Leanne's Publications


Refereed publications (incomplete):

!! Andrei Kelarev, Xun Yi, Shahriar Badsha, Xuechao Yang, Leanne Rylands and Jennifer Seberry. A multistage protocol for aggregated queries in distributed cloud databases with privacy protection. Future Generation Computer Systems, 90, 368-380, 2019.
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!! Jiansheng Huang, Michael Negnevitsky, Zhuhan Jiang, Leanne Rylands and Fushuan Wen. Tiered Energy Storage System for Auxiliary Service of Power Systems with Wind Farms. IJTRD, Dec, 2018.
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!! Andrei Kelarev, Joe Ryan, Leanne Rylands, Jennifer Seberry, Xun Yi. Discrete algorithms and methods for security of statistical databases related to the work of Mirka Miller. Journal of Discrete Algorithms, 52-53, 112–121, 2018.
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!! Leanne Rylands and Don Shearman. Mathematics learning support and engagement in first year engineering. iJMEST, 49(8), 1133–1147, 2018. The paper
Abstract: This paper considers the effects of both free optional mathematics learning support and engagement on the mathematics performance in a foundation mathematics subject of a cohort of engineering students entering university with poor mathematical skills. New engineering students were directed to either a foundation or standard mathematics subject based on the results of a placement test. For students in the foundation subject, it was found that high levels of learning support were associated with greater improvement over the semester. Some form of learning support was used by 57.9% of the students, a reasonably high proportion of the cohort. Some factors for this high level of use of learning support are considered. One possible factor, the placement test, appears to have had a positive effect. Engagement in the subject activities as measured by tutorial attendance and learning management system use was found to have a positive association with final mark. Students who utilized a high level of learning support were more likely to be more engaged with the subject, making it impossible to draw conclusions about improvements being solely due to the use of learning support.

!! Geiger, Mulligan, Date-Huxtable, Ahlip, Jones, May, Rylands and Wright. An interdisciplinary approach to designing online learning: Fostering pre-service mathematics teachers’ capabilities in mathematical modelling. ZDM, 50(1), 217–232, 2018.
Abstract: In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service secondary mathematics teachers. Development of the module was underpinned by Bybee’s five E’s enquiry-based approach and Goos et al.’s twenty-first century numeracy model. Module evaluation data is examined in relation to the quality of pre-service teachers’ learning experiences and interview data from the study is analysed through the lens of ‘boundary crossing’. While the evaluation of the module was generally positive, aspects that required improvement were also identified including more meaningful inclusion of pre-service teachers and other stakeholders in the development process.

!! Jiansheng Huang, Zhuhan Jiang, Leanne Rylands and Michael Negnevitsky. SVM-Based PQ Disturbance Recognition System. IET Generation, Transmission & Distribution. 12(2):328–334, 2018.
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!! Andrei V. Kelarev, Xun Yi, Hui Cui, Leanne Rylands and Herbert F. Jelinek. A survey of state-of-the-art methods for securing medical databases. AIMS Medical Science, 5(1):1–22, 2018.
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!! Andrei Kelarev, Jennifer Seberry, Leanne Rylands, Xun Yi. Combinatorial Algorithms and Methods for Security of Statistical Databases Related to the Work of Mirka Miller. 28th InternationalWorkshop, IWOCA 2017, Newcastle, NSW, Australia, July 17–21, 2017. Ed Ljiljana Brankovi, Joe Ryan, William F. Smyth. LNCS 10765. p.383–394.
Abstract: This article gives a survey of combinatorial algorithms and methods for database security related to the work of Mirka Miller. The main contributions of Mirka Miller and coauthors to the security of statistical databases include the introduction of Static Audit Expert and theorems determining time complexity of its combinatorial algorithms, a polynomial time algorithm for deciding whether the maximum possible usability can be achieved in statistical database with a special class of answerable statistics, NP-completeness of similar problems concerning several other types of databases, sharp upper bounds on the number of compromise-free queries in certain categories of statistical databases, and analogous results on applications of Static Audit Expert for the prevention of relative compromise.

