MTH2019 Multivariate mathematics for data science

When you finish this unit, you should be able to:

1. 1

   Successfully describe, and apply multivariate mathematics to problems in data science;

2. 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. 3

   Compute line, surface and volume integrals in a range of coordinate systems;

4. 4

   Demonstrate their comprehension of basic concepts related to linear transformations and vector spaces, including subspace, span, linear independence, basis, kernel and range;

5. 5

   Diagonalise real matrices by computing their eigenvalues and finding their eigenspaces;

6. 6

   Explain and apply basic concepts related to inner product spaces to problems such as least-squares data fitting;

7. 7

   Use appropriate technology (e.g. computer algebra packages) to solve certain classes of mathematical problems;

8. 8

   Present clear mathematical arguments in written and oral form.