By William Stein

It is a ebook approximately leading numbers, congruences, mystery messages, and elliptic curves so you might learn hide to hide. It grew out of undergr- uate classes that the writer taught at Harvard, UC San Diego, and the collage of Washington. The systematic learn of quantity conception was once initiated round 300B. C. whilst Euclid proved that there are in?nitely many best numbers, and in addition cleverly deduced the basic theorem of mathematics, which asserts that each confident integer elements uniquely as a made of primes. Over one thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent quantity challenge that asks for how to choose even if a given optimistic integer n is the world of a correct triangle, all 3 of whose aspects are rational numbers. Then one other thousand years later (in 1976), Di?e and Hellman brought the ?rst ever public-key cryptosystem, which enabled humans to speak secretely over a public communications channel without predetermined mystery; this invention and those that it revolutionized the area of electronic verbal exchange. within the Nineteen Eighties and Nineteen Nineties, elliptic curves revolutionized quantity idea, offering awesome new insights into the congruent quantity challenge, primality checking out, publ- key cryptography, assaults on public-key platforms, and enjoying a principal position in Andrew Wiles’ answer of Fermat’s final Theorem.