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Mathematics for Foundations of Machine Learning & Deep Learning, evening course

Course aims

This evening course, taught in person over 4 weekly sessions, covers the mathematical background required to follow the Foundations of Machine Learning and Foundations of Deep Learning courses. It is aimed at people who would like to take one or both of these courses but do not feel secure enough in the mathematical prerequisites. By the end of the course you will have a good understanding of several core mathematical concepts, and the tools required to understand the theory behind the machine learning and deep learning algorithms covered in those courses.

Summary of syllabus

Probability and statistics

  • Probability theory. Sum and product rules of probability. Joint, conditional and marginal probability. Bayes’ theorem.

  • Discrete and continuous probability distributions. Probability densities, cumulative distribution function.

  • Expectation, variance and covariance of random variables.

  • Likelihood functions, prior and posterior distributions. Statistical estimators. Maximum likelihood estimation (MLE), maximum a posteriori (MAP) estimation.

  • Standard statistical distributions: binomial, Bernoulli, categorical/multinoulli, Gaussian, logistic etc.

Linear algebra

  • Vectors and matrices. Matrix and vector operations.

  • Vector space, basis, linear independence. Change of basis.

  • Vector norms and inner products.

  • Orthogonality, orthonormal vectors. Orthogonal projections.

  • Gram-Schmidt procedure.

  • Linear transformations. Eigenvectors and eigenvalues.

  • Orthogonal matrices and rigid transformations.

  • Solving linear systems of equations. Matrix inverse and determinant.

  • Singular value decomposition.

Calculus and optimisation

  • Function derivatives. Interpretation as gradient or slope. Product rule and chain rule of differentiation.

  • Multivariate calculus, partial differentiation. Local optima.

  • Jacobian matrix and the Hessian.

  • Gradient descent.

Information theory

  • Information gain, bits and nats.

  • Entropy of a random variable. Average coding lengths.

  • Joint, conditional and cross entropy.

  • Relative entropy / Kullback-Leibler divergence and mutual information.


The FeedForward AI Academy programmes are led by Dr Kevin Webster, Honorary Research Fellow in Mathematics at Imperial College. Kevin recently completed teaching the graduate level course on Deep Learning in the mathematics department at Imperial College London in Autumn 2018.

Who is this course for?

This course is for anyone interested in Machine Learning & Deep Learning who has not previously learnt the core mathematical concepts, or has not visited these topics for a long time. These core mathematical concepts will prepare you for taking the Foundations of Machine Learning and Foundations of Deep Learning courses

Dates, times & location

Dates & times: Course running weekly over 4 evenings from Tue 30 April to Tue 21 May 2019, 18.00 - 21.00

Location: Central London, TBC

If you have any questions about the course, please email