عنوان

An experimental introduction to number theory /

شابک

1470430975

شابک

9781470430979

عنوان اصلي

An experimental introduction to number theory /

نام عام مواد

[Book]

نام نخستين پديدآور

Benjamin Hutz.

محل نشرو پخش و غیره

Providence, Rhode Island :

نام ناشر، پخش کننده و غيره

American Mathematical Society,

تاریخ نشرو بخش و غیره

[2018]

نام خاص و کميت اثر

xii, 313 pages :

ساير جزييات

illustrations ;

ابعاد

26 cm.

عنوان فروست

Pure and applied undergraduate texts ;

عنوان فروست

The Sally series

مشخصه جلد

31

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

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

متن يادداشت

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

متن يادداشت

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.

بدون عنوان

0

بدون عنوان

0

بدون عنوان

0

موضوع مستند نشده

Number theory, Textbooks.

موضوع مستند نشده

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

موضوع مستند نشده

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

موضوع مستند نشده

Number theory-- Diophantine equations-- Diophantine equations.

موضوع مستند نشده

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

موضوع مستند نشده

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

موضوع مستند نشده

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

موضوع مستند نشده

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

موضوع مستند نشده

Number theory.

موضوع مستند نشده

Zahlentheorie

شماره

ويراست

شماره رده

نشانه اثر

شماره رده

کد سيستم

مستند نام اشخاص تاييد نشده

Hutz, Benjamin,1978-

تاريخ عمليات

20200823025742.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y