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Department of Mathematical Sciences, Unit Catalogue 2010/11

MA10210: Algebra 1B

Click here for further information Credits: 6
Click here for further information Level: Certificate
Click here for further information Period: This unit is available in...
Semester 2
Click here for further information Assessment: EX 100%
Click here for further informationSupplementary Assessment: MA10210 Mandatory extra work (where allowed by programme regulations)
Click here for further information Requisites: Before taking this unit you must take MA10209 and while taking this unit you must take MA10207
Click here for further information Description: Aims:
To introduce the abstract theories of groups and vector spaces and demonstrate their power through applications.

Learning Outcomes:
After taking this unit the students should be able to:
* State and prove fundamental results of group theory and linear algebra.
* Demonstrate competence applying abstract ideas in specific examples.
* Compute determinants, eigenvalues and eigenvectors.

Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials)

Axiomatic development of group theory.
Subgroups, homomorphisms, kernel and image.
Order of an element and of a group; cyclic groups. Isomorphism.
Permutations: cycle notation, sign of a permutation.
Actions, orbits and Cayley's theorem. Cosets, Lagrange's theorem and applications. Orbit-Stabilizer theorem and applications.
Axiomatic development of vector spaces.
Extending a linearly independent set to a basis. Dimension, rank, nullity. Rank-Nullity theorem.
Determinants: definition, properties and computation. Adjugate and inverse formula. Invertibility of matrices. Cramer's rule.
Eigenvalues, eigenvectors and eigenspaces. Characteristic polynomial. Algebraic and geometric multiplicities. Diagonalisation.
NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.