Dr Rachel Quinlan
Phone: +353 91 493796
Office: Room 105, Áras de Brún (Ground Floor)
Fax: +353 91 525700
email: rachel.quinlan@nuigalway.ie
News

My paper with James McTigue on Partial matrices of constant rank has just been published in Linear Algebra and its Applications.

My paper with James Cruickshank, Allen Herman and Fernando Szechtman on unitary groups over local rings appeared last month in the Journal of Algebra and its Applications.

I am the vicedean for Promotion of Science in the College of Science at NUI Galway. Activties coming up soon include the Open Day on April 5th and the Science Experience Summer Event in June.

I am just back from the 50th BT Young Scientist and Technology Exhibition. Well done to all the student participants and to the organisers on a wonderful event.

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 on January 17 2014.
Courses 201314
Semester 1
 MA134/MA106 Calcalas
Tá an modúl se ar fáil do mhic léinn i
gColáiste na hEolaíochta agus Coláiste na
nDán, na nEolaíochtaí Sóisialta, agus an
Léinn Cheiltigh. Is leagan Gaeilge den chúrsa
onóracha sa Mhatamaitic sa chéad bhlian atá i gceist (MA180 san Eolaíocht nó MA133 sa Dán).
Tá acmhainní don chúrsa seo ar fáil
anseo, ar
córas Blackboard OÉ Gaillimh.
 MA343 Group Theory I
Electronic resources for this course will be available
here,
on the NUI Galway Blackboard system.
 MA435 Undergraduate Ambassador Module in Mathematics
The website for this course is
here.
Semester 2
 MA180/190 Calcalas
Electronic resources for this course are available at
this dedicated website,
and on
Blackboard.
 MA335 Algebraic Structures
Electronic resources for this course will be available
here,
on the NUI Galway Blackboard system.
Research Interests
My research interests are generally in the area of algebra. My recent
and current
research activity focusses on interactions between linear algebra,
combinatorics, and field theory. 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, James McTigue and Olga O'Mahony.
My former PhD student Kirsten Pfeiffer defended her thesis in April
2011.
I was a coorganiser 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
 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
348360 (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
22592271 (2011).
 R. Quinlan,
Spaces
of matrices without nonzero eigenvalues in their field of definition,
and a question of Szechtman, Linear Algebra and its Applications, Vol. 434, no. 6, pages 15801587 (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 89, 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 nonabelian 2groups,
J. Combin. Theory Ser. A, Vol 113, no. 4,
2006.
 R. Quinlan,
Real elements and
realvalued characters of covering
groups of elementary abelian 2groups,
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.