Description:

This Group Theory-I course is designed to introduce students to the fundamental concepts and principles of group theory in mathematics. Group theory is a branch of abstract algebra that deals with the study of symmetry and structure of mathematical objects known as groups. In this course, students will explore the properties of groups, various types of group operations, subgroups, and group isomorphisms. They will also learn about group actions, group homomorphisms, and the concept of normal subgroups. This course serves as a solid foundation for further study in advanced algebra and other areas of mathematics.

Key Highlights:

• Fundamental concepts of group theory
• Properties and operations of groups
• Subgroups and group isomorphisms
• Group actions and homomorphisms
• Understanding normal subgroups

What you will learn:

• Learning Outcome 1
  Understand the basic concepts and definitions of group theory, including group operations and properties
• Learning Outcome 2
  Identify and analyze subgroups, cosets, and group isomorphisms
• Learning Outcome 3
  Explore group actions and their applications in symmetry and combinatorics
• Learning Outcome 4
  Analyze group homomorphisms, normal subgroups, and quotient groups