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Enabling personalised learning through formative and summative assessment (2009)
Book Chapter
Gordon, N. A. (2009). Enabling personalised learning through formative and summative assessment. Technology-Supported Environments for Personalized Learning: Methods and Case Studies (268-284). Information Science Publishing. https://doi.org/10.4018/978-1-60566-884-0.ch015

This chapter considers some ways in which personalised learning can potentially be delivered by means of appropriate assessment and the use of associated technologies. Recognising that for many students, learning is driven by summative assessment, th... Read More about Enabling personalised learning through formative and summative assessment.

The cubic Segre variety in PG(5,2) (2008)
Journal Article
Shaw, R., & Gordon, N. A. (2009). The cubic Segre variety in PG(5,2). Designs, codes, and cryptography, 51(2), 141-156. https://doi.org/10.1007/s10623-008-9250-2

The Segre variety S 1,2 in PG(5, 2) is a 21-set of points which is shown to have a cubic equation Q(x) = 0. If T(x, y, z) denotes the alternating trilinear form obtained by completely polarizing the cubic polynomial Q, then the associate U # of an r-... Read More about The cubic Segre variety in PG(5,2).

The polynomial degree of the Grassmannian G1,n,2 (2006)
Journal Article
Shaw, R., & Gordon, N. A. (2006). The polynomial degree of the Grassmannian G1,n,2. Designs, codes, and cryptography, 39(2), 289-306. https://doi.org/10.1007/s10623-005-4524-4

For a subset ψ of PG(N, 2) a known result states that ψ has polynomial degree ≤ r, r ≤ N, if and only if ψ intersects every r-flat of PG(N, 2) in an odd number of points. Certain refinements of this result are considered, and are then applied in the... Read More about The polynomial degree of the Grassmannian G1,n,2.

Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2 (2005)
Journal Article
Shaw, R., Gordon, N. A., & Maks, J. G. (2005). Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2. Discrete Mathematics, 301(1), 137-146. https://doi.org/10.1016/j.disc.2004.11.023

We consider the following 'even hyperplane construction'of flats in the projective space PG(9, 2) = P(boolean AND(2) V(5, 2)) which are external to the Grassmannian G(1,4,2) of lines of PG(4,2). Let the Grassmann image in G(1,4,2) of a partial spread... Read More about Partial spreads in PG(4,2) and flats in PG(9,2) external to the Grassmannian G1,4,2.

The classification of flats in PG (9, 2) which are external to the grassmannian script G sign1,4,2 (2005)
Journal Article
Shaw, R., Maks, J. G., & Gordon, N. A. (2005). The classification of flats in PG (9, 2) which are external to the grassmannian script G sign1,4,2. Designs, codes, and cryptography, 34(2-3), 203-227. https://doi.org/10.1007/s10623-004-4855-6

Constructions are given of different kinds of flats in the projective space$$PG(9,2)={\mathbb P}(\wedge^{2}V(5,2))$$which are external to the Grassmannian$${\cal G}_{\bf 1,4,2}$$of lines ofPG(4,2). In particular it is shown that there exist precisely... Read More about The classification of flats in PG (9, 2) which are external to the grassmannian script G sign1,4,2.

Aspects of the linear groups GL(n,2) (2005)
Journal Article
Gordon, N. A., Jarvisy, T. M., & Shawy, R. (2005). Aspects of the linear groups GL(n,2). Journal of combinatorial mathematics and combinatorial computing, 53, 13 - 31

We provide tables which summarize various aspects of the Önite linear groups GL(n; 2); n < 7; in their action upon the vector space Vn = V (n; 2) and upon the associated projective space PG(n 1; 2): It is intended that the tabulated results should be... Read More about Aspects of the linear groups GL(n,2).

Experiences of embedding Information Technology into discipline based teaching (2005)
Journal Article
Gordon, N. (2005). Experiences of embedding Information Technology into discipline based teaching. Innovation in teaching and learning in information and computer sciences, 4(1), 1-9. https://doi.org/10.11120/ital.2005.04010002

In this paper we will reflect upon some of the experiences that the author had whilst supporting the embedding of Information Technology (I.T.) into a U.K. mathematics department’s undergraduate teaching. The paper includes some examples of the kinds... Read More about Experiences of embedding Information Technology into discipline based teaching.

The quintic Grassmannian g(1,4,2) in PG(9,2) (2004)
Journal Article
Shaw, R., & Gordon, N. (2004). The quintic Grassmannian g(1,4,2) in PG(9,2). Designs, codes, and cryptography, 32(1-3), 381 - 396. https://doi.org/10.1023/B%3ADESI.0000029236.10701.61

The 155 points of the Grassmannian g(1,4,2) of lines of PG(4,2) = PV(5,2) are those points x is an element of PG(9,2) = P(boolean AND V-2(5,2)) which satisfy a certain quintic equation Q(x) = 0. (The quintic polynomial Q is given explicitly in Shaw a... Read More about The quintic Grassmannian g(1,4,2) in PG(9,2).

Wither mathematics, whither science? (2004)
Journal Article
Gordon, N. (2004). Wither mathematics, whither science?. Teaching mathematics and its applications / the Institute of Mathematics and Its Applications, 23(1), 15-32. https://doi.org/10.1093/teamat/23.1.15

This paper gives an overview of some of the problems facing the higher education mathematics community, and some examples of methods that departments of mathematics and related disciplines can use to try to deal with the problems. This is relevant to... Read More about Wither mathematics, whither science?.

