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Higher Education Science and Mathematics Mathematics

A Friendly Introduction to Number Theory, 3/e

by Joseph H Silverman

Price	:	INR 499.00	11% Off
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Refer A Friendly Introduction to Number Theory, 3/e to a friend

For courses in Elementary Number Theory for math majors, for mathematics education students, and for Computer Science students.

This introductory undergraduate text is designed to entice a wide variety of majors into learning some mathematics, while teaching them to think mathematically at the same time. Starting with nothing more than basic high school algebra, the reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.


Features

A low-key introduction to Number Theory – Enables students to explore an area of math different from standard calculus sequences. Five basic steps emphasized – Experimentation, pattern recognition, hypothesis formation, hypothesis testing, and formal proof. RSA cryptosystem, elliptic curves, and Fermat's Last Theorem are featured, enabling students to see real-life applications of mathematics. Proof of Fermat's Last theorem by Andrew Wiles – Provides overview, introducing students to one of the most significant mathematical achievements of the 20th century.

Contents

What Is Number Theory? Pythagorean Triples Pythagorean Triples and the Unit Circle Sums of Higher Powers and Fermat’s Last Theorem Divisibility and the Greatest Common Divisor Linear Equations and the Greatest Common Divisor Factorization and the Fundamental Theorem of Arithmetic Congruences Congruences, Powers, and Fermat’s Little Theorem Congruences, Powers, and Euler’s Formula Euler’s Phi Function and the Chinese Remainder Theorem Prime Numbers Counting Primes Mersenne Primes Mersenne Primes and Perfect Numbers8 Powers Modulo m and Successive Squaring Computing kth Roots Modulo m Powers, Roots, and “Unbreakable” Codes Primality Testing and Carmichael Numbers Euler’s Phi Function and Sums of Divisors Powers Modulo p and Primitive Roots Primitive Roots and Indices Squares Modulo p Is —1 a Square Modulo p? Is 2? Quadratic Reciprocity Which Primes Are Sums of Two Squares? Which Numbers Are Sums of Two Squares? The Equation X4 + Y 4 = Z4 Square-Triangular Numbers Revisited Pell’s Equation Diophantine Approximation Diophantine Approximation and Pell’s Equation Number Theory and Imaginary Numbers The Gaussian Integers and Unique Factorization Irrational Numbers and Transcendental Numbers Binomial Coefficients and Pascal’s Triangle Fibonacci’s Rabbits and Linear Recurrence Sequences Oh, What a Beautiful Function The Topsy-Turvy World of Continued Fractions Continued Fractions, Square Roots and Pell’s Equation Generating Functions Sums of Powers Cubic Curves and Elliptic Curves Elliptic Curves with Few Rational Points Points on Elliptic Curves Modulo p Torsion Collections Modulo p and Bad Primes Defect Bounds and Modularity Patterns Elliptic Curves and Fermat’s Last Theorem