The Higher Arithmetic

An Introduction to the Theory of Numbers

Author: H. Davenport

Publisher: Cambridge University Press

ISBN: 9780521634465

Category: Mathematics

Page: 241

View: 7872

Seventh edition of a classic elementary number theory book.

Higher Arithmetic

An Algorithmic Introduction to Number Theory

Author: Harold M. Edwards

Publisher: American Mathematical Soc.

ISBN: 9780821844397

Category: Mathematics

Page: 210

View: 822

Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classic Disquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry--some would say it is superior to Euclidean geometry--as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument. Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory. Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990), Linear Algebra (1995), and Essays in Constructive Mathematics (2005). For his masterly mathematical exposition he was awarded a Steele Prize as well as a Whiteman Prize by the American Mathematical Society.

Higher arithmetic

or the science and application of numbers, combining the analytic and synthetic modes of instruction ...

Author: James Bates Thomson

Publisher: N.A


Category: Arithmetic

Page: 422

View: 9124

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts

Author: David C. Geary,Daniel B. Berch,Robert Ochsendorf,Kathleen Mann Koepke

Publisher: Academic Press

ISBN: 0128133686

Category: Psychology

Page: 360

View: 8198

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children’s developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. Covers innovative measures and recent methodological advances in mathematical thinking and learning Contains contributions that improve instruction and education in these domains Informs policy aimed at increasing the level of mathematical proficiency in the general public

Philosophy of Arithmetic

Psychological and Logical Investigations with Supplementary Texts from 1887–1901

Author: Edmund Husserl

Publisher: Springer Science & Business Media

ISBN: 9401000603

Category: Mathematics

Page: 515

View: 3954

This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time.


A Path to Geometry

Author: R. P. Burn

Publisher: Cambridge University Press

ISBN: 9780521347938

Category: Mathematics

Page: 242

View: 1024

Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions.

An Introduction to the Theory of Numbers

Author: Godfrey Harold Hardy,E. M. Wright,Roger Heath-Brown,Joseph Silverman

Publisher: Oxford University Press

ISBN: 9780199219865

Category: Mathematics

Page: 621

View: 5498

An Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. This Sixth Edition has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter on one of the mostimportant developments in number theory -- modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader and the clarityof exposition is retained throughout making this textbook highly accessible to undergraduates in mathematics from the first year upwards.