Algebraic Geometry

Download E-books Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics) PDF

By William Stein

This can be a e-book approximately top numbers, congruences, mystery messages, and elliptic curves so you might learn disguise to hide. It grew out of undergr- uate classes that the writer taught at Harvard, UC San Diego, and the college of Washington. The systematic research of quantity idea was once initiated round 300B. C. while Euclid proved that there are in?nitely many top numbers, and in addition cleverly deduced the basic theorem of mathematics, which asserts that each confident integer components uniquely as a manufactured from primes. Over 1000 years later (around 972A. D. ) Arab mathematicians formulated the congruent quantity challenge that asks for how to make a decision even if a given optimistic integer n is the world of a correct triangle, all 3 of whose facets 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 realm of electronic conversation. within the Eighties and Nineties, elliptic curves revolutionized quantity conception, delivering remarkable new insights into the congruent quantity challenge, primality trying out, publ- key cryptography, assaults on public-key platforms, and enjoying a principal position in Andrew Wiles’ solution of Fermat’s final Theorem.

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Read or Download Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics) PDF

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