Del i serien Springer Undergraduate Mathematics Series
377 kr
Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt över 249 kr.
Beskrivning
Produktinformation
- Utgivningsdatum:1998-01-14
- Mått:178 x 235 x 17 mm
- Vikt:482 g
- Format:Häftad
- Språk:Engelska
- Serie:Springer Undergraduate Mathematics Series
- Antal sidor:302
- Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- ISBN:9783540761976
Utforska kategorier
Recensioner i media
From the reviews: BULLETIN OF MATHEMATICS BOOKS "?as a nice concluding chapter on Fermat? Last Theorem, with a brief discussion on the coup de grace." G.A. Jones and J.M. Jones Elementary Number Theory "A welcome addition ... a carefully and well-written book."-THE MATHEMATICAL GAZETTE "This book would make an excellent text for an undergraduate course on number theory." -MATHEMATICAL REVIEWS
Innehållsförteckning
- 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.
Mer från samma författare
Isomorphisms, Symmetry and Computations in Algebraic Graph Theory
Gareth A. Jones, Ilia Ponomarenko, Jozef Širáň
1 578 kr
Isomorphisms, Symmetry and Computations in Algebraic Graph Theory
Gareth A. Jones, Ilia Ponomarenko, Jozef Širáň
1 578 kr
Algorithmic Algebraic Combinatorics and Gröbner Bases
Mikhail Klin, Gareth A. Jones, Aleksandar Jurisic, Mikhail Muzychuk, Ilia Ponomarenko
1 892 kr
Algorithmic Algebraic Combinatorics and Gröbner Bases
Mikhail Klin, Gareth A. Jones, Aleksandar Jurisic, Mikhail Muzychuk, Ilia Ponomarenko
1 892 kr
Mer från samma serie
Numerical Methods for Ordinary Differential Equations
David F. Griffiths, Desmond J. Higham
377 kr
Essential Partial Differential Equations
David F. Griffiths, John W. Dold, David J. Silvester
377 kr
Finitely Generated Abelian Groups and Similarity of Matrices over a Field
Christopher Norman
377 kr
Du kanske också är intresserad av
Handbook of Plant Lectins
Els. J. M. Van Damme, Willy J. Peumans, Arpad Pusztai, Susan Bardocz
4 887 kr