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Dr Rachel Quinlan

Phone: +353 91 493796
Office: Room 105, Áras de Brún (Ground Floor)
Fax: +353 91 525700
e-mail: rachel.quinlan@nuigalway.ie

News

• None really at the moment. This site was last updated on February 25 2013.

Courses 2012-13

Semester 2

• Calculus (MA180/190/186)
  Resources for this course are available here.
• MA314 (Part 2) Introduction to Rings and Fields
  This is the second segment of the MA314 (Linear Algebra) it consists of an introduction to abstract algebra. Electronic resources for this course are 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 one PhD student at NUI Galway, James McTigue.
My former PhD student Kirsten Pfeiffer defended her thesis in April 2011.
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

• 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).
• 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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