Dr James Cruickshank

PhD

Contact Details

Lecturer Above The Bar
------------------------
Room ADB-1009
Áras De Brún
School of Mathematics, Statistics and Applied Mathematics

T: Ext. 3965
E: james.cruickshank@nuigalway.ie
Lecturer Above The Bar
School of Mathematics, Statistic
1009 Arus de Brun
NUI Galway

T: Ext. 3965
E: james.cruickshank@nuigalway.ie
 

Biography

I studied at UCG from 1988 to 1993 obtaining a B.Sc (Mathematics) and an M.Sc. (Mathematics). Following that I obtained my PhD from University of Alberta in 1999 under the supervision of Prof George Peschke. I have been a lecturer at NUI Galway since September 2001

Research Interests

Geometric Rigidity Theory
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)

Research Projects

  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

  Year Publication
(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]

Book Chapters

  Year Publication
(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]

Edited Books

  Year Publication
(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]

Electronic Publication

  Year Publication
(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]

Professional Associations

  Association Function From / To
Irish Mathematical Society President 01-JAN-10 / 31-DEC-11

Employment

  Employer Position From / To
University College Cork Lecturer 01-SEP-98 / 31-AUG-01

Community Engagement

  Title Type From / To
Teaching (e.g. Service learning / comunity based learning) Mathematical Enrichment Programme 01-JAN-02 / 15-JUN-17

Other Activities

  Description

I am a member of the editorial board of the Bulletin of the Irish Mathematical Society

Teaching Interests

Problem Solving in Mathematics
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 developed an online e-assessment system for mathematics called Ubbr. This exploits the power of SageMath and Django to provide an easy methid of creating web assessments for all levels of undergraduate mathematics. It is, to my knowledge, the first such system to be based on SageMath, which is the leading open source computer algebra system. Because of this it allows the user to easily create problems in topics such as abstract algebra/graph theory/set theory that have not traditionally been adressed by other e-assessment systems. 

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. 

See https://eams.ncl.ac.uk/session/ubbr-a-python-sagemath-package-for-mathematical-e-assessment/
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

  Graduation Name Degree Primary Supervisor
2010 Jonathan McLaughlin PhD Y
2014 Christine Marshall Msc
2009 Seamus Kelly PhD

Current Postgraduate Students (Research)

  Student Degree Type Type
Qays Shakir Doctorate - Structured PhD (Science) Supervisor
Christine Marshall Doctorate - Structured Ph.D (Engineering) Co-supervisor (1)

Modules Taught

  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

Internal Collaborators

  Name Description of Collaboration
Colm O'Riordan
Random geometric graphs in evolutionary game theory
Rachel Quinlan
Linear algebra

External Collaborators

  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