!! Jiansheng Huang, Zhuhan Jiang and Leanne Rylands. Aggregate power demand model and parameter identification for voltage stability enhancement. Universal Journal of Electrical and Electronic Engineering, 4(2):57–66, 2016.
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!! Vince Geiger, Liz Date-Huxtable, Rehez Ahlip, Marie Herberstein, D. Heath Jones, Julian May, Leanne Rylands, Ian Wright and Joanne Mulligan. Designing Online Learning for Developing Pre-service Teachers’ Capabilities in Mathematical Modelling and Applications. 262–270, MERGA 2016.
Abstract: The purpose of this paper is to describe the processes utilised to develop an online learning module within the Opening Real Science (ORS) project – Modelling the present: Predicting the future. The module was realised through an interdisciplinary collaboration, among mathematicians, scientists and mathematics and science educators that drew on the enquirybased approach underpinning ORS as well as structuring devices and working practices that emerged during the course of the module development. The paper is a precursor to further research that will investigate the effectiveness of the module in terms of students’ learning and attitudes as well as the module development team members’ perspectives on the interdisciplinary collaboration that took place.

!! Leanne Rylands and Don Shearman. K. Matthews, S. Belward, C. Coady, L.J. Rylands and V. Simbag. Curriculum development for quantitative skills in degree programs: A cross-institutional study situated in the life sciences. Higher Education Research & Development, 35(3):545–559, 2015.
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!! Gunnar Brinkmann, Dieter Mourisse and Leanne Rylands. On the existence of nanojoins with given parameters. Journal of Mathematical Chemistry, 53(9):2078–2094, 2015.
Abstract: Nanojoins are parts of large carbon molecules joining several nanotubes with the same or different parameters and chemical and electrical properties. It is known that Euler’s formula implies that such nanojoins must contain faces that are not hexagons if at least three tubes are joined. As the atoms in a nanojoin are carbon atoms preferring hexagonal rings, it is normally assumed that apart from hexagons only pentagons and heptagons occur. In this paper we will give necessary and sufficient conditions for the existence of nanojoins joining nanotubes with given parameters and given numbers of pentagons and heptagons.

!! Leanne Rylands and Don Shearman. Huang, J., Jiang, Z. and Rylands, L. Aggregate power demand modelling for voltage stability enhancement, International Symposium on Electrical, Electronic Engineering and Digital Technology, pp 367–378, 2015.
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!! Leanne Rylands and Don Shearman. Supporting engagement or engaging support? IJISME, 23(1):64-73, 2015.
Abstract: The need for learning support in first year mathematics subjects in universities in Australia is increasing as student diversity increases. In this paper we study the use of learning support in a first year mathematics subject for which there is no assumed mathematics knowledge. Many students in this subject have a poor mathematics background, noticeably worse than five years previously. The interplay between learning support and engagement is found to be significant and the use of support can be used as a measure of engagement. The success of support is tied up with the success of engagement, making it difficult to measure the success of learning support. However student outcomes appear to be substantially improved through both mechanisms. We also highlight some concerns and consequences of the declining level of mathematics preparation of incoming students.

!! M. Miller, O. Phanalasy, J. Ryan and L.J. Rylands. A note on antimagic labelings of trees. Bull. Inst. Combin. Appl., 72:94-100, 2014.
Abstract: In 1990, Hartsfield and Ringel conjectured ``Every tree except \(K_2\) is antimagic'', where antimagic means that there is a bijection from \(E(G)\) to \(\{1,2,\dots,|E(G)|\}\) such that at each vertex the weight (sum of the labels of incident edges) is different. We call such a labeling a vertex antimagic edge labeling. As a step towards proving this conjecture, we provide a method whereby, given any degree sequence pertaining to a tree, we can construct an antimagic tree based on this sequence. Furthermore, swapping the roles of edges and vertices with respect to a labeling, we provide a method to construct an edge antimagic vertex labeling for any tree and we consider edge antimagic vertex labeling of graphs in general.

