3 Review(s)

A Friendly Introduction to Number Theory, 4th Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facetâÂÂnumber theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience 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.Table of Contents:Chapter 1: What Is Number Theory?Chapter 2: Pythagorean TriplesChapter 3: Pythagorean Triples and the Unit CircleChapter 4: Sums of Higher Powers and Fermat Last TheoremChapter 5: Divisibility and the Greatest Common DivisorChapter 6: Linear Equations and the Greatest Common DivisorChapter 7: Factorization and the Fundamental Theorem of ArithmeticChapter 8: CongruencesChapter 9: Congruences, Powers, and Fermat Little TheoremChapter 10: Congruences, Powers, and Euler FormulaChapter 11: Euler Phi Function and the Chinese Remainder TheoremChapter 12: Prime NumbersChapter 13: Counting PrimesChapter 14: Mersenne PrimesChapter 15: Mersenne Primes and Perfect NumbersChapter 16: Powers Modulo m and Successive SquaringChapter 17: Computing kth Roots Modulo mChapter 18: Powers, Roots, and âÂÂUnbreakableâ CodesChapter 19: Primality Testing and Carmichael NumbersChapter 20: Squares Modulo pChapter 21: Is -1 a Square Modulo p? Is 2?Chapter 22: Quadratic ReciprocityChapter 23: Proof of Quadratic ReciprocityChapter 24: Which Primes Are Sums of Two Squares?Chapter 25: Which Numbers Are Sums of Two Squares?Chapter 26: As Easy as One, Two, ThreeChapter 27: Euler Phi Function and Sums of DivisorsChapter 28: Powers Modulo p and Primitive RootsChapter 29: Primitive Roots and IndicesChapter 30: The Equation X4 + Y4 = Z4Chapter 31: SquareâÂÂTriangular Numbers RevisitedChapter 32: Pell EquationChapter 33: Diophantine ApproximationChapter 34: Diophantine Approximation and Pell EquationChapter 35: Number Theory and Imaginary NumbersChapter 36: The Gaussian Integers and Unique FactorizationChapter 37: Irrational Numbers and Transcendental NumbersChapter 38: Binomial Coefficients and Pascal TriangleChapter 39: Fibonacci Rabbits and Linear Recurrence SequencesChapter 40: Oh, What a Beautiful FunctionChapter 41: Cubic Curves and Elliptic CurvesChapter 42: Elliptic Curves with Few Rational PointsChapter 43: Points on Elliptic Curves Modulo pChapter 44: Torsion Collections Modulo p and Bad PrimesChapter 45: Defect Bounds and Modularity PatternsChapter 46: Elliptic Curves and Fermat Last Theorem Chapter 47: The Topsy-Turvey World of Continued Fractions [online]Chapter 48: Continued Fractions, Square Roots, and Pell Equation [online]Chapter 49: Generating Functions [online]Chapter 50: Sums of Powers [online]