Mathematics

Number Theory

Module code: G5140
Level 4
15 credits in spring semester
Teaching method: Lecture, Workshop
Assessment modes: Computer based exam, Coursework

  • Arithmetic over Z. Fundamental theorem, Diophantine equations.
  • Polynomial arithmetic and parallels with Z.
  • Modular arithmetic, Euler’s theorem, Fermat’s theorem, and Chinese remainder theorem.
  • Elementary group theory. Abelian groups, generators.

Module learning outcomes

  • Understand the parallels between arithmetic of Z and arithmetic of polynomials over Z;
  • Understand the notion of a Diophantine equation, and solve Diophantine equations;
  • Apply theorems of modular arithmetic to a wide class of problems;
  • 4. Identify and classify algebraic group structures.