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Dr Rachel Quinlan

School of Mathematics, Statistics and Applied Mathematics

Phone: +353 91 493796
Office: Room G-007, Áras de Brún (Ground Floor)
Fax: +353 91 525700
e-mail: rachel.quinlan@nuigalway.ie

News

• 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.
• This site was last updated in January 2021.

Courses 2020-2021

Semester 1

• MA3343 Groups
  Electronic resources for this course will be available here. This site is linked from the Blackboard page ofor the module, which will be used for announcements, communications and keeping track of assessment.

Semester 2

• MA180/186/190 Calculus
  Electronic resources for this course will be available here. This site is linked from the Blackboard pages for the module, which will be used for announcements, communications and keeping track of assessment.

Research Interests

My research interests are generally in the area of algebra, especially linear algebra and its interactions with group theory, combinatorics, and field theory. I have a particular interest in linear and affine spaces of matrices that have special properties relating to rank. I am also interested in the ordinary and projective representation theory of finite groups and in group rings. My PhD thesis, completed in 2000 at the University of Alberta, was concerned with the classification of irreducible projective representations of finite groups over fields, using the group ring of a generic central extension.
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 Linear Algebra and Matrix Theory, and of the Groups in Galway conferences in 2006, 2007, 2008 and 2010.

Selected Publications and Preprints

• 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.

Other Interests

I am involved in the running of a Mathematics Enrichment Programme for interested second level students at NUI Galway, and in Ireland's participation in the International Mathematical Olympiad (IMO). I was Ireland's leader at the 2006 IMO in Slovenia. My report on the 2006 IMO is available here.
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.

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