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MA136 Introduction to Abstract Algebra

Lecturer: Samir Siksek and Andrew Brendon-Penn

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

Status for Mathematics students: Core for Maths

Commitment: 15 One hour lectures

Assessment: Assignments (15%), written exam (85%).

Corequisites: MA132 Foundations

Leads To: MA249 Algebra II


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


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


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.


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

Additional Resources

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