Numbers and Geometry

academic year 2023/24

Academic Coordinator: Pietro Corvaja

Period: First semester

Duration: 28 hours

Program:

  1. Number Systems: Rational numbers, issues of irrationality. Real numbers. Complex numbers.
  2. Geometric transformations of the plane; complex numbers and affinities; roots of unity.
  3. Order of a root of unity, Euler's phi function.
  4. Finite fields, algebraic extensions, roots of unity.
  5. The field of real quaternions and the group SO(3).
  6. Planar lattices.
  7. Multiplicative quadratic forms. Representation of integers through binary quadratic forms.