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| Genre/Form: | Textbooks |
|---|---|
| Document Type: | Book |
| All Authors / Contributors: |
Benjamin Hutz |
| ISBN: | 9781470430979 1470430975 |
| OCLC Number: | 999672103 |
| Description: | xii, 313 pages : illustrations ; 26 cm. |
| Contents: | Machine generated contents note: ch. 1 Integers -- 1.The Integers and the Well Ordering Property -- 2.Divisors and the Division Algorithm -- 3.Greatest Common Divisor and the Euclidean Algorithm -- 4.Prime Numbers and Unique Factorization -- Exercises -- ch. 2 Modular Arithmetic -- 1.Basic Arithmetic -- 2.Inverses and Fermat's Little Theorem -- 3.Linear Congruences and the Chinese Remainder Theorem -- Exercises -- ch. 3 Quadratic Reciprocity and Primitive Roots -- 1.Quadratic Reciprocity -- 2.Computing mth Roots Modulo n -- 3.Existence of Primitive Roots -- Exercises -- ch. 4 Secrets -- 1.Basic Ciphers -- 2.Symmetric Ciphers -- 3.Diffie -- Hellman Key Exchange -- 4.Public Key Cryptography (RSA) -- 5.Hash Functions and Check Digits -- 6.Secret Sharing -- Exercises -- ch. 5 Arithmetic Functions -- 1.Euler Totient Function -- 2.Mobius Function -- 3.Functions on Divisors -- 4.Partitions -- Exercises -- ch. 6 Algebraic Numbers -- 1.Algebraic or Transcendental Note continued: 2.Quadratic Number Fields and Norms -- 3.Integers, Divisibility, Primes, and Irreducibles -- 4.Application: Sums of Two Squares -- Exercises -- ch. 7 Rational and Irrational Numbers -- 1.Diophantine Approximation -- 2.Height of a Rational Number -- 3.Heights and Approximations -- 4.Continued Fractions -- 5.Approximating Irrational Numbers with Convergents -- Exercises -- ch. 8 Diophantine Equations -- 1.Introduction and Examples -- 2.Working Modulo Primes -- 3.Pythagorean Triples -- 4.Fermat's Last Theorem -- 5.Pell's Equation and Fundamental Units -- 6.Waring Problem -- Exercises -- ch. 9 Elliptic Curves -- 1.Introduction -- 2.Addition of Points -- 3.Points of Finite Order -- 4.Integer Points and the Nagel-Lutz Theorem -- 5.Mordell -- Weil Group and Points of Infinite Order -- 6.Application: Congruent Numbers -- Exercises -- ch. 10 Dynamical Systems -- 1.Discrete Dynamical Systems -- 2.Dynatomic Polynomials -- 3.Resultant and Reduction Modulo Primes Note continued: 4.Periods Modulo Primes -- 5.Algorithms for Rational Periodic and Preperiodic Points -- Exercises -- ch. 11 Polynomials -- 1.Introduction to Polynomials -- 2.Factorization and the Euclidean Algorithm -- 3.Modular Arithmetic for Polynomials -- 4.Diophantine Equations for Polynomials -- Exercises. |
| Series Title: | Pure and applied undergraduate texts, 31.; Sally series (Providence, R.I.) |
| Responsibility: | Benjamin Hutz. |
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Related Subjects:(10)
- Number theory -- Textbooks.
- Number theory.
- Number theory -- Instructional exposition (textbooks, tutorial papers, etc.)
- Number theory -- Elementary number theory -- Elementary number theory.
- Number theory -- Diophantine equations -- Diophantine equations.
- Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Elliptic curves over global fields.
- Number theory -- Probabilistic theory: distribution modulo $1$; metric theory of algorithms -- Diophantine approximation.
- Number theory -- Finite fields and commutative rings (number-theoretic aspects) -- Polynomials.
- Dynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Polynomial and rational maps.
- Zahlentheorie
