Dr Rachel Quinlan
Head of 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 2020.
-
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 September 2019.
Courses 2019-2020
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
- MA180/190 Calculus
Electronic resources for this course will be available at
here. This site is linked from the Blackboard page ofor 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 three PhD students at NUI
Galway, Malak Almutairi, Dana Saleh and Cian O'Brien.
My former PhD students are Kirsten Pfeiffer (PhD 2011), James McTigue (PhD 2015), Olga O'Mahony (PhD 2018) and Hieu Ha Van (PhD 2019).
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
- K. Pfeiffer and R. Quinlan, Proof-evaluation as a step towards proof authorsip, 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.