03046nam a22003975i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153072001600169072002300185072001500208100007400223245007700297250001800374264006900392300006400461336002600525337002600551338003600577347002400613490005800637505046700695520121201162650001902374650001902393710003402412773002602446776003602472776003602508830005802544856004602602978-3-031-63814-5DE-He21320251030112934.0cr nn 008mamaa240903s2024    sz |    s    |||| 0|eng d  a97830316381457 a10.1007/978-3-031-63814-52doi 4aQA241-247.5 7aPBH2bicssc 7aMAT0220002bisacsh 7aPBH2thema1 aShiu, Peter.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aNumber Theory with Computationsh[electronic resource] /cby Peter Shiu.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXVI, 442 p. 10 illus., 8 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Undergraduate Mathematics Series,x2197-41440 aPart I Elementary Number Theory -- 1 Basics -- 2 Arithmetic functions I -- 3 Prime numbers: Euclid and Eratosthenes -- 4 Quadratic residues and congruences -- 5 Primitive roots -- 6 Sums of squares -- 7 Continued fractions -- Part II Analytic Number Theory -- 8 Diophantine approximations -- 9 Distribution of prime numbers -- 10 Arithmetic functions II -- 11 Prime number theorem -- 12 Primes in arithmetic progressions -- 13 Smooth numbers -- 14 Circle method.  aThis introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory. The book emphasises computational aspects, including algorithms and their implementation in Python. The book is divided into two parts. The first part, on elementary number theory, deals with concepts such as induction, divisibility, congruences, primitive roots, cryptography, and continued fractions. The second part is devoted to analytic number theory and includes chapters on Dirichlet’s theorem on primes in arithmetic progressions, the prime number theorem, smooth numbers, and the famous circle method of Hardy and Littlewood. The book contains many topics not often found in introductory textbooks, such as Aubry’s theorem, the Tonelli–Shanks algorithm, factorisation methods, continued fraction representations of e, and the irrationality of ����(3). Each chapter concludes with a summary and notes, as well as numerous exercises. Assuming only basic calculus for the first part of the book, the second part assumes some knowledge of complex analysis. Familiarity with basic coding syntax will be helpful for the computational exercises. 0aNumber theory.14aNumber Theory.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303163813808iPrinted edition:z9783031638152 0aSpringer Undergraduate Mathematics Series,x2197-414440uhttps://doi.org/10.1007/978-3-031-63814-5