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Mathematics, Statistics & Applied Mathematics
Dr James Cruickshank
Áras De Brún
School of Mathematics, Statistics and Applied Mathematics
T: Ext. 3965
This is concerned with the geometric and combinatorial mathematics associated with bar and joint frameworks and other related structures. In particular I have worked on 3D rigidity of bar and joint frameworks and rigidity theory of surface graphs and of block-and-hole graphs. Collaborators: Steve Power (Lancaster University), Derek Kitson (Lancaster University), Qays Shakir (NUI Galway)
Linear and multiilinear algebra over local rings
Local rings arise naturally in several mathematical contexts. We have studied hermitian and skew hermitian forms over such rings and proved several new classification theorems for such forms. We have also investigated analogues of the classical matrix groups in this context. Collaborators: Fernando Szechtman (University of Regina), Rachel Quinlan (NUI Galway)
Random geometric graphs
We have investigated the use of random geometric graphs to model networks in evolutionary game theory and related areas. Collaborators: Colm O'Riordan (NUI Galway), Christine Marshall (NUI Galway)
|Project||Start Date||End Date|
|QAYS RASHID SHAKIR EMBASSY OF IRAQ SCHOLARSHIP||21-JUL-14||30-SEP-15|
|HP JAMES CRUICKSHANK TEACHING & LEARNING MATHEMATICS IN A DIGITAL ENVIRONMENT||23-JUN-09||31-DEC-13|
|MF2003 MF86 03 M JAMES CRUICKSHANK||01-SEP-04||20-JUL-07|
Peer Reviewed Journals
|(2018)|| 'Rigidity of linearly constrained frameworks'
James Cruickshank, Hakan Guler, Bill Jackson, Anthony Nixon (2018) 'Rigidity of linearly constrained frameworks'. International Mathematics Research Notices, [DOI] [Details]
|(2018)|| 'The generic minimal rigidity of a partially triangulated torus'
James Cruickshank, Derek Kitson, Stephen Power (2018) 'The generic minimal rigidity of a partially triangulated torus'. Proceedings Of The London Mathematical Society, [DOI] [Details]
|(2018)|| 'Unitary groups and ramified extensions'
James Cruickshank and Fernando Szechtman (2018) 'Unitary groups and ramified extensions'. Communications In Algebra, [DOI] [Details]
|(2018)|| 'Hermitian and skew hermitian forms over local rings'
Cruickshank, J,Quinlan, R,Szechtman, F (2018) 'Hermitian and skew hermitian forms over local rings'. Linear Algebra And Its Applications, 551 :147-161 [DOI] [Details]
|(2018)|| 'Generators and relations for the unitary group of a skew hermitian form over a local ring'
Cruickshank, J,Szechtman, F (2018) 'Generators and relations for the unitary group of a skew hermitian form over a local ring'. Linear Algebra And Its Applications, 552 :1-28 [DOI] [Details]
|(2017)|| 'Positive polynomials on Riesz spaces'
Cruickshank, J,Loane, J,Ryan, RA (2017) 'Positive polynomials on Riesz spaces'. Positivity, 21 :885-895 [DOI] [Details]
|(2017)|| 'The generic rigidity of triangulated spheres with blocks and holes'
Cruickshank, J,Kitson, D,Power, SC (2017) 'The generic rigidity of triangulated spheres with blocks and holes'. Journal Of Combinatorial Theory Series B, 122 :550-577 [DOI] [Details]
|(2014)|| 'The smooth structure of the moduli space of a weighted series-parallel graph'
Cruickshank, J,McLaughlin, J (2014) 'The smooth structure of the moduli space of a weighted series-parallel graph'. Topology And Its Applications, 164 :242-247 [DOI] [Details]
|(2014)|| 'Unitary groups over local rings'
Cruickshank, J,Herman, A,Quinlan, R,Szechtman, F (2014) 'Unitary groups over local rings'. Journal Of Algebra And Its Applications, 13 [DOI] [Details]
|(2014)|| 'On Spaces of Infinitesimal Motions and Three Dimensional Henneberg Extensions'
Cruickshank, J (2014) 'On Spaces of Infinitesimal Motions and Three Dimensional Henneberg Extensions'. Discrete & Computational Geometry, 51 :702-721 [DOI] [Details]
|(2011)|| 'Series Parallel Linkages'
Cruickshank, J,McLaughlin, J (2011) 'Series Parallel Linkages'. Publicacions Matematiques, 55 :359-378 [Details]
|(2007)|| 'Software for calculating blood lactate endurance markers'
Newell, J ; Higgins, D; Madden, N; Cruickshank, J; Einbeck, J; McMillan, K; McDonald, R (2007) 'Software for calculating blood lactate endurance markers'. Journal Of Sports Sciences, [Details]
|(2006)|| 'Rearrangement inequalities and the alternahedron'
Cruickshank, J,Kelly, S (2006) 'Rearrangement inequalities and the alternahedron'. Discrete & Computational Geometry, 35 :241-254 [DOI] [Details]
|(2003)|| 'Twisted homotopy theory and the geometric equivariant l-stem'
Cruickshank, J (2003) 'Twisted homotopy theory and the geometric equivariant l-stem'. Topology And Its Applications, 129 :251-271 [DOI] [Details]
|(2008)|| 'Functional Equations'
James Cruickshank, Gary McGuire, Anthony G. O'Farrell, David B. Redmond, Richard O. Watson and David J. Wraith. Edited by Anthony G. O'Farrell. (2008) 'Functional Equations' In: Irish Mathematical Olympiad Manual. Maynooth, Ireland: Logic Press. [Details]
|(2005)|| Bulletin of the Irish Mathematical Society: Special edition.
