**The School of Mathematics and Statistics will be offering a number of individual undergraduate summer research placements in 2020. The list of potential projects is given below. A stipend of €800 will be paid per student, with an enhanced stipend of €1,200 for a number of non-local students. However, transport costs to UCD cannot be paid. The programme is aimed specifically at penultimate-year undergraduate students, although students in other years may be admitted in exceptional circumstances. The programme is not restricted to UCD students.**

Applicants should submit:

- their application form online here https://forms.gle/
DFzUo49wL7trqAEN8 , - a cover letter (max 1 page) and CV (max 2 pages) as a single PDF file with filename <lastname_firstname.pdf> to be uploaded here https://www.dropbox.com/
request/OohAZoYYfiH5eOj1R4Rt . Please see guidance on writing a CV suitable for this programme.

The deadline for applications is **Friday 27th March 2020 at 17:00**. Where a mismatch occurs between the number of offers and the demand for projects, candidates will be ranked according to a weighted average of GPA and other factors (e.g. quality of CV, suitability of candidate to a particular project). Successful candidates will be notified in early to mid-April. It is envisaged that the projects will last a minimum of 6 weeks, starting in early June. Details of start dates can be negotiated with individual supervisors.

An undergraduate research project is a great opportunity for students to develop their research skills. See previous year's reports and what some of our alumni have gone on to do! Also, see this recent article on their success.

**Project Titles and Supervisors and Abstracts**

This is a joint research project with Dr. Igor Kontorovich of the Mathematics Education Unit at the University of Auckland, New Zealand. In the daily teaching-and-learning reality, we treat mistakes as something to be avoided. If you think about assessment, for example, it often acts as an institutionalized punishment for those who “don’t get it right”. From the perspective of mathematics education research, the instances of “not getting it right” provide a window into silent mechanisms of students’ thinking. Hence, the enhanced interest in the systematic mistakes that students make.

The scholarship student will engage with final exams in Stage-2 mathematics courses and dissect the ‘logic’ behind students’ reasoning and common answers. This work might lead to insights about the sources of these mistakes and pedagogies to overcome them. The student will be expected to undertake a literature review on mathematical thinking. This project is intended for students with a solid mathematical background and a genuine interest in educational issues.

Sports such as long-distance running and cycling are often performed over complex routes - around bends and over mountains. Athletes must negotiate these changes of direction (with associated gravity, centripetal

acceleration, etc.) going uphill and downhill, becoming a part of the race. Typical modern racing strategies involve constant speed or power output. As such, quantifying these long-term (gravity) and short-term

of an athlete along such curves, or portions of them. With the path fixed, we can determine a strategy for racing at constant speed or constant power output along certain sections. We will use idealised examples of

routes as well as real GPX files of a range of famous events in road running and cycling.

• Consider simple mechanics of motion on known paths

Dr. Aoibhinn Ní Shúilleabháin

Title: Sense of Belonging in Undergraduate Mathematics

Given the shortage of undergraduate students pursuing mathematics-related degrees and careers, it is important to investigate students’ experiences of their mathematical learning and consider the factors which may contribute to student attrition in this subject. A sense of belonging has been established as an important feature in predicting students’ further involvement in mathematics (Bartholomew, Darragh, Ell &Saunders, 2011; Good, Rattan & Dweck, 2012). However, research has demonstrated that the transition from post-primary to third level education can have a negative impact on students’ sense of belonging to mathematics (Meehan, Howard & Ni Shuilleabhain, 2018) and may contribute to the low numbers of students pursuing maths-related degree pathways.

This study will build on previous research in the Irish context and utilise qualitative data in investigating students’ sense of belonging in the transition from post-primary to university mathematics. The research will examine students’ reflections of their own learning (Moon, 2006) and consider how their learning experiences impacted their decisions to pursue a mathematics-based degree.

As part of this project the undergraduate student will assist in the qualitative analysis of anonymous student reflections, according to the theoretical framework of Good, Rattan & Dweck (2012). The undergraduate student will also undertake a literature review on students’ sense of belonging in mathematics and situate this particular research of undergraduate Irish student in the international context.

