Algebra: basic group theory;
Analysis: differential and integral calculus of functions in several variables as treated in a first year course, convergence of series, (uniform) convergence of sequence of functions, basic complex analysis, and the basic theorems from integration theory.
More detailed information about this course can be found on the course webpage http://pub.math.leidenuniv.nl/~evertsejh/ant-mastermath.html .
Under the header "Course notes" there is a link to a pdf with Chapter 0 containing the Prerequisites. Students are requested to read this through before the start of the course.
- Aim of the course
The first part of the course is about prime number theory.
We will discuss elementary prime number theory, Dirichlet series, Dirichlet characters, the Riemann zeta function and L-functions and give a proof of the prime number theorem for primes in arithmetic progressions.
In the second part we will give an introduction to sieve methods, including the fundamental lemma of sieve theory, Selberg's method, bilinear form methods, and the Large Sieve inequality.
If time permits, we will discuss in more depth primes in arithmetic progressions and the Bombieri-Vinogradov Theorem, as well as applications to the ternary Goldbach problem.
- Lecture notes
During the course we will post lecture notes on the course webpage.