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020 _a9783031638145
_9978-3-031-63814-5
024 7 _a10.1007/978-3-031-63814-5
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
072 7 _aPBH
_2thema
100 1 _aShiu, Peter.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_983597
245 1 0 _aNumber Theory with Computations
_h[electronic resource] /
_cby Peter Shiu.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXVI, 442 p. 10 illus., 8 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Undergraduate Mathematics Series,
_x2197-4144
505 0 _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.
520 _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.
650 0 _aNumber theory.
650 1 4 _aNumber Theory.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031638138
776 0 8 _iPrinted edition:
_z9783031638152
830 0 _aSpringer Undergraduate Mathematics Series,
_x2197-4144
_975368
856 4 0 _uhttps://doi.org/10.1007/978-3-031-63814-5
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c63055
_d63055