2018 summer research interns

Summer Research Internships

This year we have about 50 interns, working on 11 different projects in conjunction with local and international businesses and in collaboration with a number of our partner universities. 

  • Calculating compensation for loss of future earnings
  • Assumptions of the USS valuation: are they feasible?
  • Double-debt problem
  • Car insurance in Egypt
  • Probability of default (in collaboration with a microfinance company in Ghana and AIMS (African Institute of Mathematical Sciences)- Ghana. Four Ghanaian graduate students from AIMS will join our team in Liverpool for this project)
  • Credit scoring
  • Analysis of Social Security Systems in China
  • Triangle-free reserving
  • Automobile insurance and claim severities (in conjunction with Brazilian partners)
  • Traffic flows (in conjunction with Eddie Stobart)
  • Profitability matrix (in conjunction with Eddie Stobart)

The internship commenced on June 4th and ended on July 12th with a workshop and presentations at the University of Liverpool London campus. See the film below detailing this years intern projects.

Details of the 2019 programme will be advertised shortly.

  • 2017 Internship (current research topic)


    The 2017 summer research internship saw 4, second-year UG students looking at micro-scale modelling of drug transport, for instance the spread of a paracetamol in a human body, emphasising the role of the cell’s membranes. The mathematics behind it involved diffusion processes and partial differential equations (pde) with various boundary conditions.

    Here is what the 2017 Summer Research Interns have to say about the work they achieved and their experience:

    Philip (Junyingjie Bao):

    Our task was to simulate the drug transport process across membranes using Biological Mathematics. During this process, Joe helped us construct the foundations for this topic and directed us as to how to proceed with the smaller details. Through this internship, I learned about how academic research is conducted. Although it was challenging, I really enjoyed this period of time working in group and solving scientific problems.

    Cissy (Jinkun Xing):

    I was amazed by the scope of micro-scale modelling. It can use multiple models simultaneously, focusing on different scales to describe the dynamics of a system. We focused on the impact of the membrane on drug transport kinetics. In this research, I, together with the three other interns, employed micro-scale modelling to simulate the drug diffusion process from the release point to the interior of the recipient cells. After reviewing a large volume of literature, we simplified the process into one-dimensional partial differential equations. Using MATLAB, Joe taught us bit by bit how to use pdepe to solve the three partial differential equations and employed MATLAB to draw the GIF of drug diffusion.

    I enjoyed the process of modelling the biological problems using mathematics to contribute to the study of drug transport and the treatment of patients. The work experience with Joe was beneficial; we learned to use pdepe in MATLAB and to design algorithms to show different patterns of GIFs according to different values of parameters. It was rewarding to spend a vacation doing meaningful research

    Apple (Xiaoshuo Cui):

    The experience with the Healthcare group was a really in depth process with lots of programming and mathematical equations. We learned specific knowledge required to solve diffusion equations with various boundary conditions. Enhancing our technical skills, we used MATLAB to present the biological processes using graphs. It was a practical experience which closely related biological transport processes with mathematics. The internship was invaluable to me because we successfully utilized the tools of mathematics to solve a real and practical problem in Medicine and Biology, allowing me to realise the amazing applied side of mathematics; I was able to put what I have learnt during classes into practice.

    We all appreciated this experience all the more because of Joe, an excellent PhD student who was very patient and always willing to answer our questions. He was always there to help and and pushed us to go further on the topic. 

    Floyd (Renfei Huang):

    The precious time spent with so many excellent students and doctors was short but unforgettable. During the one-month period, we all shared our knowledge and studied multiscale modelling. It was worth the hard work and all the final presentations were carried out brilliantly. It was the most wonderful learning experience I have ever had!

  • 2017 Internship (with Liverpool Businesses)


    During these internships, students answer real-work questions and see mathematical theory applied in practice. Currently in it's fifth year, these internships are led by our IFAM academics and their PhD students in cooperation with Liverpool business partners, aiming to assess some of the risk they are facing in the ever changing economic landscape. Students work on providing methods, data analysis or risk management solutions varying from strategic planning recommendations to personalised insurance.

    The 2017 summer business internship saw students working with Charles Oddy on enterprise risk management, with SatSafe on pricing drivers behaviour, with Eddie Stobart on networks optimization, and with Barnett Waddingham in analyzing non-financial risks of universities.

    Prof. Kurt Langfeld, Head of Department of Mathematical Sciences explains “our students experience is of paramount importance for our department. Partnering with our UG students and Liverpool businesses in research is not only a success story for our Department and our university, but also for the city of Liverpool.”

    Hear what the internship business partners have to say about the students taking part: 

    Charles Oddy, ERM, CERA, says “this was the second summer I worked alongside University of Liverpool students and academics and I am impressed by their enthusiasm and professionalism. The students work as real ambassadors of the university”.

    Stuart Millward, CEO of SatSafe Technologies, "Working with the students on this project was an absolute privilege and the quality of work was testament to the extremely high standards of Liverpool University's Department of Mathematical Sciences"