Lecture Notes of Courses (.ps and .pdf files)

  • Introduction to number theory - ps file (495K)
  • Introduction to number theory - pdf file (242K)

    This is a first course in number theory. It includes p-adic numbers.

  • Commutative algebra - ps file (381K)
  • Commutative algebra - pdf file (202K)

    This course is an introduction to modules over rings, Noetherian modules, unique factorization domains and polynomial rings over them, modules over principal ideal domains, localization.

  • Introduction to algebraic number theory - ps file (432K)
  • Introduction to algebraic number theory - pdf file (193K)

    This course (40 hours) is a relatively elementary course which requires minimal prerequisites from Commutative Algebra (see above) for its understanding.

    Following an algebraic prerequisited review part, integral structures, Dedekind rings, splitting of maximal ideals in field extensions, finiteness of the ideal class group and Dirichlet's theorem on units are treated next, p-adic numbers and class field theory for the field of rational numbers are introduced in the last part of the course.

  • Homological algebra - ps file (479K)
  • Homological algebra - pdf file (228K)

    This is a very short introduction to homological algebra

    This course (25 hours) presents categories, functors, chain complexes, homologies, free, projective and injective obejcts in the category of modules over a ring, projective and injective resolutions, derived functors, Tor and Ext, cohomologies of modules over a finite group, restriction and corestriction.

  • Lectures on Local Fields - ps file (687K)
  • Lectures on Local Fields - pdf file (430K)

    This is a very short introduction to local fields and local class field theory which uses an explicit description of the local reciprocity homomorphism and its inverse and does not use Galois cohomology and the Brauer group.
    See also 10 magic lectures on local fields .