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Author: Arthur T. Benjamin
Publisher: American Mathematical Soc.
ISBN: 1470458438
Category : Mathematics
Languages : en
Pages : 311
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Book Description
Author: Arthur T. Benjamin
Publisher: American Mathematical Soc.
ISBN: 1470458438
Category : Mathematics
Languages : en
Pages : 311
Get Book
Book Description
Author: Abraham Sinkov
Publisher: MAA
ISBN: 9780883856475
Category : Business & Economics
Languages : en
Pages : 240
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Book Description
An introduction to the basic mathematical techniques involved in cryptanalysis.
Author: Oystein Ore
Publisher: American Mathematical Soc.
ISBN: 0883856530
Category : Number theory
Languages : en
Pages : 134
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Book Description
Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.
Author: John J. Watkins
Publisher: Princeton University Press
ISBN: 1400848741
Category : Mathematics
Languages : en
Pages : 592
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Book Description
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)
Author: Roger B. Nelsen
Publisher: American Mathematical Soc.
ISBN: 1470448467
Category : Mathematics
Languages : en
Pages : 153
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Book Description
Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory. Figurate numbers and Pythagorean triples feature prominently, of course, but there are also proofs of Fermat's Little and Wilson's Theorems. Fibonacci and perfect numbers, Pell's equation, and continued fractions all find visual representation in this charming collection. It will be a rich source of visual inspiration for anyone teaching, or learning, number theory and will provide endless pleasure to those interested in looking at number theory with new eyes. [Author]; Roger Nelsen is a long-time contributor of ``Proofs Without Words'' in the MAA's Mathematics Magazine and College Mathematics Journal. This is his twelfth book with MAA Press.
Author: Andrew Granville
Publisher: American Mathematical Soc.
ISBN: 1470441578
Category : Education
Languages : en
Pages : 264
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Book Description
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.
Author: Andrew Granville
Publisher: American Mathematical Society
ISBN: 1470463709
Category : Mathematics
Languages : en
Pages : 587
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Book Description
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 $p$ 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 $abc$-conjecture including its proof for polynomials. About the Author: Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.
Author: Underwood Dudley
Publisher: MAA
ISBN: 9780883853474
Category : Mathematics
Languages : en
Pages : 156
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Book Description
An introductory guide to elementary number theory for advanced undergraduates and graduates.
Author: Steven G. Krantz
Publisher: MAA
ISBN: 9780883853467
Category : Mathematics
Languages : en
Pages : 128
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Book Description
A Guide to Topology is an introduction to basic topology for graduate or advanced undergraduate students. It covers point-set topology, Moore-Smith convergence and function spaces. It treats continuity, compactness, the separation axioms, connectedness, completeness, the relative topology, the quotient topology, the product topology, and all the other fundamental ideas of the subject. The book is filled with examples and illustrations. Students studying for exams will find this book to be a concise, focused and informative resource. Professional mathematicians who need a quick review of the subject, or need a place to look up a key fact, will find this book to be a useful resource too.
Author: Tristin Cleveland
Publisher: Scientific e-Resources
ISBN: 1839473266
Category :
Languages : en
Pages : 328
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Book Description
In spite of the fact that arithmetic majors are generally familiar with number hypothesis when they have finished a course in conceptual polynomial math, different students, particularly those in training and the human sciences, regularly require a more essential prologue to the theme. In this book the writer takes care of the issue of keeping up the enthusiasm of understudies at the two levels by offering a combinatorial way to deal with basic number hypothesis. In concentrate number hypothesis from such a point of view, arithmetic majors are saved reiteration and furnished with new bits of knowledge, while different understudies advantage from the subsequent effortlessness of the verifications for some hypotheses. Of specific significance in this content is the creator's accentuation on the estimation of numerical cases in number hypothesis and the part of PCs in getting such illustrations. The point of this book is to acquaint the reader with essential subjects in number hypothesis: hypothesis of distinctness, arithmetrical capacities, prime numbers, geometry of numbers, added substance number hypothesis, probabilistic number hypothesis, hypothesis of Diophantine approximations and logarithmic number hypothesis.