!! I. Roberts, L. Rylands and M. Gr\"uttm\"uller. Antichains and completely separating systems---a catalogue and applications. Discrete Applied Mathematics, 163:165-180, 2014.
Abstract: This paper extends known results on the existence, number and structure of antichains and completely separating systems. Both these structures are classified in several ways, and both an enumeration and listing of each type of object are given in a catalogue, which is described in detail in this paper. The antichain catalogue provides a complete listing of all non-isomorphic antichains on m points for \(m \le 7\).

!! L. Rylands, O. Phanalasy, J. Ryan and M. Miller. An application of completely separating systems to graph labeling. In Combinatorial Algorithms: 24th International Workshop, IWOCA 2013, LNCS 8288, pages 376–387, 2013.
Abstract: In this paper a known algorithm used for the construction of completely separating systems (CSSs), Roberts’ Construction, is modified and used in a variety of ways to build CSSs. The main interest is in CSSs with different block sizes. A connection between CSSs and vertex antimagic edge labeled graphs is then exploited to prove that various non-regular graphs are antimagic. An outline for an algorithm which produces some of these non-regular graphs together with a vertex antimagic edge labeling is presented.

!! Leanne Rylands, Vilma Simbag, Kelly E. Matthews, Carmel Coady and Shaun Belward. Scientists and mathematicians collaborating to build quantitative skills in undergraduate science. International Journal of Mathematical Education in Science and Technology. 44:6, 834-845, 2013.
Abstract: There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better QS than at any time in the past. Ways in which mathematics and science academics are working together to build the QS of their undergraduate science students, together with the mathematics and statistics needed or desired in a science degree, are reported on in this paper. The emphasis is on the life sciences. Forty-eight academics from eleven Australian and two USA universities were interviewed about QS in science. Information is presented on: what QS academics want in their undergraduate science students; who is teaching QS; how mathematics and science departments work together to build QS in science and implications for building the QS of science students. This information leads to suggestions for improvement in QS within a science curriculum.

!! L.J. Rylands. Mathematics and ocean swimming. In Proceedings of Lighthouse Delta 2013. In Proceedings of Lighthouse Delta 2013.
Abstract: Mathematics is often taught in first year as a service subject. It is important that mathematics academics provide a good service to those whose students they teach. The income of many mathematics groups in universities in Australia largely depends on this teaching. At times mathematics academics are seen as not succeeding in this teaching and are blamed for the lack of skills of the students taught, or blamed for not being able to pass more students. It is claimed here that mathematicians are often given a very difficult task, that learning mathematics has some aspects of what has been called “complex learning” and that some mathematics students are involuntary learners. It is up to mathematicians to educate those whom we serve about the challenges faced and about what is realistic for their students. An analogy which might assist in this is presented.

!! Deborah King, Birgit Loch, and Leanne Rylands. Perceptions of feedback in mathematics—results from a preliminary investigation at three Australian universities. In Proceedings of Lighthouse Delta 2013.

!! M.Miller, O. Phanalasy, J.Ryan and L.Rylands. Sparse graphs with vertex antimagic edge labelings. AKCE 193-198, 2013.

!! Leon Poladian and Leanne Rylands. Thinking deeply of simple things: 45 years of the National Mathematics Summer School. AAMT, 142-148, 2013.
Abstract: The purpose of this paper is to better inform the mathematics community about the ANU-AAMT National Mathematics Summer School. This two week residential program is for the discovery and development of mathematically gifted and talented students. It takes about 64 mathematics students who have one year of high school to go and about a dozen students who have just completed high school from all over Australia. We present the summer school goals, how we attempt to achieve them and why we believe that we are successful.

!! Jiansheng Huang, Zhuhan Jiang, Leanne Rylands and auMichael Negnevitsky. Power quality disturbance recognition employing state vector machine methods. IASTED, 22-28, 2013.
Abstract: This paper presents a power quality disturbance recognition system employing support vector machine (SVM) techniques. Based on site measurements, a waveform generator is designed to emulate different power quality disturbances existing in modern power distribution systems. Digital wavelet transform (DWT) is then applied to the sampled waveforms for feature extraction. Thereby obtained DWT coefficients are further exploited to identify the associated disturbances through constructing an SVM classifier for each type of waveforms. Simulation results demonstrate that the SVM based classifiers can achieve significantly higher recognition rates compared with conventional methods.

