CSMMS: Mathematics and Statistics for Data Science

Module code: CSMMS

Module provider: Computer Science; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Postgraduate Masters

When you'll be taught: Semester 1

Module convenor: Dr Fazil Baksh, email: m.f.baksh@reading.ac.uk

Pre-requisite module(s):

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: No

Talis reading list: No

Last updated: 21 May 2024

Overview

Module aims and purpose

This module is a maths and stats primer module containing key mathematics and statistics concepts. The module aims to bring students up to the appropriate level as regards the mathematics and statistics necessary for the modules taught as part of the MSc in Data Science and Advanced Computing.ÌýÌý

Module learning outcomes

By the end of the module, it is expected that students will be able to:

1. Understand and use appropriate mathematical notation and concepts;
2. Understand and apply mathematical and statistical techniques for data analytics; and
3. Apply appropriate mathematical and statistical techniques for small-scale and well-defined data analytics and tasks.

Module content

The module covers the following topics:

Matrices and Vectors

• Basic operations; linear independence; rank of a matrix; determinants and inverses; linear systems of equations; eigenvalues and eigenvectors; positive definite and negative definite matrices; dot and cross products; singular values, vector and matrix norms; linear vector spaces.

Calculus

• Reminder of differentiation; integration; differential equations; numerical solution of ODEs; functions of several variables; vector functions; partial differentiation; gradient vector; Jacobian and Hessian matrices; Taylor series expansions; unconstrained optimisation of differentiable functions of several variables; Computational optimisation techniques.

Probability and Distribution Theory

• Introduction to combinatorics; conditional probability; independence; Bayes theorem; random variables; distributions; expectation; co-variance; entrophy; mean square error; point and interval estimation methods; bootstrapping; sums of random variables; approximation theorems.

Basic statistical modelling

• Hypothesis testing; statistical significance; ANOVA; linear and non-linear regression; regularisation methods, spline regression; time series; Bayesian inference; Linear discriminant analysis (LDA); Principal component analysis (PCA).

Structure

Teaching and learning methods

The module comprises lectures introducing the topics with appropriate tutorial support for learning the material. Practical time is provided where students can use a mathematical/statistical computing package to practice and further develop their understanding of the material covered.ÌýÌýÌý

Study hours

At least 48 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 50% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: /cqsd/-/media/project/functions/cqsd/documents/qap/penaltiesforlatesubmission.pdf

You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Weekly practical exercises will be used as formative assessment. Feedback on weekly practical exercises will be given to students which will act as feedforward for the coursework assessments.Ìý

Reassessment

Additional costs