Dr JudyAnne Osborn
Lecturer
School of Mathematical and Physical Sciences (Mathematics)
 Email:judyanne.osborn@newcastle.edu.au
 Phone:02 4921 5543
Career Summary
Biography
As a researcher, I am interested in structural and existence problems in applied and pure combinatorics and in mathematics education. Some of my mathematics research work arises out of statistical physics, in which I apply methods from enumerative combinatorics to gain insight into the behaviour of polymers such as DNA. In design theory I am working on understanding the structure of maximal determinant matrices, which have applicability to codes, signal processing and statistical designs. In mathematics education I am interested in the conditions that generate resilience in students engaging in mathematics, and how to effectively engage students with diverse backgrounds, interests and needs. I am also interested in visualisation of mathematics, and in enabling the general public to access and appreciate mathematics.
My own mathematics education commenced with great teachers in school. I then went to Melbourne University where I did a Bachelor of Science, Honours, with a major in mathematics, followed by a PhD in mathematics. I then went to the ANU as a postdoctoral fellow. I completed a Graduate Certificate in Higher Education at ANU. I then came to the University of Newcastle as a postdoctoral fellow in the CARMA research Centre. I commenced a continuing position as lecturer at Newcastle in 2013.
Qualifications
 PhD, University of Melbourne
 Bachelor of Science (Honours)(Mathematics), University of Melbourne
 Graduate Certificate of Higher Education, Australian National University
Keywords
 Combinatorics
 Mathematics Education
Fields of Research
Code  Description  Percentage 

080299  Computation Theory and Mathematics not elsewhere classified  100 
Professional Experience
UON Appointment
Title  Organisation / Department 

Lecturer  University of Newcastle School of Mathematical and Physical Sciences Australia 
Publications
For publications that are currently unpublished or inpress, details are shown in italics.
Chapter (1 outputs)
Year  Citation  Altmetrics  Link  

2014 
Osborn JH, Badham J, 'Zombies in the City: a Netlogo Model', Mathematical Modelling of Zombies, University of Ottawa Press, Canada (2014)

Journal article (13 outputs)
Year  Citation  Altmetrics  Link  

2016 
Brent RP, Osborn JAH, Smith WD, 'Probabilistic lower bounds on maximal determinants of binary matrices', Australasian Journal of Combinatorics, 66 350364 (2016) [C1] Â© 2016, University of Queensland. All rights reserved. Let D(n) be the maximal determinant for n Ã n {Â±1}matrices, and R(n) = D(n)/n n/2 be the ratio of D(n) to the Hadamard u... [more] Â© 2016, University of Queensland. All rights reserved. Let D(n) be the maximal determinant for n Ã n {Â±1}matrices, and R(n) = D(n)/n n/2 be the ratio of D(n) to the Hadamard upper bound. Using the probabilistic method, we prove new lower bounds on D(n) and R(n) in terms of d = n  h, where h is the order of a Hadamard matrix and h is maximal subject to h = n. For example, (Formula Presented) By a recent result of Livinskyi, d 2 /h 1/2 Â¿ 0 as n Â¿ 8, so the second bound is close to (pe/2) d/2 for large n. Previous lower bounds tended to zero as nÂ¿8with d fixed, except in the cases d Â¿ {0, 1}. For d = 2, our bounds are better for all sufficiently large n. If the Hadamard conjecture is true, then d = 3, so the first bound above shows that R(n) is bounded below by a positive constant (pe/2) 3/2 > 0.1133.


2016 
Brent RP, Ohtsuka H, Osborn JAH, Prodinger H, 'Some binomial sums involving absolute values', Journal of Integer Sequences, 19 (2016) [C1] Â© 2016, University of Waterloo. All Right Reserved. We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, ... [more] Â© 2016, University of Waterloo. All Right Reserved. We consider several families of binomial sum identities whose definition involves the absolute value function. In particular, we consider centered double sums of the form (formula presented) obtaining new results in the cases a = 1, 2. We show that there is a close connection between these double sums in the case a = 1 and the single centered binomial sums considered by Tuenter.


2015 
Brent RP, Osborn JAH, Smith WD, 'Note on best possible bounds for determinants of matrices close to the identity matrix', LINEAR ALGEBRA AND ITS APPLICATIONS, 466 2126 (2015) [C1]


2015 
PrietoRodriguez E, Howley P, Holmes K, Osborn J, Roberts M, Kepert A, 'Quality Teaching Rounds in Mathematics Teacher Education', Mathematics Teacher Education and Development (MTED), 17 98110 (2015) [C1]


2013 
Brent RP, Osborn JAH, 'On minors of maximal determinant matrices', Journal of Integer Sequences, 16 (2013) [C1]


2013 
Brent RP, Osborn JAH, 'Bounds on minors of binary matrices', Bulletin of the Australian Mathematical Society, 88 280285 (2013) [C1] Abstract We prove an upper bound on sums of squares of minors of {+1, 1\}matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin [' (1,1)m... [more] Abstract We prove an upper bound on sums of squares of minors of {+1, 1\}matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin [' (1,1)matrices with nearextremal properties', SIAM J. Discrete Math. 23(2009), 14221440], but our proof is simpler. We give several corollaries relevant to minors of H adamard matrices. Copyright Â© 2012 Australian Mathematical Publishing Association Inc.


