Biscuits of Number Theory

Author: Arthur T. Benjamin,Ezra Brown

Publisher: MAA

ISBN: 9780883853405

Category: Mathematics

Page: 311

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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: Business & Economics

Page: 212

View: 7694

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Originally published in the New Mathematical Library almost half a century ago, this charming book explains how to solve cryptograms based on elementary mathematical principles, starting with the Caesar cipher and building up to progressively more sophisticated substitution methods. Todd Feil has updated the book for the technological age by adding two new chapters covering RSA public-key cryptography, one-time pads, and pseudo-random-number generators.
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Number Theory

A Historical Approach

Author: John J. Watkins

Publisher: Princeton University Press

ISBN: 1400848741

Category: Mathematics

Page: 592

View: 7811

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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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Number Theory Revealed: A Masterclass

Author: Andrew Granville

Publisher: American Mathematical Soc.

ISBN: 1470441586

Category: Education

Page: 587

View: 8347

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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: 2197

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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: 5736

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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: 8593

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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: 1805

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First-ever comprehensive introduction to the major new subject of quantum computing and quantum information.
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Giovanni Gentile and the State of Contemporary Constructivism

A Study of Actual Idealist Moral Theory

Author: James Wakefield

Publisher: Andrews UK Limited

ISBN: 1845407989

Category: Philosophy

Page: 328

View: 2146

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This book presents Giovanni Gentile’s actual idealism as a radical constructivist doctrine for use in moral theory. The first half describes the moral theory that Gentile explicitly identifies with actual idealism, according to which all thinking, rather than an exclusive domain of ‘practical reason’, has a moral character. It is argued that after Gentile’s turn to Fascism in the early 1920s, this theory is increasingly conflated with his political doctrine. This entails several major changes that cannot be squared with the underlying metaphysics. The second half of the book develops a more plausible account of Gentilean moral constructivism based on the pre-Fascist idea of reasoning as an internal dialogue. Comparisons and contrasts are drawn with contemporary constructivist doctrines, as well as theories employing dialogical conceptions of reason. The internal dialogue is presented as a device enabling the thinking subject to make objective judgments about real-world problems despite the impossibility of her occupying a fully objective standpoint. Thus actual idealist moral theory is offered as an example of constructivism at its most radical, inviting advocates of less radical varieties to reassess the foundations on which their theories are built.
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The Longest Winter

Scott's Other Heroes

Author: Meredith Hooper

Publisher: Catapult

ISBN: 1582438382

Category: History

Page: 399

View: 7004

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Through the eyes of the men involved, Meredith Hooper recounts one of the greatest tales of adventure and endurance, which has often been overshadowed by the tragedy that befell Scott. Their tents were torn, their food was nearly finished, and the ship had failed to pick them up as planned. Gale-force winds blew, bitter with the cold of approaching winter. Stranded and desperate, Lieutenant Victor Campbell and his five companions faced disaster. They burrowed inside a snowdrift, digging an ice-cave with no room to stand upright, but space for six sleeping bags on the floor—the three officers on one side, the tree seamen on the other. Circumstances forced them closer together, their roles blurred, and a shared sense of reality emerged. This mutual suffering made them indivisible and somehow they made it through the longest winter. To the south, the men waiting at headquarters knew that Scott and his Polar party must be dead and hoped that another six lives would not be added to the death toll. Working from diaries, journals, and letters written by expedition members, Meredith Hooper tells the intensely human story of Scotts other expedition.
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