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Viser: Elementary Number Theory

Elementary Number Theory
Søgbar e-bog

Elementary Number Theory Vital Source e-bog

Gareth A. Jones og Josephine M. Jones
(2012)
Springer Nature
317,00 kr.
Leveres umiddelbart efter køb
Elementary Number Theory

Elementary Number Theory Vital Source e-bog

Gareth A. Jones og Josephine M. Jones
(2012)
Springer Nature
317,00 kr.
Leveres umiddelbart efter køb
Elementary Number Theory, 1. udgave

Elementary Number Theory

Gareth A. Jones og Josephine M. Jones
(1998)
Sprog: Engelsk
Springer London, Limited
387,00 kr.
Print on demand. Leveringstid vil være ca 2-3 uger.

Detaljer om varen

  • Vital Source searchable e-book (Reflowable pages)
  • Udgiver: Springer Nature (December 2012)
  • Forfattere: Gareth A. Jones og Josephine M. Jones
  • ISBN: 9781447106135
An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.
Licens varighed:
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.

Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
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Detaljer om varen

  • Vital Source 365 day rentals (dynamic pages)
  • Udgiver: Springer Nature (December 2012)
  • Forfattere: Gareth A. Jones og Josephine M. Jones
  • ISBN: 9781447106135R365
An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.
Licens varighed:
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: 5 år fra købsdato.

Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)

Detaljer om varen

  • 1. Udgave
  • Paperback
  • Udgiver: Springer London, Limited (Juli 1998)
  • Forfattere: Gareth A. Jones og Josephine M. Jones
  • ISBN: 9783540761976
An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

1. Divisibility. -
1.
1 Divisors. -
1.
2 Bezout's identity. -
1.
3 Least common multiples. -
1.
4 Linear Diophantine equations. -
1.
5 Supplementary exercises. -
2. Prime Numbers. -
2.
1 Prime numbers and prime-power factorisations. -
2.
2 Distribution of primes. -
2.
3 Fermat and Mersenne primes. -
2.
4 Primality-testing and factorisation. -
2.
5 Supplementary exercises. -
3. Congruences. -
3.
1 Modular arithmetic. -
3.
2 Linear congruences. -
3.
3 Simultaneous linear congruences. -
3.
4 Simultaneous non-linear congruences. -
3.
5 An extension of the Chinese Remainder Theorem. -
3.
6 Supplementary exercises. -
4. Congruences with a Prime-power Modulus. -
4.
1 The arithmetic of ?p. -
4.
2 Pseudoprimes and Carmichael numbers. -
4.
3 Solving congruences mod (pe). -
4.
4 Supplementary exercises. -
5. Euler's Function. -
5.
1 Units. -
5.
2 Euler's function. -
5.
3 Applications of Euler's function. -
5.
4 Supplementary exercises. -
6. The Group of Units. -
6.
1 The group Un. -
6.
2 Primitive roots. -
6.
3 The group Une, where p is an odd prime. -
6.
4 The group U2e. -
6.
5 The existence of primitive roots. -
6.
6 Applications of primitive roots. -
6.
7 The algebraic structure of Un. -
6.
8 The universal exponent. -
6.
9 Supplementary exercises. -
7. Quadratic Residues. -
7.
1 Quadratic congruences. -
7.
2 The group of quadratic residues. -
7.
3 The Legendre symbol. -
7.
4 Quadratic reciprocity. -
7.
5 Quadratic residues for prime-power moduli. -
7.
6 Quadratic residues for arbitrary moduli. -
7.
7 Supplementary exercises. -
8. Arithmetic Functions. -
8.
1 Definition and examples. -
8.
2 Perfect numbers. -
8.
3 The Mobius Inversion Formula. -
8.
4 An application of the Mobius Inversion Formula. -
8.
5 Properties of the Mobius function. -
8.
6 The Dirichlet product. -
8.
7 Supplementary exercises. -
9. The Riemann Zeta Function. -
9.
1 Historical background. -
9.
2 Convergence. -
9.
3 Applications to prime numbers. -
9.
4 Random integers. -
9.
5 Evaluating ?(2). -
9.
6 Evaluating ?(2k). -
9.
7 Dirichlet series. -
9.
8 Euler products. -
9.
9 Complex variables. -
9.
10 Supplementary exercises. -
10. Sums of Squares. -
10.
1 Sums of two squares. -
10.
2 The Gaussian integers. -
10.
3 Sums of three squares. -
10.
4 Sums of four squares. -
10.
5 Digression on quaternions. -
10.
6 Minkowski's Theorem. -
10.
7 Supplementary exercises. -
11. Fermat's Last Theorem. -
11.
1 The problem. -
11.
2 Pythagoras's Theorem. -
11.
3 Pythagorean triples. -
11.
4 Isosceles triangles and irrationality. -
11.
5 The classification of Pythagorean triples. -
11.
6 Fermat. -
11.
7 The case n =
4. -
11.
8 Odd prime exponents. -
11.
9 Lame and Kummer. -
11.
10 Modern developments. -
11.
11 Further reading. - Solutions to Exercises. -
Index of symbols. -
Index of names.
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