Biscuits of Number Theory

Author: Arthur T. Benjamin,Ezra Brown

Publisher: MAA

ISBN: 9780883853405

Category: Mathematics

Page: 311

View: 9788

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An anthology of articles designed to supplement a first course in number theory.
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Biscuits of Number Theory

Author: Arthur T. Benjamin,Ezra Brown

Publisher: MAA

ISBN: 9780883853405

Category: Mathematics

Page: 311

View: 4872

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An anthology of articles designed to supplement a first course in number theory.
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Elementary Cryptanalysis

Author: Abraham Sinkov,Todd Feil

Publisher: MAA

ISBN: 9780883856475

Category: Computers

Page: 212

View: 2725

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An introduction to the basic mathematical techniques involved in cryptanalysis.
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Number Theory

A Historical Approach

Author: John J. Watkins

Publisher: Princeton University Press

ISBN: 1400848741

Category: Mathematics

Page: 592

View: 1324

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The natural numbers have been studied for thousands of years, yet most undergraduate textbooks present number theory as a long list of theorems with little mention of how these results were discovered or why they are important. This book emphasizes the historical development of number theory, describing methods, theorems, and proofs in the contexts in which they originated, and providing an accessible introduction to one of the most fascinating subjects in mathematics. Written in an informal style by an award-winning teacher, Number Theory covers prime numbers, Fibonacci numbers, and a host of other essential topics in number theory, while also telling the stories of the great mathematicians behind these developments, including Euclid, Carl Friedrich Gauss, and Sophie Germain. This one-of-a-kind introductory textbook features an extensive set of problems that enable students to actively reinforce and extend their understanding of the material, as well as fully worked solutions for many of these problems. It also includes helpful hints for when students are unsure of how to get started on a given problem. Uses a unique historical approach to teaching number theory Features numerous problems, helpful hints, and fully worked solutions Discusses fun topics like Pythagorean tuning in music, Sudoku puzzles, and arithmetic progressions of primes Includes an introduction to Sage, an easy-to-learn yet powerful open-source mathematics software package Ideal for undergraduate mathematics majors as well as non-math majors Digital solutions manual (available only to professors)
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A Guide to Topology

Author: Steven G. Krantz

Publisher: MAA

ISBN: 9780883853467

Category: Mathematics

Page: 107

View: 6439

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This book is an outline of the core material in the standard graduate-level real analysis course. It is intended as a resource for students in such a course as well as others who wish to learn or review the subject. On the abstract level, it covers the theory of measure and integration and the basics of point set topology, functional analysis, and the most important types of function spaces. On the more concrete level, it also deals with the applications of these general theories to analysis on Euclidean space: the Lebesgue integral, Hausdorff measure, convolutions, Fourier series and transforms, and distributions. The relevant definitions and major theorems are stated in detail. Proofs, however, are generally presented only as sketches, in such a way that the key ideas are explained but the technical details are omitted. In this way a large amount of material is presented in a concise and readable form.
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Number Theory Revealed: A Masterclass

Author: Andrew Granville

Publisher: American Mathematical Soc.

ISBN: 1470441586

Category: Education

Page: 587

View: 9299

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Number Theory Revealed: A Masterclass acquaints enthusiastic students with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p p and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many additional chapters and appendices not found in Number Theory Revealed: An Introduction, highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, a new proof of Mordell's Theorem for congruent elliptic curves, and a discussion of the abc abc-conjecture including its proof for polynomials.
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Number Theory Revealed: An Introduction

Author: Andrew Granville

Publisher: American Mathematical Soc.

ISBN: 1470441578

Category: Education

Page: 264

View: 4848

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Number Theory Revealed: An Introduction acquaints undergraduates with the “Queen of Mathematics”. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p p and modern twists on traditional questions like the values represented by binary quadratic forms and large solutions of equations. Each chapter includes an “elective appendix” with additional reading, projects, and references. An expanded edition, Number Theory Revealed: A Masterclass, offers a more comprehensive approach to these core topics and adds additional material in further chapters and appendices, allowing instructors to create an individualized course tailored to their own (and their students') interests.
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A Guide to Real Variables

Author: Steven G. Krantz

Publisher: MAA

ISBN: 9780883853443

Category: Mathematics

Page: 147

View: 7414

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A Guide to Real Variables is an aid and conceptual support for students taking an undergraduate course on real analysis. It focuses on concepts, results, examples and illustrative figures, rather than the details of proofs, in order to remain a concise guide which students can dip into. The core topics of a first real analysis course are covered, including sequences, series, modes of convergence, the derivative, the integral and metric spaces. The next book in this series, Folland's A Guide to Advanced Real Analysis is designed to naturally follow on from this book, and introduce students to graduate level real analysis. Together these books provide a concise guide to the subject at all levels, ideal for student preparation for exams.
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Theory of Production

A Long-Period Analysis

Author: Heinz D. Kurz,Neri Salvadori

Publisher: Cambridge University Press

ISBN: 9780521588676

Category: Business & Economics

Page: 571

View: 6716

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This book contains a systematic and comprehensive analytical treatment of the theory of production in a long-period framework. Given the scope of investigation, the methods employed, and the results derived, this study is of interest to all economic theorists. Professors Kurz and Salvadori explore economic systems in which commodities are produced by means of labor, natural resources, and commodified-means of production. They investigate the relationship between production, income distribution, and relative prices for stationary or growing economies characterized by free competition. Specific chapters deal with joint production, fixed capital (including the joint utilization of machines), scarce natural resources (both renewable and exhaustible), heterogeneous labor, the problem of capital, and alternative theories of distribution. The historical origins of the concepts used from the time of the classical economists onward are also discussed in considerable detail.
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Quantum Computation and Quantum Information

Author: Michael E. Nielsen,Michael A. Nielsen,Isaac L. Chuang

Publisher: Cambridge University Press

ISBN: 9780521635035

Category: Computers

Page: 676

View: 6455

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First-ever comprehensive introduction to the major new subject of quantum computing and quantum information.
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