Skip to main content

MA136 Introduction to Abstract Algebra

Lecturer: Samir Siksek

Term(s): Term 1 (6-10)

Status for Mathematics students: Core for Maths

Commitment: 15 One hour lectures

Assessment: Weekly assignments (15%), 1 hour written exam (85%)

Corequisites: MA132 Foundations

Leads To:

Content:

Section 1 Group Theory:

  • Motivating examples: numbers, symmetry groups
  • Definitions, elementary properties
  • Subgroups, including subgroups of $Z$
  • Arithmetic modulo n and the group $Z_n$
  • Lagrange's Theorem
  • Permutation groups, odd and even permutations (proof optional)
  • Normal subgroups and quotient groups

Section 2 Ring Theory:

  • Definitions: Commutative and non-commutative rings, integral domains, fields
  • Examples: $Z, Q, R, C, Z_n$, matrices, polynomials, Gaussian integers

Aims:

To introduce First Year Mathematics students to abstract Algebra, covering Group Theory and Ring Theory.

Objectives:

By the end of the module students should be able to understand:

  • the abstract definition of a group, and be familiar with the basic types of examples, including numbers, symmetry groups and groups of permutations and matrices.
  • what subgroups are, and be familiar with the proof of Lagrange’s Theorem.
  • the definition of various types of ring, and be familiar with a number of examples, including numbers, polynomials, and matrices.
  • unit groups of rings, and be able to calculate the unit groups of the integers modulo n.

Books:

Any library book with Abstract Algebra in the title would be useful.

Additional Resources

yr1.jpg
Year 1 regs and modules
G100 G103 GL11 G1NC

yr2.jpg
Year 2 regs and modules
G100 G103 GL11 G1NC

yr3.jpg
Year 3 regs and modules
G100 G103

yr4.jpg
Year 4 regs and modules
G103

Archived Material
Past Exams
Core module averages