Fundamentals of Data Science - 2024 entry

Data science depends on a solid grounding in mathematics and programming. In this module, you will learn essential mathematical techniques from linear algebra and probability. You will also develop programming skills specific to data analysis, including how to apply the mathematical techniques you have learned as part of computational data analysis procedures. Other computational methods with direct relevance to data science and processing of large datasets will also be included, such as data analysis packages for Python, and optimisation techniques for speeding up large computations.

Overall, this module will ensure you have the core skills and background knowledge that underpin many central topics in data science, including machine learning, statistical modelling, network analysis and computer vision.


Pre-requisite modules: None

Co-requisite modules: None

The aim of this module is to equip you with the core mathematical and computational skills essential for further study of data science. Topics will be tailored to the cohort, to address diverse backgrounds and previous experience. At the end of the module, you should possess a solid grounding in aspects of linear algebra, probability, and computational methods that are common to many areas of data science.



Most taught content will be delivered as lectures and practical work. Lectures will be accompanied by data analysis exercises and practical sessions. The module will be completed through individual study and coursework, supported by the module staff. Assessment will include assessed practical exercises and coursework.

On successful completion of this module you should be able to:



Module Specific Skills and Knowledge

:

1. Demonstrate competence in relevant aspects of linear algebra relevant to data science;

2. Demonstrate competence in aspects of probability;

3. Utilise a variety of computational methods relevant to data science.

Discipline Specific Skills and Knowledge

:

4. Use linear algebra and probability theory as part of data analysis procedures;

5. Understand the underpinning mathematical principles commonly used in machine learning and statistical modelling;

6. Carry out linear algebra and probability theory operations using Python.

Personal and Key Transferable / Employment Skills and Knowledge

:

7. Explain the relationship between mathematical principles and core techniques in data science;

8. Understand mathematical notation and use mathematical notation effectively to communicate to a specialised audience.

Topics will be chosen depending on the background and experience of the student cohort, but are likely to include:



- Aspects of linear algebra (e.g.): Vectors, Matrices, Systems of linear equations, Linear transformations, Eigenvalues and eigenvectors, Symmetry, Positive definite matrices, Singular value decompositions;

- Aspects of probability (e.g.): Basic probability, Marginal, conditional and joint probability, Bayes theorem, Probability distributions (the Normal, Gamma, Binomial and Bernoulli distributions), Central limit theorem, Moments, Multivariate distributions;

- Programming for data science in Python (e.g): Tools for handling data (Python: numpy, scipy, matplotlib, pandas), Linear algebra in code, Probability distributions and random numbers, Notebooks/markdown;

- Aspects of optimisation (e.g.): Linear least-squares, Gradient descent, Convexity (local vs global extrema), Linear programming;

- Other topics may be included as appropriate to the skills and background of the student cohort.

Reassessment will be by coursework in the failed or deferred element only. For referred candidates, the module mark will be capped at 50%. For deferred candidates, the module mark will be uncapped.

Basic reading:

ELE: http://vle.exeter.ac.uk/

 

Web based and Electronic Resources:

Other Resources:

Reading list for this module: