{"product_id":"a-course-in-computational-number-theory-hardback-9780470412152","title":"A Course in Computational Number Theory (Hardback) 9780470412152","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eA Course in Computational Number Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eDavid Bressoud (Author), Stan Wagon (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470412152, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 6 November 2008\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e384 pages\u003cbr\u003e23.8 x 18.4 x 2.5 cm, 0.874 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003ci\u003eA Course in Computational Number Theory\u003c\/i\u003e uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiments with the patterns of the integers. It presents and explains many of the fastest algorithms for working with integers. Traditional topics are covered, but the text also explores factoring algorithms, primality testing, the RSA public-key cryptosystem, and unusual applications such as check digit schemes and a computation of the energy that holds a salt crystal together. Advanced topics include continued fractions, Pell’s equation, and the Gaussian primes.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface.  \u003cp\u003eNotation.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Fundamentals.\u003c\/b\u003e\u003cbr\u003e 1.0 Introduction.\u003cbr\u003e 1.1 A Famous Sequence of Numbers.\u003cbr\u003e 1.2 The Euclidean ALgorithm.\u003cbr\u003e The Oldest Algorithm.\u003cbr\u003e Reversing the Euclidean Algorithm.\u003cbr\u003e The Extended GCD Algorithm.\u003cbr\u003e The Fundamental Theorem of Arithmetic.\u003cbr\u003e Two Applications.\u003cbr\u003e 1.3 Modular Arithmetic.\u003cbr\u003e 1.4 Fast Powers.\u003cbr\u003e A Fast Alforithm for ExponentiationPowers of Matrices, Big-O Notation.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Congruences, Equations, and Powers.\u003c\/b\u003e\u003cbr\u003e 2.0 Introduction.\u003cbr\u003e 2.1 Solving Linear Congruences.\u003cbr\u003e Linear Diophantine Equations in Two Variables.\u003cbr\u003e The Conductor.\u003cbr\u003e An Importatnt Quadratic Congruence.\u003cbr\u003e 2.2 The Chinese Remainder Theorem.\u003cbr\u003e 2.3 PowerMod Patterns.\u003cbr\u003e Fermat's Little Theorem.\u003cbr\u003e More Patterns in Powers.\u003cbr\u003e 2.4 Pseudoprimes.\u003cbr\u003e Using the Pseudoprime Test.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Euler's Function.\u003c\/b\u003e\u003cbr\u003e 3.0 Introduction.\u003cbr\u003e 3.1 Euler's Function.\u003cbr\u003e 3.2 Perfect Numbers and Their Relatives.\u003cbr\u003e The Sum of Divisors Function.\u003cbr\u003e Perfect Numbers.\u003cbr\u003e Amicalbe, Abundant, and Deficient Numbers.\u003cbr\u003e 3.3 Euler's Theorem.\u003cbr\u003e 3.4 Primitive Roots for Primes.\u003cbr\u003e The order of an Integer.\u003cbr\u003e Primes Have PRimitive roots.\u003cbr\u003e Repeating Decimals.\u003cbr\u003e 3.5 Primitive Roots for COmposites.\u003cbr\u003e 3.6 The Universal Exponent.\u003cbr\u003e Universal Exponents.\u003cbr\u003e Power Towers.\u003cbr\u003e The Form of Carmichael Numbers.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Prime Numbers.\u003c\/b\u003e\u003cbr\u003e 4.0 Introduction.\u003cbr\u003e 4.1 The Number of Primes.\u003cbr\u003e We'll Never Run Out of Primes.\u003cbr\u003e The Sieve of Eratosthenes.\u003cbr\u003e Chebyshev's Theorem and Bertrand's Postulate.\u003cbr\u003e 4.2 Prime Testing and Certification.\u003cbr\u003e Strong Pseudoprimes.\u003cbr\u003e Industrial-Grade Primes.\u003cbr\u003e Prime Certification Via Primitive Roots.\u003cbr\u003e An Improvement.\u003cbr\u003e Pratt Certificates.