- The conference of the International Linear Algebra Society (ILAS) will come to NUI Galway in June 2022.
- You can find an archive of lecture notes from courses that I've taught over the years here.
- You can find slides from some conference talks and seminars that I've given in the last few years here.
- I will give a talk about mathematical origami at this conference later in September 2021.
- This site was last updated in September 2021.

**MA3343 Groups**

Electronic resources for this course are here. This site is linked from the Blackboard page ofor the module, which will be used for announcements and for some aspects of the assessment.**MM4000**Final Year Projects

I am the coordinator of the final year project module in the School of Maths this year.

**MA180/186/190 Calculus**

Electronic resources for this course will be available here (last year's content is there currently). This site is linked from the Blackboard pages for the module, which will be used for announcements, communications and keeping track of assessment.**MA283 Linear Algebra****MA485 Mathematics for Decision Making II**, with Niall Madden

I am also interested in mathematics education research at university level.

I am currently supervising the research of two PhD students at NUI Galway, Malak Almutairi and Dana Saleh.

My former PhD students are Kirsten Pfeiffer (PhD 2011), James McTigue (PhD 2015), Olga O'Mahony (PhD 2018), Hieu Ha Van (PhD 2019), and Cian O'Brien (PhD 2020).

I was a co-organiser of the 3rd Irish Symposium on Undergraduate Mathematics Education, the 6th de Brun workshop on

- C. O'Brien, K. Jennings and R. Quinlan, Alternating signed bipartite graphs and difference-1 colourings,
*Linear Algebra and its Applications*, Vol 604, pages 370--398 (2020) - K. Pfeiffer and R. Quinlan, Proof-evaluation as a step towards proof authorship, in Beyond Lecture, Mathematical Association of America, 2016.
- J. McTigue and R. Quinlan, Partial matrices of constant rank,
*Linear Algebra and its Applications*, 2014. - J. Cruickshank, A. Herman, R. Quinlan, F. Szechtman, Unitary groups over local rings,
*Journal of Algebra and its Applications*, Vol. 13, Issue 02, 2014. - J. McTigue and R. Quinlan,
Partial matrices whose completions all have the same rank,
*Linear Algebra and its Applications*, Vol 438, no. 1, pages 348--360 (2013). - K. Pfeiffer and R. Quinlan, A proof evaluation exercise in an elementary linear algebra course, Proceedings of the Fifth National Conference on Research in Mathematics Education, St Patrick's College Drumcondra, 2013.
- J. McTigue and R. Quinlan,
Partial matrices whose completions have ranks bounded below,
*Linear Algebra and its Applications*, Vol 435, no. 9, pages 2259-2271 (2011). - R. Quinlan,
Spaces
of matrices without non-zero eigenvalues in their field of definition,
and a question of Szechtman,
*Linear Algebra and its Applications*, Vol. 434, no. 6, pages 1580-1587 (2011) - R. Quinlan, Acts of knowing in university mathematics curricula, Proceedings of the Fourth National Conference on Research in Mathematics Education, St Patrick's College Drumcondra, 2011.
- R. Quinlan,
'Guessing at our mental models' or 'committed knowing acts' - what are
our students doing?,
*Bulletin of the Irish Mathematical Society*, no. 66 (2010) - R. Quinlan, What makes mathematics attractive at university?, Proceedings of the Third National Conference on Research in Mathematics Education, St Patrick's College Drumcondra, 2009.
- R. Gow and R. Quinlan,
Galois extensions and subspaces of alternating bilinear forms with
special rank properties,
*Linear Algebra and its Applications*, Vol. 430, Issues 8-9, 2009. -
R. Gow and R. Quinlan,
Galois
theory and linear algebra,
*Linear Algebra and its Applications*, Vol. 430, Issue 7, 2009. - R. Gow and R. Quinlan,
On the vanishing of subspaces of alternating bilinear forms,
*Linear and Multilinear Algebra*, Vol. 54, no. 6, 2006 - R. Gow and R. Quinlan,
Covering groups of rank 1 of elementary
abelian groups,
*Communications in Algebra*, Vol 34, no. 4, 2006. abstract - R. Gow and R. Quinlan,
On central difference sets in certain non-abelian 2-groups,
*J. Combin. Theory Ser. A*, Vol 113, no. 4, 2006. - R. Quinlan,
Real elements and
real-valued characters of covering
groups of elementary abelian 2-groups,
*Journal of Algebra*, Vol 275, no. 1, 2004. abstract - R. Quinlan,
Twisted group rings of metacyclic groups,
*Representation Theory*, Vol. 7, 2003 - R. Quinlan,
Generic central extensions and projective
representations of finite groups,
*Representation Theory*, Vol. 5, 2001. - R. Quinlan, Irreducible Projective Representations of Finite Groups, PhD thesis, University of Alberta, 2000.

I am a member of the Irish Mathematical Society, the American Mathematical Society, the Mathematical Association of America, the International Linear Algebra Society , and the British Society for Research into the Learning of Mathematics.