!! Donald Shearman, Leanne Rylands and Carmel Coady. Improving student engagement in mathematics using simple but effective methods. AARE-APERA, 1-8, 2013.
Abstract: A significant proportion of students enrolling in mathematical subjects designed for non-STEM majors in university courses have minimal mathematical skills and poor motivation. This combination of starting attributes often leads to failure in the first mathematical subject encountered. We have been implementing simple, alternative pedagogies in an attempt to improve student performance in one such first-year subject.
The failure rate in this first-year algebra-based mathematics compulsory service subject in a non-STEM discipline has been consistently high, despite many supportive resources being available. Anecdotal evidence suggested that it was students’ lack of engagement with all aspects of the subject that accounted for the lack of use of these support mechanisms.
Last year, a major change to teaching practice was introduced. Workshops have replaced tutorials with the tutor becoming a facilitator. Problems given are graded in difficulty, allowing students to work at their level. Students’ expectations were also discussed and compared to the results of previous cohorts. Different strategies were then put in place with the aim of motivating students to engage with the subject.
In this study, results indicating an improvement in student engagement were based on comparing tutorial attendance rates, performance in assessment items and attendance rates in optional support sessions over several years.

!! G. Brinkmann, S. Crevals, H M\'elot, L.J. Rylands and E. Steffan. \(\alpha\)-labelings and the structure of trees with nonzero \(\alpha\)-deficit. Discrete Mathematics & Theoretical Computer Science, 14(1):159-174, 2012.
Abstract: We present theoretical and computational results on \(\alpha\)-labelings of trees. The theorems proved in this paper were inspired by the results of a computer investigation of \(\alpha\)-labelings of all trees with up to 26 vertices, all trees with maximum degree 3 and up to 36 vertices, all trees with maximum degree 4 and up to 32 vertices and all trees with maximum degree 5 and up to 31 vertices. We generalise a criterion for trees to have nonzero \(\alpha\)-deficit, and prove an unexpected result on the \(\alpha\)-deficit of trees with a vertex of large degree compared to the order of the tree.

!! M. Miller, O. Phanalasy, J. Ryan and L.J. Rylands. Antimagicness of some families of generalized graphs. Australas. J. Combin., 53:179-189, 2012.
Abstract: An edge labeling of a graph \(G=(V,E)\) is a bijection from the set of edges to the set of integers \(\{1, 2, ..., |E|\}\). The weight of a vertex \(v\) is the sum of the labels of all the edges incident with \(v\). If the vertex weights are all distinct then we say that the labeling is vertex-antimagic, or simply, antimagic. A graph that admits an antimagic labeling is called an antimagic graph.
In this paper, we present a new general method of constructing families of graphs with antimagic labelings. In particular, our method allows us to prove that generalized web graphs and generalized flower graphs are antimagic.

!! S.R. Belward, K.E. Matthews, K. Thompson, N. Palaez, C. Coady, P. Adams, V. Simbag, and L. Rylands. Applying mathematical thinking: the role of mathematicians and scientists in equipping the new generation scientist. In Proceedings of Volcanic Delta 2011, 2011.
Abstract: The ability to make effective use of mathematical and statistical thinking and reasoning within context is an essential skill for graduating science students. The challenge for educators in higher education is to determine how best to foster the development of these skills. Many argue this challenge is becoming greater, given the increasingly diverse student body (often with weaker mathematics backgrounds) and the increasing use of modelling and data in modern science (meaning that the need to be able to apply mathematical and statistical thinking and reasoning is increasing). This paper discusses the implementation of initiatives within four institutions (University of Queensland, James Cook University, University of Maryland and Purdue University) that address these needs. In addition to describing the initiative itself, the change process is described. Therefore each initiative is examined through a framework based on: the need for the change, vision for the change, implementation of the change and evaluation of the change. In particular we explore the role of mathematicians and statisticians in these processes.

