Stage 4 Number Theory

Number Theory:
There are several branch of Number Theory and we focus in algebraic and analytic here. As the title indicated, algebraic number theory employs algebra result to number theory, analytic one applies analysis theory. It is recommended you have a solid background of algebra before you begin to study algebraic number theory. Riemann hypothesis is one of the Millennium Prize Problems. Fermat's last theorem and the Poincaré conjecture have been solved, this is probably the biggest challenge to date.

This page consists links to online number lecture notes. Algebraic Number Theory Archives provide papers for further study.

In general:

Algebraic Number Theory:

Class Field Theory:

Analytic Number Theory:

Riemann Zeta Function and the Hypothesis:

Further readings (including Modular Forms, Elliptic Curves, etc.):
See Franz Lemmermeyer's page for further study.

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