Study information

Advanced Topics in Mathematical & Computational Biology - 2023 entry

MODULE TITLEAdvanced Topics in Mathematical & Computational Biology CREDIT VALUE15
MODULE CODEMTHM009 MODULE CONVENERDr James Rankin (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
Number of Students Taking Module (anticipated) 10
DESCRIPTION - summary of the module content

This course will cover mathematical and computational approaches that are widely used in current research on a range of topics investigating dynamics in biology, including neuroscience. The dynamical phenomena covered in this course, such as bi-stability, oscillations and synchronisation occur in a wide range of biological systems. Mathematical approaches such as bifurcation and network analysis will be taught alongside their computational counterparts relying on the implementation of robust numerical methods. The module will be delivered through a combination of lectures and computer lab sessions.

This module is recommended for mathematical-biology track students.

Pre-requisites: MTH3039 or MTH3006

Co-requisites: NSCM005 or MTHM018

 

 

AIMS - intentions of the module

This module will build upon methods used to study dynamical systems from related 3rd year and M-level modules, including bifurcation and network analyses. These approaches will be taught alongside their computational counterparts for simulating dynamical systems models and performing numerical bifurcation analysis using continuation methods. Students will also gain skills in the biological interpretation and implications of results stemming from analysis of biological and biomedical models.

 

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you will be able to:

Module Specific Skills and Knowledge:
1 Develop knowledge of biological and biomedical models of interest in current research
2 Gain an understanding of how mathematical tools can be applied in the biological sciences
Discipline Specific Skills and Knowledge:
3 Further develop skills for the mathematical analysis of dynamical systems arising in biology, e.g.
Study of coupled networks and synchronisation
Approximation of homogenous networks and heterogeneous spatially extended networks
4 Bifurcation methods for studying qualitative changes to model dynamics under parameter variation
5 Numerical methods for model simulations and systematic parameter investigation
6 Interpretation of findings from a mathematical and biological perspective
7 Use established techniques to analyse mathematical models at the research level
Personal and Key Transferable/ Employment Skills and Knowledge:
8 Develop programming and problem-solving skills
9 Report-writing skills that include communicate arguments, evidence and conclusions appropriate to the intended audience
10 Independent, open-ended study related to current research topics 
SYLLABUS PLAN - summary of the structure and academic content of the module

The syllabus will depend upon the module topic(s) offered and will be specified in detail by the lecturer(s) and agreed by the module coordinator for any particular year. Material in the syllabus will not significantly overlap with that covered in other modules offered at an equivalent level in the same year.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 33 Guided Independent Study 117 Placement / Study Abroad 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Lectures 22 Lectures and example classes
Guided independent study 117 Lecture & assessment preparation, wide reading
Computer lab sessions 11 Lab sessions focusing on formative/summative assessments

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
3-5 worksheets 1 page each with 3-5 questions 1-10 In lab sessions
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 100 Written Exams 0 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
2 course work reports (1 and 2) (choice one of 3 topics for each computational/programming focused assessment) 100 4 questions per sheet 1-10 In lab sessions; on marked reports
         

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
Coursework report 1 * Coursework report 1 All August Ref/Def period
Coursework report 2 * Coursework report 2 All August Ref/Def period
       

*Please refer to reassessment notes for details on deferral vs. Referral reassessment

RE-ASSESSMENT NOTES

Deferrals: Reassessment will be by coursework in the deferred element only. For deferred candidates, the module mark will be uncapped. 

Referrals: Reassessment will be by a single piece of coursework worth 100% of the module only. As it is a referral, the mark will be capped at 50%. 

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
Basic reading:
Strogatz, S. H. Nonlinear Dynamics and Chaos, Westview Press, 2014
 
ELE – College to provide hyperlink to appropriate pages
 
Web based and electronic resources: 
 
Other resources:
Izhikevich, E. M. Dynamical Systems in Neuroscience, MIT Press, 2007
 
Ermentrout, G. B. & Terman, D. H. Mathematical foundations of neuroscience, Springer, 2010
 
Keener, J. P. & Sneyd, J. Mathematical physiology, Springer, 1998
 
Pikovsky, A.; Rosenblum, M. & Kurths, J. Synchronization: a universal concept in nonlinear sciences Cambridge university press, 2003, 12

Reading list for this module:

There are currently no reading list entries found for this module.

CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES MTH3039, MTH3006
CO-REQUISITE MODULES NSCM005, MTHM018
NQF LEVEL (FHEQ) 7 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Tuesday 10th July 2018 LAST REVISION DATE Thursday 26th January 2023
KEY WORDS SEARCH Mathematical biology; mathematical neuroscience; computational biology; computational neuroscience; nonlinear dynamics; systems biology; population dynamics; mathematical modelling; linear algebra; differential equations.

Please note that all modules are subject to change, please get in touch if you have any questions about this module.