!! Leanne Rylands, Kelly E. Matthews, Vilma Simbag, Shaun Belward, Peter Adams, and Carmel Coady. Building quantitative skills of undergraduate science students: exploring the educational resources. In M. Sharma, A. Yeung, T. Jenkins, E. Johnson, G. Rayner, and J. West, editors, Proceedings of the Australian Conference on Science and Mathematics Education 2011, pages 145-150, 2011.
Abstract: Science and mathematics are inherently interwoven, although they are often considered as separate entities for educational purposes. Consequently, teaching and learning in these fields is dominated by discipline perspectives without explicit mention of the need for knowledge of the symbiotic relationship between them. Not only do students entering science programs in higher education need a base level of mathematical knowledge, they are expected to apply this knowledge in scientific contexts, utilising their quantitative skills (QS). Many higher education science curricula reform efforts are responding to the increasing mathematical diversity of students, although they struggle to build QS of all students to an appropriate threshold prior to graduation. This paper aims to discuss educational resources that attempt to build the QS of science graduates. Data from interviews across nine Australian universities reveals a range of resources developed and delivered by mathematics departments and science departments usually in isolation from each other, but with some instances of cross-disciplinary resource development. Implications for the ongoing divide between mathematics departments and science departments, and the tension between teaching mathematical knowledge and the need for that knowledge to be applied in science, are discussed along with areas where further research could benefit the sector.

!! S. Belward, K. Matthews, L.J. Rylands, C. Coady, P. Adams, and V. Simbag. A study of the Australian tertiary sector's portrayed view of the relevance of quantitative skills in science. In J. Clark, B. Kissane, J. Mousley, T. Spencer and S. Thornton, editors, Mathematics: Traditions and (New) Practices, pages 107-114, 2011.
Abstract: The ability to apply mathematical and statistical thinking within context is an essential skill for graduate competence in science. However, many students entering the tertiary sector demonstrate ambivalence toward mathematics. The challenge, then, is to determine how science curricula should evolve in order to illustrate the integrated nature of modern science and mathematics. This study uses a document analysis to examine degree structures within science programs at a selection of Australian tertiary institutions. Of particular interest are the signals these degree structures send in terms of the relevance of the study of mathematics prior to entry to university and the quantitative content within.

!! L.J. Rylands, O. Phanalasy, J. Ryan and M. Miller. Construction for antimagic generalized web graphs. AKCE Int. J. Graphs Comb., 8(2):141-149, 2011.
Abstract: An antimagic labeling of a graph with \(q\) edges is a bijection from the set of edges to the set of integers \(\{1, 2, ..., q\}\) such that all vertex weights are pairwise distinct, where the vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling.
Let \([n]=\{1, 2, ..., n\}\). A completely separating system on \([n]\) is a collection \(\mathcal C\) of subsets of \([n]\) in which, for each pair \(a\neq b\in [n]\), there exist \(A, B\in\mathcal C\) such that \(a\in A\), \(b\notin A\) and \(b\in B\), \(a\notin B\).
Recently, a relationship between completely separating systems and labeling of graphs has been shown to exist. Based on this relationship, antimagic labelings of various graphs have been constructed. In this paper, we extend our method to produce more general results for generalized web graphs.

!! J. Ryan, O. Phanalasy, M. Miller and L.J. Rylands. On Antimagic Labeling for Generalized Web and Flower Graphs. In Proceedings of IWOCA 2010, LNCS 6460, pages 303-313, 2011.
Abstract: An antimagic labeling of a graph with \(p\) vertices and \(q\) edges is a bijection from the set of edges to the set of integers \(\{1,2,...,q\}\) such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling.
Completely separating systems arose from certain problems in information theory and coding theory. Recently these systems have been shown to be useful in constructing antimagic labelings of particular graphs.

