Number Theory Revealed : An Introduction

Description

Number Theory Revealed: An Introduction acquaints undergraduates with the Queen of Mathematics . The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p and modern twists on traditional questions like the values represented by binary quadratic forms and large solutions of equations. Each chapter includes an elective appendix with additional reading, projects, and references. An expanded edition, Number Theory Revealed: A Masterclass, offers a more comprehensive approach to these core topics and adds additional material in further chapters and appendices, allowing instructors to create an individualized course tailored to their own (and their students') interests. Preliminary chapter on inductionThe Euclidean algorithmCongruencesThe basic algebra of number theoryMultiplicative functionsThe distribution of prime numbersDiophantine problemsPower residuesQuadratic residuesQuadratic equationsSquare roots and factoringRational approximations to real numbersBinary quadratic formsHints for exercisesRecommended further readingIndex.