Mathematical Methods for Bioengineers

Module aims

This module introduces the choice and use of appropriate mathematical modelling to model biological systems and analyse complex biological data.

Learning outcomes

Knowledge and Understanding

  • To formulate bioengineering problems in terms of appropriate mathematical modelling methods.
  • To analyse biological data using appropriate mathematical methods
  • To evaluate the output of the mathematical modelling methods in relation to the underlying biological processes
     

Intellectual Skills

  • To evaluate the best mathematical method for addressing a particular bioengineering problem
  • To critically evaluate the output of mathematical analysis of a bioengineering problem

Practical Skills

  • To implement mathematical models and data analysis algorithms in the python programming language.

Transferable Skills

  • To encode mathematical models using Python
  • To manipulate experimental data using mathematical methods

Module syllabus

This course provides an introduction to the mathematical techniques needed to model biological systems and analyse complex biological data. Fundamental concepts are presented, with emphasis on the application of these techniques to problems in neurotechnology and biomedical engineering. Topics include:

  • Linear algebra, eigenvalues and eigenvectors, principal components analysis, singular value decomposition
  • Stochastic processes, Markov chains, renewal processes
  • Linear and nonlinear time series analysis, correlation, embedding, univariate and multivariate time series.
  • Ordinary Differential Equations. Models of excitable cells.
  • Regression and Model fitting. Model selection.
  • Graph Theory and Network Analysis.
  • Systems Identification, Wiener and Volterra series. Generalized Linear Models (GLMs) for physiological processes and receptive fields.
  • Signal Detection Theory and Information Theory.

This includes understanding different approaches to mathematical modelling, choice of an appropriate method to model or analyse a given problem, coding the model in Python, evaluating the success of the modelling, interpreting the result when appropriate in terms of underlying biological processes.

Pre-requisites

Undergraduate mathematics at approximately 2nd year level. Basic-level prior programming experience in a language such as MATLAB or Python.

Teaching methods

Lectures: 18 hours
Study groups: 9 hours

Assessments

 Examinations:
●  Written exam: ; 40%% weighting
    No type of previous exam answers or solutions will be available

Courseworks:
●  Progress test: Test 1; 20% weighting; Three progress tests involving a combination of written and programming work.
●  Progress test: Test 2; 20% weighting; Three progress tests involving a combination of written and programming work.
●  Progress test: Test 3; 20% weighting; Three progress tests involving a combination of written and programming work.

Feedback : Feedback will be given within 10 working days of submission.