!! O. Phanalasy, M. Miller, L.J. Rylands and P. Lieby. On a relationship between completely separating systems and antimagic labeling of regular graphs. In Proceedings of IWOCA 2010, LNCS 6460, pages 238-241, 2011.
Abstract: A completely separating system (CSS) on \([n]\) is a collection \(\mathcal C\) of subsets of \([n]\) in which for each pair \(a\neq b\in [n]\), there exist \(A, B\in\mathcal C\) such that \(a\in A\), \(b\notin A\) and \(b\in B\), \(a\notin B\).
An antimagic labeling of a graph with \(p\) vertices and \(q\) edges is a bijection from the set of edges to the set of integers \(\{1, 2, ..., q\}\) such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling.
In this paper we show that there is a relationship between CSSs on a finite set and antimagic labeling of graphs. Using this relationship we prove the antimagicness of various families of regular graphs.

!! I. Roberts, L.J. Rylands, T. Montag and M. Grüttmüller. On the number of minimal completely separating systems and antichains in a Boolean lattice. Australas. J. Combin., 48:143-158, 2010.
Abstract: An {\bfseries \((n)\)completely separating system \(\mathcal C\)} (\((n)\)CSS) is a collection of blocks of \([n] = \{1, \ldots , n\}\) such that for all distinct \(a,b \in [n]\) there are blocks \(A,B \in \mathcal C\) with \(a \in A\setminus B\) and \(b \in B\setminus A\). An \((n)\)CSS is minimal if it contains the minimum possible number of blocks for a CSS on \([n]\). The number of non-isomorphic minimal \((n)\)CSSs is determined for \(11 \leq n \leq35\). This also provides an enumeration of a natural class of antichains.

!! L.J. Rylands and C. Coady. Year 13 or first-year university - a holistic learning design that attempts to combine elements of secondary and tertiary learning and teaching. In Proceedings of the 2009 UniServe Science symposium, pages 112-117, Oct 2009.
Abstract: For many years, Australian universities have been accepting students into their courses, including Science, with inadequate mathematical backgrounds. In addition to this lack of mathematical preparation, students are ill-prepared for the demands of independent learning as required by university courses. Thus many students are enrolling in university courses without basic numeracy skills and furthermore, they lack the ability to cope with the requirements of self-directed learning. This results in students being totally overwhelmed by their first few weeks experience at university which can result in significant ‘drop-out’ rates. This report describes a learning design used in the delivery of a first-year mathematics unit that attempts to remediate numeracy skills and develop the independent learning skills required by the ‘traditional’ university experience.

!! O. Phanalasy, I. Roberts, and L.J. Rylands. Covering separating systems and an application to search theory. Australas. J. Combin., 45:3-14, 2009.
Abstract: A Covering Separating System on a set \(X\) is a collection of blocks in which each element of \(X\) appears at least once, and for each pair of distinct points \(a,b \in X\), there is a block containing \(a\) and not \(b\), or vice versa. An introduction to Covering Separating Systems is given, constructions are described for a class of minimal Covering Separating Systems and an application to Search Theory is presented.

!! L.J. Rylands and C. Coady. Performance of students with weak mathematics in first year mathematics and science. International Journal of Mathematical Education in Science and Technology, 40(6):741-753, 2009.
Abstract: In recent years, significant numbers of academics from the science and health disciplines at our institution have found that their students lack the appropriate ‘mathematical’ background to cope with first-year science subjects. Consequently, failure rates are on the increase in these subjects. The mathematical background of students entering university has been found to be a problem in other universities in Australia, as well as in the UK, Ireland and the US. In this report, the authors analyse data on current students’ performance and present suggestions for addressing the problems found. The performance of first-year students in four different mathematics and mathematically related subjects is compared to the level of their secondary school mathematics and performance, and to their tertiary entrance score. We conclude that a student’s secondary school mathematics background, not their tertiary entrance score, has a dramatic effect on pass rates. On the basis of our findings, a way forward is suggested.