Numerical computation and analysis of the Titchmarsh-Weyl mα(λ)  function for some simple potentials (1999)
Journal Article
Witwit, M. R. M., Gordon, N. A., & Killingbeck, J. (1999). Numerical computation and analysis of the Titchmarsh-Weyl mα(λ)  function for some simple potentials. Journal of Computational and Applied Mathematics, 106(1), 131-143. https://doi.org/10.1016/S0377-0427%2899%2900061-8

This article is concerned with the Titchmarsh-Weyl mα(λ) function for the differential equation d2y/dx2+[-q(x)]y=0. The test potential q(x)=x2, for which the relevant mα(λ) functions are meromorphic, having simple poles at the points =4k+1 and =4k+3,... Read More about Numerical computation and analysis of the Titchmarsh-Weyl mα(λ)  function for some simple potentials.

Point transfer matrices for the Schrödinger equation: The algebraic theory (1999)
Journal Article
Gordon, N. A., & Pearson, D. B. (1999). Point transfer matrices for the Schrödinger equation: The algebraic theory. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 129(4), 717-732. https://doi.org/10.1017/S030821050001310X

This paper deals with the theory of point interactions for the one-dimensional Schrödinger equation. The familiar example of the δ5-potential V(x) = gδ(x - x 0 ), for which the transfer matrix across the singularity (point transfer matrix) is given b... Read More about Point transfer matrices for the Schrödinger equation: The algebraic theory.

Linear sections of GL(4, 2) (1998)
Journal Article
Gordon, N. A., Lunardon, G., & Shaw, R. (1998). Linear sections of GL(4, 2). Bulletin of the Belgian Mathematical Society, Simon Stevin, 5(2-3), 287-311. https://doi.org/10.36045/bbms/1103409012

For V = V (n; q); a linear section of GL(V ) = GL(n; q) is a vector subspace S of the n 2 -dimensional vector space End(V ) which is contained in GL(V ) [ f0g: We pose the problem, for given (n; q); of classifying the di erent kinds of maximal linear... Read More about Linear sections of GL(4, 2).

Calculations for double-well potentials of perturbed oscillator type in three-dimensional systems using the Hill-determinant approach (1998)
Journal Article
Witwit, M., & Gordon, N. (1998). Calculations for double-well potentials of perturbed oscillator type in three-dimensional systems using the Hill-determinant approach. Canadian Journal of Physics, 76(8), 609-620. https://doi.org/10.1139/cjp-76-8-609

A determination of the eigenvalues for a three-dimensional system is made by expanding the potential functionV(x,y,z;Z2, λ,β)= ?Z2[x2+y2+z2]+λ {x4+y4+z4+2β[x2y2+x2z2+y2z2]}, around its minimum. In this paper the results of extensive numerical calcula... Read More about Calculations for double-well potentials of perturbed oscillator type in three-dimensional systems using the Hill-determinant approach.

Calculating energy levels of a double-well potential in a two- dimensional system by expanding the potential function around its minimum (1997)
Journal Article
Witwit, M. R. M., & Gordon, N. A. (1997). Calculating energy levels of a double-well potential in a two- dimensional system by expanding the potential function around its minimum. Canadian Journal of Physics, 75(10), 705-714. https://doi.org/10.1139/p97-023

A determination of the eigenvalues for a three-dimensional system is made by expanding the potential functionV(x,y,z;Z2, λ,β)= ?Z2[x2+y2+z2]+λ {x4+y4+z4+2β[x2y2+x2z2+y2z2]}, around its minimum. In this paper the results of extensive numerical calcula... Read More about Calculating energy levels of a double-well potential in a two- dimensional system by expanding the potential function around its minimum.

Mathematica and finite geometry (1995)
Conference Proceeding
Gordon, N. (1995). Mathematica and finite geometry. In V. Keranen, & P. Mitic (Eds.), Mathematics With Vision: Proceedings of the First International Mathematica Symposium (159 - 166)

We describe the use of Mathematica in the investigation of some aspects of finite geometry, in particular we look at an example of finding a single polynomial function corresponding to a set of polynomial functions, and an example of finding the PGL(... Read More about Mathematica and finite geometry.

Stable forward shooting for eigenvalues and expectation values (1995)
Journal Article
Killingbeck, J. P., Gordon, N. A., & Witwit, M. R. M. (1995). Stable forward shooting for eigenvalues and expectation values. Physics Letters A, 206(5-6), 279-282. https://doi.org/10.1016/0375-9601%2895%2900632-d

Internal differentiation techniques are used to produce a simple but highly accurate forwardsshootingmethod foreigenvaluesandexpectationvaluesof the Schrödinger equation. A multi-well potential is used as a test case.

Finite Geometry and Computer Algebra, with Applications (1994)
Thesis
Gordon, N. (1994). Finite Geometry and Computer Algebra, with Applications. (Thesis). University of Hull. Retrieved from https://hull-repository.worktribe.com/output/405456

The interaction between geometry and algebra is a diverse and fruitful area to explore. Of particular interest is the area of groups and geometry. In this work we will examine various aspects of this interplay, in particular looking at geometric cano... Read More about Finite Geometry and Computer Algebra, with Applications.

Mathematica in the teaching of mathematics for computer science students in H.E.
Conference Proceeding
Gordon, N. (2006). Mathematica in the teaching of mathematics for computer science students in H.E. In Y. Papegay (Ed.), Applied Mathematica, Electronic Proceedings of the Eighth International Mathematica Symposium (IMS’06)

This paper considers the use of Mathematica in the teaching of mathematics to Computer Science students in Higher Education (H.E.). This is based on experiences in the English H.E. system, and includes examples of the kinds of illustrations and appro... Read More about Mathematica in the teaching of mathematics for computer science students in H.E..