The Higher Arithmetic

An Introduction to the Theory of Numbers

Author: H. Davenport

Publisher: Cambridge University Press

ISBN: 9780521634465

Category: Mathematics

Page: 241

View: 606

Seventh edition of a classic elementary number theory book.

Quadratic Number Theory: An Invitation to Algebraic Methods in the Higher Arithmetic

Author: J. L. Lehman

Publisher: American Mathematical Soc.

ISBN: 1470447371

Category: Algebraic fields

Page: 394

View: 875

Quadratic Number Theory is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. By restricting attention to questions about squares the author achieves the dual goals of making the presentation accessible to undergraduates and reflecting the historical roots of the subject. The representation of integers by quadratic forms is emphasized throughout the text. Lehman introduces an innovative notation for ideals of a quadratic domain that greatly facilitates computation and he uses this to particular effect. The text has an unusual focus on actual computation. This focus, and this notation, serve the author's historical purpose as well; ideals can be seen as number-like objects, as Kummer and Dedekind conceived of them. The notation can be adapted to quadratic forms and provides insight into the connection between quadratic forms and ideals. The computation of class groups and continued fraction representations are featured—the author's notation makes these computations particularly illuminating. Quadratic Number Theory, with its exceptionally clear prose, hundreds of exercises, and historical motivation, would make an excellent textbook for a second undergraduate course in number theory. The clarity of the exposition would also make it a terrific choice for independent reading. It will be exceptionally useful as a fruitful launching pad for undergraduate research projects in algebraic number theory.

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: 9735

The Nature and Growth of Modern Mathematics

Author: Edna Ernestine Kramer

Publisher: Princeton University Press

ISBN: 9780691023724

Category: Mathematics

Page: 758

View: 9572

Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.

Combinatory Analysis

Author: Percy A. MacMahon

Publisher: American Mathematical Soc.

ISBN: 0821828320

Category: Mathematics

Page: 642

View: 9538

By ``combinatory analysis'', the author understands the part of combinatorics now known as ``algebraic combinatorics''. In this book, the classical results of the outstanding 19th century school of British mathematicians are presented with great clarity and completeness. From the Introduction (1915): ``The object of this work is, in the main, to present to mathematicians an account of theorems in combinatory analysis which are of a perfectly general character, and to show the connection between them by as far as possible bringing them together as parts of a general doctrine. It may appeal also to others whose reading has not been very extensive. They may not improbably find here some new points of view and suggestions which may prompt them to original investigation in a fascinating subject ... ``In the present volume there appears a certain amount of original matter which has not before been published. It involves the author's preliminary researches in combinatory theory which have been carried out during the last thirty years. For the most part it is original work which, however, owes much to valuable papers by Cayley, Sylvester, and Hammond.''

The Development of Mathematics

Author: E. T. Bell

Publisher: Courier Corporation

ISBN: 0486152286

Category: Mathematics

Page: 656

View: 4242

Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.

Higher arithmetic

designed for the use of high schools and colleges and for self instruction

Author: Frederick Augustus Smith

Publisher: N.A


Category: Mathematics

Page: 137

View: 3197

A Day in Old Rome

A Picture of Roman Life

Author: William Stearns Davis

Publisher: Biblo & Tannen Publishers

ISBN: 9780819601063

Category: History

Page: 482

View: 712

Descriptions of daily Roman life including details about marriage, homes, food, costume, slaves, physicians, and libraries

Higher Arithmetic

An Algorithmic Introduction to Number Theory

Author: Harold M. Edwards

Publisher: American Mathematical Soc.

ISBN: 9780821844397

Category: Mathematics

Page: 210

View: 3318

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.


Probleme — Themen — Fragen


Publisher: Springer-Verlag

ISBN: 3034861176

Category: Juvenile Nonfiction

Page: 313

View: 1014

A Complete Treatise on Arithmetic, Rational and Practical

Wherein the Properties of Numbers are Clearly Pointed Out: the Theory and Practice of the Science are Deduced from First Principles and Demonstrated in a Familiar Manner; with a Great Variety of Proper Examples in All the Rules, Perfectly Suited to the Man of Business, Academies, Schools, and Students of Every Denomination, Desirousof Becoming Proficients in Accounts ...

Author: Paul Deighan

Publisher: N.A


Category: Arithmetic

Page: N.A

View: 8376

Higher Arithmetic

Designed for the Use of High Schools, Academies, and Colleges ... with an Appendix

Author: George Roberts Perkins

Publisher: N.A


Category: Arithmetic

Page: 342

View: 7739