SUBJECT

Title

Basic algebra (reading course)

Type of instruction

lecture

Level

master

Part of degree program
Credits

5

Recommended in

Semesters 1-4

Typically offered in

Autumn/Spring semester

Course description
  • Basic group theory. Permutation groups. Lagrange’s Theorem. Homomorphisms and normal subgroups. Direct product, the Fundamental theorem of finite Abelian groups. Free groups and defining relations.
  • Basic ring theory. Ideals. Chain conditions. Integral domains, PID’s, euclidean domains.
  • Fields, field extensions. Algebraic and transcendental elements. Finite fields.
  • Linear algebra. The eigenvalues, the characterisitic polynmial and the minimal polynomial of a linear transformation. The Jordan normal form. Transformations of Euclidean spaces. Normal and unitary transformations. Quadratic forms, Sylvester’s theorem.
Readings
  • I.N. Herstein: Abstract Algebra. Mc.Millan, 1990
  • P.M. Cohn: Classic Algebra. Wiley, 2000
  • I.M. Gel’fand: Lectures on linear algebra. Dover, 1989