34754 - Number Theory 2

Academic Year 2011/2012

  • Docente: Calogero Tinaglia
  • Credits: 6
  • SSD: MAT/05
  • Language: Italian
  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)

Learning outcomes

In this class, students will gain a deep understanding of some

concepts and fundamental techniques in number theory. They will also

acquire specific knowledge of how to teach mathematics.

Course contents

Minimal bases and orthogonal basis of integers. Quadratic forms. Elliptic curves and functions. Mordell Theorem. Primes of an arithmetic progression. Dirichelet Series. Zeta function and L-functions. Density. Dirichelet Theorem.

Readings/Bibliography

J.W.S. Cassels, An Introduction to the Geometry of Numbers (Springer-Verlag)

H. Davenport, Aritmetica Superiore (Zanichelli)

G. Everest and T. Ward, An Introduction to Number Theory (Springer)

G.H. Hardy and E.M. Wright, An Introduction to Theory of Numbers (Oxford University Press)

J.P. Serre, A Cours in Arithmetic (Springer-Verlag) 

Related notes will be distributed.

Teaching methods

In class we will discuss the theory and solve several exercises.

Assessment methods

Oral exam

Teaching tools

In-class lesson

Office hours

See the website of Calogero Tinaglia