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Postgraduate course

Algebraic Structures

  • ECTS credits10
  • Teaching semesterSpring, Autumn
  • Course codeMAT325
  • Number of semesters1
  • Language

    English if English-speaking students attend the seminars, otherwise Norwegian

  • Resources

Semester of Instruction

Irregular

Objectives and Content

The course gives an introduction to modern algebraic structures developed since the 1960s. These structures are frequently used and studied within algebra, topology and computational mathematics.
The course includes:
¿ Basic homological algebra
¿ Algebras, co-algebras, bi-algebras, Lie algebras and differential graded algebras
¿ Koszul-algebras and Koszul-duality
¿ Algebraic operads and algebras over these
¿ Hopf-algebras

Learning Outcomes

On completion of the course

the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student¿..

  • Knows basic homological algebra
  • Knows the definitions and basic properties of algebras, co-algebras, bi-algebras, Lie-algebras, DG-algebras, and modules over these.
  • Knows Koszul algebras, and Koszul duality.
  • Knows the definitions and basic properties algebraic operads and algebras over these. Specifically one knows the operads: Com, Ass, Lie, Poisson, pre-Lie, post-Lie, Leibiniz, Zinbiel, and Diass, and algebras over these.
  • Knows basic properties of Hopf-algebras, and examples of such algebras, like the Connes-Kreimer algebra, and other combinatorial Hopf-algebras.

Skills

The student¿..

  • Can use algebraic tools which are important for many problems in algebra, topology, and computational mathematics.
  • Has solid experience and training in reasoning withabstract mathematical structures

General competence

The student¿..

  • Has insight into the development of modern algebraic structures from the last fifty years.
  • Has insight into how algebraic structures is a tool to describe structural phenomena in both applied and theoretical mathematics.

Required Previous Knowledge

MAT220 Algebra

Recommended Previous Knowledge

At least one of MAT242 Topology, MAT243 Manifolds, or MAT224 Commutative Algebra

Compulsory Assignments and Attendance

No compulsory assignments or attendance

Forms of Assessment

Oral examination

Grading Scale

The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.

Exam information

  • Type of assessment: Oral examination

    Withdrawal deadline
    01.11.2017