# CS131 Mathematics for Computer Scientists II

## Academic Aims

- To provide students with sufficient mathematical knowledge to enable them to understand the foundations of their subject for both study purposes and later career development
- To bridge the gap in style and content between A-level and university mathematics and to introduce students to the language and methods of professional mathematics.

## Learning Outcomes

By the end of the module the 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 and integral calculus with confidence and precision
- Understand the basics of probabilistic analysis and be able to apply the methods in practical examples.

## Content

- Linear Algebra: Vectors, linear independence, subspaces, basis, dimension.
- Matrix Algebra: Linear equations, inverses, linear transformations, eigenvalues/vectors.
- Sequences and Series: Limit and convergence properties of sequences and series.
- Calculus: Limits, continuity, differentiable functions, differentiation of inverse functions, integration, logarithms, exponentials, Taylor’s theorem.
- Abstract Algebra: Introduction to some abstract structures such as groups, rings, fields and vector spaces.