MTH2019 · Multivariate mathematics for data science

Overview

This unit introduces and develops a range of basic concepts and techniques related to two main subjects: multivariate calculus and linear algebra. The programme is targeted for students following a degree in data science and the material will have emphasis on assimilating important principles, on developing classical techniques, and on facilitating the use of the theoretical framework and practical methods in the context of common applicative problems. The unit will cover partial derivatives, extrema of multivariate functions, integration, linear transformations, matrices and orthogonalisation, eigenvalues and eigenvectors, and applications to data science.

Offerings

Assessment

The Handbook lists an examination for this unit.

Requisites

Learning outcomes

1. Successfully describe, and apply multivariate mathematics to problems in data science;
2. Exhibit key skills in the calculus of functions of several variables including the computation of partial derivatives, finding tangent planes and identifying stationary points, root finding, and convexity for optimisation;
3. Compute line, surface and volume integrals in a range of coordinate systems;
4. Demonstrate their comprehension of basic concepts related to linear transformations and vector spaces, including subspace, span, linear independence, basis, kernel and range;
5. Diagonalise real matrices by computing their eigenvalues and finding their eigenspaces;
6. Explain and apply basic concepts related to vector spaces and subspaces;
7. Present clear mathematical arguments in written and oral form.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.