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Laddar... An Introduction to the Theory of Numbers (1938)av G. H. Hardy
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Gå med i LibraryThing för att få reda på om du skulle tycka om den här boken. Det finns inga diskussioner på LibraryThing om den här boken. I'm not a mathematician, but I was interested enough to make my way through the first few chapters and found them relatively accessible. Though I imagine most university courses use more contemporary texts, this is still a decent introduction to the topic for advanced undergraduates/graduate students. Besides, it's G.H. Hardy. inga recensioner | lägg till en recension
Hänvisningar till detta verk hos externa resurser. Wikipedia på engelska (10)An Introduction to the Theory of Numbers by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter by J. H. Silverman on one of the most important developments in number theory -- modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader. The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists. Inga biblioteksbeskrivningar kunde hittas. |
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Google Books — Laddar... GenrerMelvil Decimal System (DDC)512.7Natural sciences and mathematics Mathematics Algebra Number theoryKlassifikation enligt LCBetygMedelbetyg:
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This book starts out by discussing the terminology and symbols used. It is divided into twenty-four chapters starting out with Prime Numbers. The chapters go like this:
(1. The Series of Primes (1)
(2. The Series of Primes (2)
(3. Farey Series and a Theorem of Minkowski
(4. Irrational Numbers
(5. Congruences and Residues
(6. Fermat’s Theorem and its Consequences
(7. General Properties of Congruences
(8. Congruences to Composite Moduli
(9. The Representation of Numbers by Decimals
(10. Continued Fractions
(11. Approximation of Irrationals by Rationals
(12. The Fundamental Theorem of Arithmetic in k(1), k(i), and k(ρ)
(13. Some Diophantine Equations
(14. Quadratic Fields (1)
(15. Quadratic Fields (2)
(16. The Arithmetical Functions ϕ(n), μ(n), d(n), σ(n), r(n)
(17. Generating Functions of Arithmetical Functions
(18. The Order of Magnitude of Arithmetical Functions
(19. Partitions
(20. The Representation of a Number by Two or Four Squares
(21. Representation by Cubes and Higher Powers
(22. The Series of Primes (3)
(23. Kronecker’s Theorem
(24. Some More Theorems of Minkowski
Most of the chapters are self-explanatory. Some of them are rather opaque at first glance. Take chapter 19 for example, it is called Partitions. What exactly is a partition? Looking into it tells you that a partition is a way to show a number using any number of positive integral parts.
I especially liked the chapters on modular arithmetic since that is something I never really learned in school for some reason. This particular version was written in 1938 and I don't know what edition it is. ( )