2013 
Brent RP, Osborn JAH, 'General lower bounds on maximal determinants of binary matrices', ELECTRONIC JOURNAL OF COMBINATORICS, 20 (2013) [C1]


2012 
Borwein JM, Osborn JAH, 'Response to 'Experimental Approaches to Theoretical Thinking: Artefacts and Proofs Proof and Proving in Mathematics Education'', Proof and Proving in Mathematics Education: The 19th ICMI Study, 15 138143 (2012) [C3]


2011 
Borwein JM, Osborn JAH, 'Loving and Hating Mathematics by Reuben Hersh and Vera JohnSteiner [Book Review]', The Mathematical Intelligencer, 33 6369 (2011) [C3]


2010 
Osborn J, Prellberg T, 'Forcing adsorption of a tethered polymer by pulling', Journal of Statistical Mechanics: Theory and Experiment, 2010 (2010) We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fix... [more] We present an analysis of a partially directed walk model of a polymer which at one end is tethered to a sticky surface and at the other end is subjected to a pulling force at fixed angle away from the point of tethering. Using the kernel method, we derive the full generating function for this model in two and three dimensions and obtain the respective phase diagrams. We observe adsorbed and desorbed phases with a thermodynamic phase transition in between. In the absence of a pulling force this model has a secondorder thermal desorption transition which merely gets shifted by the presence of a lateral pulling force. On the other hand, if the pulling force contains a nonzero vertical component this transition becomes first order. Strikingly, we find that, if the angle between the pulling force and the surface is below a critical value, a sufficiently strong force will induce polymer adsorption, no matter how large the temperature of the system. Our findings are similar in two and three dimensions, an additional feature in three dimensions being the occurrence of a reentrance transition at constant pulling force for low temperature, which has been observed previously for this model in the presence of pure vertical pulling. Interestingly, the reentrance phenomenon vanishes under certain pulling angles, with details depending on how the threedimensional polymer is modeled. Â© 2010 IOP Publishing Ltd and SISSA.


2009 
Brak R, Osborn J, 'Chebyshev type lattice path weight polynomials by a constant term method', Journal of Physics A: Mathematical and Theoretical, 42 (2009) We prove a constant term theorem which is useful for finding weight polynomials for Ballot/Motzkin paths in a strip with a fixed number of arbitrary 'decorated' weights ... [more] We prove a constant term theorem which is useful for finding weight polynomials for Ballot/Motzkin paths in a strip with a fixed number of arbitrary 'decorated' weights as well as an arbitrary 'background' weight. Our CT theorem, like Viennot's lattice path theorem from which it is derived primarily by a change of variable lemma, is expressed in terms of orthogonal polynomials which in our applications of interest often turn out to be nonclassical. Hence, we also present an efficient method for finding explicit closedform polynomial expressions for these nonclassical orthogonal polynomials. Our method for finding the closedform polynomial expressions relies on simple combinatorial manipulations of Viennot's diagrammatic representation for orthogonal polynomials. In the course of the paper we also provide a new proof of Viennot's original orthogonal polynomial lattice path theorem. The new proof is of interest because it uses diagonalization of the transfer matrix, but gets around difficulties that have arisen in past attempts to use this approach. In particular we show how to sum over a set of implicitly defined zeros of a given orthogonal polynomial, either by using properties of residues or by using partial fractions. We conclude by applying the method to two lattice path problems important in the study of polymer physics as the models of steric stabilization and sensitized flocculation. Â© 2009 IOP Publishing Ltd.


Show 10 more journal articles 
Grants and Funding
Summary
Number of grants  1 

Total funding  $297,871 
Click on a grant title below to expand the full details for that specific grant.
20141 grants / $297,871
Inspiring Mathematics and Science in Teacher Education$297,871
Funding body: Office for Learning and Teaching
Funding body  Office for Learning and Teaching 

Project Team  Doctor JudyAnne Osborn, Associate Professor Kathryn Holmes, Doctor Elena PrietoRodriguez, Associate Professor Peter Howley, Doctor Andrew Kepert, Doctor Malcolm Roberts 
Scheme  Commissioned Strategic Projects 
Role  Lead 
Funding Start  2014 
Funding Finish  2016 
GNo  G1301449 
Type Of Funding  Aust Competitive  Commonwealth 
Category  1CS 
UON  Y 
Research Supervision
Number of supervisions
Total current UON EFTSL
Current Supervision
Commenced  Level of Study  Research Title  Program  Supervisor Type 

2015  Masters  Average and Extremal Properties of Graphs with Restricted Cycle Structure  M Philosophy (Mathematics), Faculty of Science, The University of Newcastle  Principal Supervisor 
2014  PhD  Teaching and Learning in Tertiary Algebra  PhD (Mathematics), Faculty of Science, The University of Newcastle  CoSupervisor 
News
Tipping the balance towards humanity in World War Z
June 20, 2013
Dr JudyAnne Osborn
Position
Lecturer
CARMA
School of Mathematical and Physical Sciences
Faculty of Science
Focus area
Mathematics
Contact Details
judyanne.osborn@newcastle.edu.au  
Phone  02 4921 5543 
Mobile   
Fax  02 4921 6898 
Office
Room  V228 

Building  V  Mathematics Building 
Location  Callaghan University Drive Callaghan, NSW 2308 Australia 