and practical techniques. Therefore, upon completion, students will have a solid skill base to solve related problems in math competitions. More information, including table of contents, pre-assessment etc, can be found at http: //www.mathallstar.org/
Book Synopsis Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 by : Gerd Faltings
Download or read book Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127), Volume 127 written by Gerd Faltings and published by Princeton University Press. This book was released on 2016-03-02 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The arithmetic Riemann-Roch Theorem has been shown recently by Bismut-Gillet-Soul. The proof mixes algebra, arithmetic, and analysis. The purpose of this book is to give a concise introduction to the necessary techniques, and to present a simplified and extended version of the proof. It should enable mathematicians with a background in arithmetic algebraic geometry to understand some basic techniques in the rapidly evolving field of Arakelov-theory.
Book Synopsis An Introduction to the Theory of Numbers by : Godfrey Harold Hardy
Download or read book An Introduction to the Theory of Numbers written by Godfrey Harold Hardy and published by Oxford University Press. This book was released on 1979 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford, Cambridge, Aberdeen, and other universities. It is neither a systematic treatise on the theory ofnumbers nor a 'popular' book for non-mathematical readers. It contains short accounts of the elements of many different sides of the theory, not usually combined in a single volume; and, although it is written for mathematicians, the range of mathematical knowledge presupposed is not greater thanthat of an intelligent first-year student. In this edition the main changes are in the notes at the end of each chapter; Sir Edward Wright seeks to provide up-to-date references for the reader who wishes to pursue a particular topic further and to present, both in the notes and in the text, areasonably accurate account of the present state of knowledge.
