Algebra II - groups

MATH-211 / 5 credits

Teacher: Negut Andrei

Language: English

Summary

This course deals with group theory, with particular emphasis on group actions and notions of category theory.

Content

Topics covered include quotient groups, the isomorphism theorems, abelian groups, Sylow subgroups, group actions and representations, basic notions of category theory.

Keywords

Group, quotient, isomorphism, Sylow subgroup, action, representation, category.

Learning Prerequisites

Required courses

MATH-110(a) Advanced linear algebra I

MATH-115(a) Advanced linear algebra II

MATH-113 Algebraic structures

Important concepts to start the course

Definitions of groups and basic examples: symmetric groups, reflection groups, dihedral groups.

Learning Outcomes

  • Prove basic results of group theory
  • Construct examples of groups and their actions
  • Systematize groups, homomorphisms and categories
  • Formulate the main theorems of the course

Teaching methods

Lectures and exercise sessions

Expected student activities

Students are expected to attend all lectures and participate in all problem sessions.

Assessment methods

Written exam

Supervision

Office hours No
Assistants Yes
Forum Yes

Resources

Bibliography

J. J. Rotman, "An introduction to the Theory of Groups"

D. S. Dummit, R. M. Foote, "Abstract algebra, 3rd edition"

Moodle Link

In the programs

  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Algebra II - groups
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: mandatory

Reference week

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