**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 x^{n}.

** Darren Swersky.**
The mathematical work of Hermann Minkowski.

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