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Introduction to number theory / Richard Michael Hill, University College London, UK.

By: Series: Essential textbooks in mathematicsPublisher: New Jersey, USA : World Scientific, ©2018Description: xiv, 247 pages ; 24 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9781786344717 (hc : alk. paper)
  • 9781786344892 (pbk : alk. paper)
Other title:
  • Number theory
Subject(s): DDC classification:
  • 512.7 H55 2018 23
LOC classification:
  • QA241 .H4845 2018
Contents:
Machine generated contents note: 1.Euclid's Algorithm -- 1.1.Some Examples of Rings -- 1.2.Euclid's Algorithm -- 1.3.Invertible Elements Modulo n -- 1.4.Solving Linear Congruences -- 1.5.The Chinese Remainder Theorem -- 1.6.Prime Numbers -- Hints for Some Exercises -- 2.Polynomial Rings -- 2.1.Long Division of Polynomials -- 2.2.Highest Common Factors -- 2.3.Uniqueness of Factorization -- 2.4.Irreducible Polynomials -- 2.5.Unique Factorization Domains -- Hints for Some Exercises -- 3.Congruences Modulo Prime Numbers -- 3.1.Fermat's Little Theorem -- 3.2.The Euler Totient Function -- 3.3.Cyclotomic Polynomials and Primitive Roots -- 3.4.Public Key Cryptography -- 3.5.Quadratic Reciprocity -- 3.6.Congruences in an Arbitrary Ring -- 3.7.Proof of the Second Nebensatz -- 3.8.Gauss Sums and the Proof of Quadratic Reciprocity -- Hints for Some Exercises -- 4.p-Adic Methods in Number Theory -- 4.1.Hensel's Lemma -- 4.2.Quadratic Congruences -- 4.3.p-Adic Convergence of Series Note continued: 4.4.p-Adic Logarithms and Exponential Maps -- 4.5.Teichmuller Lifts -- 4.6.The Ring of p-Adic Integers -- Hints for Some Exercises -- 5.Diophantine Equations and Quadratic Rings -- 5.1.Diophantine Equations and Unique Factorization -- 5.2.Quadratic Rings -- 5.3.Norm-Euclidean Quadratic Rings -- 5.4.Decomposing Primes in Quadratic Rings -- 5.5.Continued Fractions -- 5.6.Pell's Equation -- 5.7.Real Quadratic Rings and Diophantine Equations -- Hints for Some Exercises -- Solution to Exercises.
Holdings
Item type Current library Collection Call number Status Barcode
Books Books College Library General Circulation Section GC GC 512.7 H55 2018 (Browse shelf(Opens below)) Available HNU000279

Textbook, with answers to some exercises.

Includes bibliographical references.

Machine generated contents note: 1.Euclid's Algorithm --
1.1.Some Examples of Rings --
1.2.Euclid's Algorithm --
1.3.Invertible Elements Modulo n --
1.4.Solving Linear Congruences --
1.5.The Chinese Remainder Theorem --
1.6.Prime Numbers --
Hints for Some Exercises --
2.Polynomial Rings --
2.1.Long Division of Polynomials --
2.2.Highest Common Factors --
2.3.Uniqueness of Factorization --
2.4.Irreducible Polynomials --
2.5.Unique Factorization Domains --
Hints for Some Exercises --
3.Congruences Modulo Prime Numbers --
3.1.Fermat's Little Theorem --
3.2.The Euler Totient Function --
3.3.Cyclotomic Polynomials and Primitive Roots --
3.4.Public Key Cryptography --
3.5.Quadratic Reciprocity --
3.6.Congruences in an Arbitrary Ring --
3.7.Proof of the Second Nebensatz --
3.8.Gauss Sums and the Proof of Quadratic Reciprocity --
Hints for Some Exercises --
4.p-Adic Methods in Number Theory --
4.1.Hensel's Lemma --
4.2.Quadratic Congruences --
4.3.p-Adic Convergence of Series Note continued: 4.4.p-Adic Logarithms and Exponential Maps --
4.5.Teichmuller Lifts --
4.6.The Ring of p-Adic Integers --
Hints for Some Exercises --
5.Diophantine Equations and Quadratic Rings --
5.1.Diophantine Equations and Unique Factorization --
5.2.Quadratic Rings --
5.3.Norm-Euclidean Quadratic Rings --
5.4.Decomposing Primes in Quadratic Rings --
5.5.Continued Fractions --
5.6.Pell's Equation --
5.7.Real Quadratic Rings and Diophantine Equations --
Hints for Some Exercises --
Solution to Exercises.

College of Education Bachelor of Secondary Education major in Mathematics

Text in English

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