James Cruickshank, Dane Flannery (Ed.). (2005) Bulletin of the Irish Mathematical Society: Special edition. Ireland: Irish Mathematical Sociey. [Details]
|(2017)|| Unitary groups and ramified extensions.
J. Cruickshank, F. Szechtman (2017) Unitary groups and ramified extensions. Electronic Publication [Details]
|(2016)|| Generators and relations for the unitary group of a skew hermitian form over a local ring.
James Cruickshank, Fernando Szechtman (2016) Generators and relations for the unitary group of a skew hermitian form over a local ring. Electronic Publication [Details]
|(2017)|| Hermitian and skew hermitian forms over local rings.
James Cruickshank, Rachel Quinlan, Fernando Szechtman (2017) Hermitian and skew hermitian forms over local rings. Electronic Publication [Details]
|Association||Function||From / To|
|Irish Mathematical Society||President||01-JAN-10 / 31-DEC-11|
|Employer||Position||From / To|
|University College Cork||Lecturer||01-SEP-98 / 31-AUG-01|
|Title||Type||From / To|
|Teaching (e.g. Service learning / comunity based learning)||Mathematical Enrichment Programme||01-JAN-02 / 15-JUN-17|
I am a member of the editorial board of the Bulletin of the Irish Mathematical Society
I am interested in the role of problem solving as a driver of learning in mathematics. Undergraduate mathematics faces special challenges in implementing a research-led approach. Due to the highly abstract and technical nature of contemporary research in many (but not all!) mathematical disciplines it can often be difficult to introduce undergrad students to open problems in contemporary mathematics. However there is a rich tradition of mathematical problem solving that can provide a bridge. Throughout my career at NUI Galway I have tried to promote student interest in problem solving contest at all levels. In particular
- The mathematical enrichment programme seeks to engage preuniversity students in extracurricular mathematics with a particular focus on preparing for so-called Olympiad contests such as the Irish Mathematical Olympiad and the International Mathematical Olympiad. I been heavily involved in the administration and teaching of this course for the last 15 years.
- The PRISM contest is also for preuniversity students and is one of the largest one day mathematical contests in Ireland with typically 4000-5000 students participating. I was one of the founders of this contest and have been responsible for maintaining and upgrading its website for the last 10 years.
E-assessment in mathematics
I am very interested in using new technologies to support learning. Mathematics is a subject that offers particular opportunity to support student learning with automated assessment technologies. In recent years, several new developments contributed to an rapid growth in the area of mathematical e-assessment. In particular
- MathJax essentially solved the problem of presenting complex mathematical notation on the web
- Open source computer algebra systems such as SageMath and Maxima have advanced to a high level of sophistication - comparable to state of the art systems such as Mathematics/Maple.
- Widespread student access to the web through a variety of devices and platforms
- Web development in general has changed dramatically in the last decade. The latest web development frameworks have made it much easier to develop sophisticated/responsive applications without requiring a large team of developers
I have used this system successfully in the last two academic years, both for large group teaching to first year service courses and for more specialised courses in actuarial mathematics for third year students. I plan to roll out the system to several other courses in the 2017-18 academic year.
for a talk that I gave about this system at the E-Assessment in Mathematical Sciences conference at Newcastle University in September 2016.
Recent Postgraduate Students
Current Postgraduate Students (Research)
|Qays Shakir||Doctorate - Structured PhD (Science)||Supervisor|
|Christine Marshall||Doctorate - Structured Ph.D (Engineering)||Co-supervisor (1)|
|Term/Year||Module Title||Module Code||Subject / Desc|
|I/2016||Advanced Calculus and Computer Packages||MA3301|
|I/2016||Analysis and Algebra 1||MA133|
|I/2016||Linear Algebra I and Computer Packages||MA3313|
|I/2016||Annuities and Life Assurance||MA311|
|Name||Description of Collaboration|
Random geometric graphs in evolutionary game theory
|Name||Organisation / Institute||Country||Description of Collaboration|
|Derek Kitson||Lancaster University||UNITED KINGDOM||
Geometric rigidity theory
|Steve Power||Lancaster University||UNITED KINGDOM||
Geometric rigidity theory
|Fernando Szechtman||University of Regina||CANADA||
Linear and multilinear algebra over local rings