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189-346 / 377B: Number Theory

Project topics already chosen

Agnès Beaudry. Rational points on elliptic curves (following the book by Silverman and Tate.)

Stéphane Bersier. The Berlekamp factorization algorithm.

Nathan Budd. Continued Fractions.

Pilippe Chaput. Matijasevich's theorem.

Gheorghe Comanici. Elliptic curve cryptosystems.

Julia Evans. Cubic and biquadratic reciprocity.

Farah Fariz. The prime number theorem.

Ioan Filip. Lenstra's factorization algorithm based on elliptic curves over finite fields.

Daniel Hambleton. Quadratic reciprocity.

Jean-David Houle. The Agrawal-Kayal-Saxena primality testing algorithm.

David Kawrykow. Chapter 2 of Scharlau and Opolka. The mathematics of Fermat.

Pavel Levin. p-adic numbers.

Alexandra Ortan. Quadratic reciprocity.

Daniel Pomerantz. The Miller-Rabin primality test.

Vincent Quenneville-Bélair. Dirichlet's theorem on primes in arithmetic progressions.

Maksym Radziwill. Pisot numbers, Salem numbers, and the distribution of the fractional part of xn.

Darren Swersky. The mathematical work of Hermann Minkowski.

Artour Tomberg. Shor's factorization algorithm based on quantum computers.