!! C. Coady and L.J. Rylands. The use of reflective journals in a first year mathematics unit. In Proceedings of the 2008 UniServe Science symposium, pages 166-170, Oct 2008.
Abstract: For many years society at large has proudly commented that ‘maths was my worst subject at school’. This statement is then usually followed by some explanation of why this was so, for example, ‘numbers scare me’ or ‘I just freeze when doing a test’. Anecdotal evidence suggests that more and more students are entering university with this mind set and this attitude may be part of the reason why fewer students are attempting higher levels of mathematics at school. In 2008 our institution decided to introduce a new unit that was specifically designed to help students develop strategies to lessen the effects of maths anxiety and test phobia. This report details the introduction of a reflective journal as part of the assessment in a mathematics unit. Students were required to make journal entries every two weeks. These entries required students to reflect on their current examination preparation practices and to put strategies in place to lessen the effects of maths anxiety. Preliminary findings indicate that although students found this exercise helpful, it did not necessarily improve their mathematics marks. However, even if the student’s feelings towards mathematics improve, we will have gained. A positive attitude towards mathematics, by those who love it and are successful at it, as well as by those who struggle with mathematics, can only be of benefit.

!! I.T. Roberts and L.J. Rylands. Minimal \((n)\) and \((n,h,k)\) completely separating systems. Australas. J. Combin., 33:57-66, 2005.
Abstract: \(R(n)\) denotes the minimum possible size of a completely separating system C on an \(n\)-set. \(R(n, h, k)\) denotes the minimum possible size of a completely separating system C on an \(n\)-set with \(h \le |A| \le k\) for each \(A \in C\). In this paper a catalogue of non-isomorphic systems which achieve \(R(n)\) for \(n \le 10\) is given. Values of \(R(n, h, k)\) are determined for \(n \le 10\) and for \(n > k^2 / 2\).

!! I. Roberts, S. D'Arcy, K. Gilbert, L.J. Rylands and O. Phanalasy. Separating systems, Sperner systems, search theory. In J. Ryan, P. Manyem, K. Sugeng, and M. Miller, editors, Proceedings of the sixteenth Australasian workshop on combinatorial algorithms, pages 279-288, Sept 2005.
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!! R. B. Howlett, L.J. Rylands and D. E. Taylor. Matrix generators for exceptional groups of Lie type. J. Symbolic Comput., 31(4):429-445, Apr 2001.
Abstract: This paper gives a uniform method of constructing generators for matrix representations of finite groups of Lie type with particular emphasis on the exceptional groups. The algorithm constructs matrices for the action of root elements on the lowest dimension representation of an associated Lie algebra. These generators have been implemented in the computer algebra system Magma and this completes the provision of pairs of matrix generators for all finite groups of Lie type.

!! L.J. Rylands and D. E. Taylor. Constructions for octonion and exceptional Jordan algebras. Des. Codes Cryptogr., 21(1-3):191-203, Oct 2000. Special issue dedicated to Dr. Jaap Seidel on the occasion of his 80th birthday (Oisterwijk, 1999).
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!! L.J. Rylands and D.E. Taylor. Matrix generators for the orthogonal groups. J. Symbolic Comput., 25(3):351-360, Mar 1998.
Abstract: 1962 Steinberg gave pairs of generators for all finite simple groups of Lie type. In this paper, for each finite orthogonal group we provide a pair of matrices which generate its derived group: the matrices correspond to Steinberg's generators modulo the centre. These generators have been implemented in the computer algebra system MAGMA and this completes the provision of pairs of generators in MAGMA for all (perfect) finite classical groups.

!! R. Ollerton, L.J. Rylands and T. Shannon. Divide and conquer. Australian Mathematics Teacher, 52(3):30-33, 1996.
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!! R.A. Bryce and L.J. Rylands. A note on groups with noncentral norm. Glasgow Math. J., 36(1):37-43, Jan 1994.
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!! G. I. Lehrer and L.J. Rylands. The split building of a reductive group. Math. Ann., 296(4):607-624, 1993.
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!! J. Wiles, A. Bloesch and L.J. Rylands. Towards a neural network implementation of Hoffman's Lie algebra for vision. In Proceedings of the third Australian conference on neural networks, p282, Feb 1992.
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Books

!! (with Don Taylor) Cube Games, (Greenhouse Publications, Melbourne; Holt, Rinehart and Winston, New York; etc. 1981) [No. 6 on the New York Times Best Sellers list.]

