SUBJECT
Title
Basic algebra (reading course)
Type of instruction
lecture
Level
master
Faculty
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