عنوان

An experimental introduction to number theory /

1470430975

9781470430979

An experimental introduction to number theory /

[Book]

Benjamin Hutz.

Providence, Rhode Island :

American Mathematical Society,

[2018]

xii, 313 pages :

illustrations ;

26 cm.

Pure and applied undergraduate texts ;

The Sally series

31

Includes bibliographical references and index.

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.

0

0

0

Number theory, Textbooks.

Dynamical systems and ergodic theory-- Arithmetic and non-Archimedean dynamical systems-- Polynomial and rational maps.

Number theory-- Arithmetic algebraic geometry (Diophantine geometry)-- Elliptic curves over global fields.

Number theory-- Diophantine equations-- Diophantine equations.

Number theory-- Elementary number theory-- Elementary number theory.

Number theory-- Finite fields and commutative rings (number-theoretic aspects)-- Polynomials.

Number theory-- Instructional exposition (textbooks, tutorial papers, etc.)

Number theory-- Probabilistic theory: distribution modulo $1$; metric theory of algorithms-- Diophantine approximation.

Number theory.

Zahlentheorie

Hutz, Benjamin,1978-

20200823025742.0

rda

[Book]

Y