Introductory description

This module follows on from module Sets and Proofs.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

Linear Algebra (Matrices, Determinants, SVD, Inner/Outer Products, PCA, Least Square Estimation, Rank, Systems of Equations)
Vector Spaces (Examples of Vector Spaces, Subspaces, Span, Linear Independence, Basis)
Inner Product Spaces (Norms, Orthogonality, Orthonormal Bases, Gram - Schmidt process)
Linear Transformations (Range, Kernel, Rank, and Nullity)
Eigenvalues and Eigenvectors (Calculation, Symmetric Matrices, Matrix Diagonalization, Cayley Hamilton Theorem, Iterates of Matrices)
Differentiation (Mean Value Theorem, Taylor Expansion, Gradient-Based Optimization)

Learning outcomes

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

• - Carry out formal and informal mathematical proofs.
• - Use effectively techniques for the analysis and transformation of vector spaces and the solution of sets of linear equations.
• - Perform operations of the differential calculus with confidence and precision.
• - Use effectively techniques for the calculations and analysis matrix algebra

Indicative reading list

Please see Talis Aspire link for most up to date list.

View reading list on Talis Aspire

Subject specific skills

• Matrix Algebra
• Proof by contradiction
• Proof by induction
• Differentiation
• Solving systems of linear equations

Transferable skills

• Problem solving
• Quantitative reasoning
• Analytical thinking
• Construction of logical argumentsCritical thinking
• Technical
• Good working habits of being thorough and independent
• Creativity