Unit information: Modern Mathematical Biology and Biophysics in 2024/25

Unit name Modern Mathematical Biology and Biophysics
Unit code MATHM0051
Credit points 20
Level of study M/7
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Professor. Liverpool
Open unit status Not open
Units you must take before you take this one (pre-requisite units)

MATH11005 Linear Algebra and Geometry; MATH10013 Probability and Statistics; MATH20015 Multivariable Calculus and Complex Functions (or equivalent courses from Physics/Engineering)

Units you must take alongside this one (co-requisite units)

None

Units you may not take alongside this one

None

School/department School of Mathematics
Faculty Faculty of Science

Unit Information

Why is the unit important?

This unit will provide students with the mathematical tools used to study and solve a variety of problems in biology at different scales. Examples will be taken from problems at different length and timescales - from the scale of the cell, tissue to organisms. Mathematical modelling in Biology is one of the most rapidly growing and exciting areas of Applied Mathematics. This is because new experimental techniques developed by Biophysicists are being applied in the Biological and Biomedical sciences, and are generating an unprecedented amount of quantitative data. This new 'quantitative revolution' is changing the way biology is done - requiring methods for understanding the biophysical methods of data collection, ways of generating hypotheses, and then testing them that rely heavily on sophisticated mathematical analyses. In summary, biological systems are complex systems and the modern process of studying them requires an iterative process of communication between mathematicians, biophysicists and biologists.

How does this unit fit into your programme of study?

This is an advanced specialised unit for students in year 4 who want to learn more about this exciting area of applied mathematics.

Your learning on this unit

An overview of content

By the end of the unit the students will be familiar with :

  1. the applications of ODE models in a variety of biological systems,
  2. the statistical mechanics approach to chemically reacting biological systems,
  3. non-equilibrium aspects of the mechanics of soft biological matter,
  4. reaction-diffusion equations and their applications in biology,
  5. the use of linear and nonlinear stability analysis to study the dynamics of complex systems,
  6. stochastic dynamics in biology,
  7. the dynamical systems approach to describing excitable media.

How will students, personally, be different as a result of the unit

Students will know more about the mathematics that describes many interesting phenomena observed in nature, such as the swimming of microorganisms, spread of infectious diseases, and the emergence of patterns in the development and growth.

Learning Outcomes

In this unit students will learn how to apply mathematics in a concrete context which has the scope for significant impact on society. We shall use a number of fundamental biological problems as the motivation and starting point. Students will gain expertise in developing mathematical models, learn how to explore methods for solving these models and be able todiscuss the implications of the predictions that can be made based on them.

How you will learn

Lectures, with occasional problems classes or informal discussion to meet the needs of individual students.

How you will be assessed

Tasks which help you learn and prepare you for summative tasks (formative):

Regular homework problems set. Homework will include simple numerical exercises using Maple and MATLAB.

Tasks which count towards your unit mark (summative):

10% coursework, 90% timed exam.

When assessment does not go to plan

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period). The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM0051).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the University Workload statement relating to this unit for more information.

Assessment
The assessment methods listed in this unit specification are designed to enable students to demonstrate the named learning outcomes (LOs). Where a disability prevents a student from undertaking a specific method of assessment, schools will make reasonable adjustments to support a student to demonstrate the LO by an alternative method or with additional resources.

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.