\u003cbr\u003e 4.3 Refinements and Other Directions.\u003cbr\u003e Other PRimality Tests.\u003cbr\u003e Strong Liars are Scarce.\u003cbr\u003e Finding the nth Prime.\u003cbr\u003e 4.4 A Doszen Prime Mysteries.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Some Applications.\u003c\/b\u003e\u003cbr\u003e 5.0 Introduction.\u003cbr\u003e 5.1 Coding Secrets.\u003cbr\u003e Tossing a Coin into a Well.\u003cbr\u003e The RSA Cryptosystem.\u003cbr\u003e Digital Signatures.\u003cbr\u003e 5.2 The Yao Millionaire Problem.\u003cbr\u003e 5.3 Check Digits.\u003cbr\u003e Basic Check Digit Schemes.\u003cbr\u003e A Perfect Check Digit Method.\u003cbr\u003e Beyond Perfection: Correcting Errors.\u003cbr\u003e 5.4 Factoring Algorithms.\u003cbr\u003e Trial Division.\u003cbr\u003e Fermat's Algorithm.\u003cbr\u003e Pollard Rho.\u003cbr\u003e Pollard p-1.\u003cbr\u003e The Current Scene.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Quadratic Residues.\u003c\/b\u003e\u003cbr\u003e 6.0 Introduction.\u003cbr\u003e 6.1 Pepin's Test.\u003cbr\u003e Quadratic Residues.\u003cbr\u003e Pepin's Test.\u003cbr\u003e Primes Congruent to 1 (Mod.\u003cbr\u003e 6.2 Proof of Quadratic Reciprocity.\u003cbr\u003e Gauss's Lemma.\u003cbr\u003e Proof of Quadratic Recipocity.\u003cbr\u003e Jacobi's Extension.\u003cbr\u003e An Application to Factoring.\u003cbr\u003e 6.3 Quadratic Equations.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Continuec Faction.\u003c\/b\u003e\u003cbr\u003e 7.0 Introduction.\u003cbr\u003e 7.1 FInite COntinued Fractions.\u003cbr\u003e 7.2 Infinite Continued Fractions.\u003cbr\u003e 7.3 Periodic Continued Fractions.\u003cbr\u003e 7.4 Pell's Equation.\u003cbr\u003e 7.5 Archimedes and the Sun God's Cattle.\u003cbr\u003e Wurm's Version: Using Rectangular Bulls.\u003cbr\u003e The Real Cattle Problem.\u003cbr\u003e 7.6 Factoring via Continued Fractions.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 Prime Testing with Lucas Sequences.\u003c\/b\u003e\u003cbr\u003e 8.0 Introduction.\u003cbr\u003e 8.1 Divisibility Properties of Lucas Sequencese.\u003cbr\u003e 8.2 Prime Tests Using Lucas Sequencesse.\u003cbr\u003e Lucas Certification.\u003cbr\u003e The Lucas-Lehmer Algorithm Explained.\u003cbr\u003e Luca Pseudoprimes.\u003cbr\u003e Strong Quadratic Pseudoprimes.\u003cbr\u003e Primality Testing's Holy Grail.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9 Prime Imaginaries and Imaginary Primes.\u003c\/b\u003e\u003cbr\u003e 9.0 Introduction.\u003cbr\u003e 9.1 Sums of Two Squares.\u003cbr\u003e 9.2 The Gaussian Intergers.\u003cbr\u003e Complex Number Theory.\u003cbr\u003e Gaussian Primes.\u003cbr\u003e The Moat Problem.\u003cbr\u003e The Gaussian Zoo.\u003cbr\u003e 9.3 Higher Reciprocity  325.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A. Maathematica Basics.\u003c\/b\u003e\u003cbr\u003e 1.0 Introduction.\u003cbr\u003e A.1 Plotting.\u003cbr\u003e A.2 Typesetting.\u003cbr\u003e Sending Files By E-Mail.\u003cbr\u003e A.3 Types of Functions.\u003cbr\u003e A.4 Lists.\u003cbr\u003e A.5 Programs.\u003cbr\u003e A.6 Solving Equations.\u003cbr\u003e A.7 Symbolic Algebra.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B Lucas Certificates Exist.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex of Mathematica Objects.\u003c\/p\u003e \u003cp\u003eSubject Index.\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Wiley","offers":[{"title":"Brand New","offer_id":52276255785240,"sku":"9780470412152","price":108.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470412152.jpg?v=1781365827","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/a-course-in-computational-number-theory-hardback-9780470412152","provider":"Freshly Printed Books","version":"1.0","type":"link"}