Dublin City University (2022–2025)
At Fiontar agus Scoil na Gaeilge I taught through Irish, on the Gnó agus Gaeilge degree and at graduate level. Modules:
MTH1083 Quantitative Methods for Business (Autumn 2024, 2025)
FBA10377 Financial Management (Spring 2023, 2024, 2025)
MNA1131 Management and Organisational Behaviour (Spring 2022–2025)
BAA1085 Research Methods, graduate level (full year 2023, 2025)
ENI1014 Founding a Start-up, final-year project equivalent (Spring 2022–2025)
FBA1038 Finance and Spreadsheets, graduate level (Autumn 2022, 2024)
I developed new modules in quantitative methods and in artificial intelligence for business for the Gnó agus Gaeilge degree. I obtained €10,000 in funding to develop graduate-level linear algebra training; the workshop series has been delivered five times, to about 100 researchers. With SATLE funding I developed and delivered AI literacy workshops for humanities lecturers and Gaeltacht professionals.
Worcester Polytechnic Institute (2016–2021)
In the Department of Mathematical Sciences I taught combinatorics, discrete mathematics, linear algebra and algebra, at undergraduate and graduate level. Courses:
MA1801 Denksport, co-ordinator (B-term 2017, 2018, 2019; C-term 2021)
MA2071 Matrices and Linear Algebra (D-term 2020)
MA2073 Matrices and Linear Algebra II (C-term 2019, 2020)
MA3823 Group Theory (B-term 2016–2020; see below)
MA3825 Rings and Fields (C-term 2018)
MA502 Linear Algebra, graduate level (Fall 2020)
MA530 Discrete Mathematics I, graduate level (Fall 2018)
MA533 Discrete Mathematics II, graduate level (Spring 2017)
MA535 Algebra, graduate level (Fall 2017)
I also ran independent studies for groups of two to four students in geometric algebra (2017), association schemes (2018), representation theory of finite groups (2019), differential Galois theory (2020) and differential geometry (2021).
I revised and expanded the syllabus for MA3823 Group Theory, wrote a complete set of lecture notes, and developed a series of interactive workshops for the course, funded by a 2019 Teaching Innovation Grant from WPI's Morgan Center, "Making the abstract concrete". With Qingshuo Song and Joseph Fehribach I developed an online version of MA2071 for 300 students, and I developed online versions of MA3823 and MA502. I hold WPI's Certificate in Online Teaching and Learning. On the Undergraduate Committee I led the revision of the linear algebra courses, introducing MA2072 and redesigning MA2073.
In 2019 I was named a Faculty Champion by the Student Athletic Advising Committee, and in 2021 I was nominated for the Moruzzi Award.
Interactive Group Theory (developed course)
This course, typically taken by third year students at WPI is an introduction to abstract algebra and to axiomatic methods. I have taught the course since 2016. While the required syllabus finishes with the first isomorphism theorem, I generally finish the course with discussion of the Sylow theorems and (unexamined) discussion of free groups, paradoxical decompositions and the Banach-Tarski paradox. My lecture notes follow, with the weekly assessment.
M1_AxiomsEtc.pdf (Assignment1.pdf)
M2_Subgroups.pdf (Assignment2.pdf)
M3_PermGroups.pdf (Assignment3.pdf)
M6_Sylow.pdf (Assignment5.pdf)
Between 2017 and 2021, I developed a series of interactive learning sessions which take place in parallel to traditional lectures. Most of the sessions focus on using techniques developed in class to analyze the symmetries of regular n-gons in two dimensions and the cube in three dimensions. S
Other lecturing experience
University of Queensland (2012–2014)
I taught the coding theory part of MATH3302 Coding and Cryptography (Semester 1, 2013), and gave an Honours reading course on permutation groups (Semester 1, 2014), running from the Sylow theorems to the O'Nan–Scott theorem.
NUI Galway (2007–2012)
In January–March 2012 I designed and delivered two courses, setting and marking their exams: MA313 Linear Algebra II, a final-year course of about 70 students (lecture notes available here), and the algebra half of Introduction to Mathematics, an access course for about 35 mature and disadvantaged students. From 2007 to 2012 I tutored representation theory (MSc), probability (MA387/533), cryptography and number theory (CS402), group theory (MA344) and first-year honours mathematics (MA180), including its Irish-language version.