!! (with Don Taylor) Mastering Rubik's Clock, (Simon & Schuster, 1988)


Non-refereed publications (incomplete):

!! Jackie Nicholas and Leanne Rylands. Mathematics support: promoting student learning and factors that may work against student learning. IMA conference 10–12 July 2017, Mathematics Education beyond 16: Pathways and Transitions. Birmingham, England.
Abstract: In Australia, learning support in mathematics has been a part of the university landscape for many years. In 1973, a ‘counsellor in mathematics’ was appointed to the Communication and Study Skills Unit at the Australian National University, and in 1984 the first dedicated ‘mathematics learning centres’ were established in two Australian universities. The Mathematics Learning Centre at the University of Sydney was established in 1984 and offers mathematics support to students who enrol at the University without the appropriate level of mathematics for their degree programs. Western Sydney University has provided some mathematics support for students for roughly 20 years. Since 2011, all mathematics support at Western Sydney University has been coordinated through the Mathematics Education Support Hub. The Mathematics Education Support Hub offers mathematics support to all students both on-campus and off-campus. In this paper, we will discuss the ways we endeavour to ensure that mathematics support at our universities promotes independent learning. We will also discuss the pressures on mathematics support that may have an adverse impact on student learning. These pressures may come from the institution and include cost cutting measures, pressures on staff teaching in mathematics support and pressures on the students themselves.

!!Jackie Nicholas, Leanne Rylands, Carmel Coady, Lyn Armstrong, Harkirat Dhindsa, Susan McGlynn, John Nicholls, Jim Pettigrew and Don Shearman. A tale of two very different Mathematics Support Centres at two very different universities. In M.A. Hersh and M. Kotecha, editors, Proceedings of the IMA International Conference on Barriers and Enablers to Learning Maths: Enhancing Learning and Teaching for All Learners, pages 1–8. Institute of Mathematics and its Applications, 2015.
Abstract: Participation in the higher levels of senior secondary school mathematics courses has fallen alarmingly in Australia over the past twenty years resulting in many students enrolling in degrees for which they are mathematically under-prepared. Students who do so are at risk of failing their university mathematics and statistics units. In this paper we discuss how student support in mathematics is provided in two large but very different universities in Sydney, Australia and the various measures we use to assess the success of the mathematics support provided.

!!Jackie Nicholas and Leanne Rylands. HSC mathematics choices and consequences for students coming to university without adequate maths preparation. Reflections, 40(1), 2015.

!! Kelly E. Matthews, Peter Adams, Shaun Belward, Carmel Coady, Leanne Rylands, Nancy Pelaez and Katerina Thompson. The end of an ALTC-OLT project: Findings point toward new projects, HERDSA News, April 2013. (Invited article for academic society newsletter.)

!! L.J. Rylands. Book review of “Handbook of Cubik Math” by Alexander H. Frey, Jr and David Singmaster. The Australian Mathematical Society Gazette, 39(5):232–234, November 2012.

!! L.J. Rylands. Book review of “Handbook of Cubik Math” by Alexander H. Frey, Jr and David Singmaster. The Asia Pacific Mathematics Newsletter, 3(1):47–48, January 2013. (Reprinted from the Aust Math Soc Gaz.)

!! Kelly E. Matthews, Shaun Belward, Carmel Coady, Leanne Rylands, and Vilma Simbag. The state of quantitative skills in undergraduate science education: Findings from an Australian study, July 2012. (Report prepared for the ACDS.)

!! Carmel Coady and Leanne Rylands. The University of Western Sydney. In Forum on preparedness for first year mathematics: Issues and strategies for dealing with diverse cohorts, IISME 15 February, 2012.

!! Rylands, L.J. Book review of "Geometric puzzle design" by Stewart Coffin. The Australian Mathematical Society Gazette, 36(2):138-140, May 2009.


Ph.D.

Last changed: 2 August, 2018.