______________________________

Dr. Lennon O'Naraigh

Title: Exploring Mathematical Models for Cancer Growth

This is a joint project with Dr Sourav Bhattacharjee in the School of Veterinary Medicine in UCD. In this project, the student will look at different Mathematical Models for cancer growth. The focus will be on reaction-diffusion-type models which are capable of describing the spatial heterogeneity of cancerous tissue - in addition to the dynamics of the cancer growth. The methodology for this part of the project will primarily be literature review. The student will be encouraged to look especially at mathematical models of Colorectal cancer, and to implement the mathematical models numerically, with a view to characterizing the morphology of the cancerous tissue. The student will then investigate if this morphological information is consistent with medical imaging of Colorectal cancer tissue obtained by Dr Bhattarcharjee. As such, the ultimate aim of the project is to improve the accuracy of detection of Colorectal Cancer.

Title: A model-based approach to assess epidemic risk

In recent years, the extensive development of the transportation infrastructure has radically changed how connected our world is. In today's "small-world" we can travel around the globe in a matter of days, if not hours. This has important implications on international security, especially in regard to the potential spread of pandemic diseases.

The recent 2019-nCov outbreak has forced many countries to take drastic measures to contain and slow down the spread of the virus. Due to the urgency of the situation, several countries have immediately reacted by creating quarantines and cancelling flights. It may be argued that these preventive measures are often taken without full awareness of the effective pandemic risk, or without a formal modelling framework.

The goal of this project is to study a network of international flight routes and how its topology may play a role in the spread of disease. An essential aspect of this project is the development of a statistical network model that can take into account the flight routes data and the distribution of the infected population.

The outcome of the project is to give a model-based quantification of pandemic risk, and to identify optimal interventions within the network. Due to the large size of the dataset and due to the complexity of the data, the project will require very good familiarity with a programming language like Python or R.

______________________________

## Alumni

**2013**

Aideen Costello (TCD; Morgan Stanley and First Derivatives)

Julian Eberley (Theoretical Physics, UCD; Software Developer at Citi)

Daniela Mueller (Mathematical Science UCD; PhD candidate in UCD)

Benen Harrington (TCD, PhD candidate at University of York)

**2014**

James Fannon (Theoretical Physics, UCD; PhD candidate in UL)

Andrew Gloster (Theoretical Physics, UCD; MSc at Imperial College London; PhD candidate in UCD)

Shane Walsh (Theoretical Physics, UCD; PhD Candidate in UCD and IRC scholar)

Adam Keilthy (TCD; PhD candidate in Oxford University)

**2015**

Patrick Doohan (Mathematical Studies, UCD; MSc in Applied Mathematics at Imperial; PhD candidate at Imperial College London)

Maria Jacob (ACM, UCD; PhD candidate at University of Reading/Imperial College London)

Owen Ward (TCD; PhD candidate at Columbia University, New York)

Paul Beirne (Mathematics, UCD; now a PhD at candidate in UCD)

Daniel Camazon Portela

**2016**

Christopher Kennedy (ACM, UCD; statistics PhD candidate at UCD)

Emily Lewanowski-Breen (Maths and Science Education, UCD; second-level maths and biology teacher at Wesley College, Dublin)

Michael O’Malley (Stats and Maths, UCD; postgraduate at the University of Lancaster, UK)

**2017**

Adam Ryan (Mathematics, UCD; Analyst for Brown Thomas and Arnotts) - Report

Luke Corcoran (Theoretical Physics, TCD; completed part iii in Cambridge (with distinction), PhD student at Humboldt University Berlin) - Report

Conor McCabe (ACM, UCD; MS Statistical Science at Oxford, Machine Learning Scientist at ASOS) - Report

Joseph Curtis (Statistics, UCD; Core Operations Engineer at Virtu Financial in Dublin) - Report

**2018**

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