TY  - BOOK
AU  - Hutz,Benjamin
TI  - An experimental introduction to number theory
T2  - Pure and Applied Undergraduate Texts
SN  - 9781470430979
PY  - 2018///
CY  - Providence, Rhode Island
PB  - American Mathematical Society
KW  - Number theory
KW  - sears
KW  - Textbooks
N1  - 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
N2  - Presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise conjectures from experimental data
UR  - https://drive.google.com/file/d/1J9gwaRqtcrBfQrNSP2M66wY18tO1VBdc/view?usp=sharing
ER  -