Dr Judy-Anne Osborn

Dr Judy-Anne Osborn

Lecturer

School of Mathematical and Physical Sciences (Mathematics)

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
  • Graduate Diploma of Learning and Teaching, University of Southern Queensland

Keywords

  • Combinatorics
  • Mathematics Education

Professional Experience

UON Appointment

Title Organisation / Department
Lecturer University of Newcastle
School of Mathematical and Physical Sciences
Australia
Lecturer University of Newcastle
School of Mathematical and Physical Sciences
Australia
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Book (1 outputs)

Year Citation Altmetrics Link
2020 Bailey DH, Borwein NS, Brent RP, Burachik RS, Osborn J-AH, Sims B, Zhu QJ, From Analysis to Visualization A Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017, Springer, 439 (2020)
Co-authors Brailey Sims, Judy-Anne Osborn

Chapter (2 outputs)

Year Citation Altmetrics Link
2021 Osborn J, Prieto-Rodriguez E, Butler E, 'Shaping our Collective Identity as Mathematics Teacher Educators.', The Learning and Development of Mathematics Teacher Educators, Springer, Australia 245-262 (2021)
DOI 10.1007/978-3-030-62408-8_13
Co-authors Judy-Anne Osborn, Elena Prieto
2014 Osborn JH, Badham J, 'Zombies in the City: a Netlogo Model', Mathematical Modelling of Zombies, University of Ottawa Press, Canada (2014)
Co-authors Judy-Anne Osborn

Journal article (18 outputs)

Year Citation Altmetrics Link
2020 O Toole JM, McKoy K, Freestone M, Osborn JA, ' Scientific Literacy : An Exercise in Model Building', Education Sciences, 10 1-16 (2020) [C1]
DOI 10.3390/educsci10080204
Co-authors Mitch Otoole, Judy-Anne Osborn
2020 Osborn JA, Larkins JA, McBain B, Ellerton P, Black J, Borwein N, et al., 'Foundations of the DEFT Project: tertiary educators Developing Expertise Fostering Thinking', International Journal of Innovation in Science and Mathematics Education, 28 2-15 (2020)

We describe the rationale, creation, and activity of a long-term co-constructed voluntary professional development initiative for tertiary educators. This is a Community of Practi... [more]

We describe the rationale, creation, and activity of a long-term co-constructed voluntary professional development initiative for tertiary educators. This is a Community of Practice (CoP) formed to investigate ¿thinking¿ as a topic which may be explicitly taught. The aim of this paper is to share the value of this CoP in one context and insights into how similar approaches may be useful to other tertiary educators. The project has run for a year to date, involving a small butgrowing collective of tertiary educators, withmembers from one Canadian and several Australian Universities. Our methodology is participatory: we regularly meet,reflect,and record our reflections. Our records contain data relatingto our motivation, our insights, and the impact of these upon our choices in our teaching practices. In particular,our rationaleincludes the mutual desire to invest in developing understanding of our teaching challenges, to enable us to create thoughtful teaching approaches fit for our purposes and contexts. Hence, the central focus of our CoP isthe Development of our Expertise in Fostering Thinking (DEFT). This focus hasilluminatedgaps in existing scholarly literaturepertainingto communal development of theory, personal development of schemata, capacity for reflexivity, and instantiation in our disciplines. Opportunities and risks associated with our other sources of professional learningare identified and discussed. We elaborate on adouble-layered approach, in which we explore the constructionofour ownschemataas a precursor to helpingstudents buildtheirschemataas a foundation for their own understanding, and the role offlexible, critical,and creativethinking on our part. We utilise the scholarship of expertise, frequently returning to such questionsas ¿How do we know what our students are thinking?¿Insights gleaned from our reflections are shared, and recommendations are presented on the formation of similar projects.

DOI 10.30722/IJISME.28.02.001
Co-authors Bonnie Mcbain, Judy-Anne Osborn
2019 Butler E, Prieto-Rodriguez E, Osborn J-A, Howley P, Lloyd A, Kepert A, Roberts M, 'Learning Across Discipline Boundaries Through Narrative Inquiry: A Study of Collaboration to Improve Mathematics Teacher Education', Mathematics Teacher Education and Development, 21 87-105 (2019) [C1]
Co-authors Adam Lloyd, Judy-Anne Osborn, Peter Howley, Andrew Kepert, Elena Prieto
2017 Osborn JH, Hussain M, Trudgian T, 'Number Theory Down Under 2016. Dedicated to Professor Richard Brent on his 70th birthday.', Gazette of the Australian Mathematical Society, 44 82-88 (2017)
Co-authors Judy-Anne Osborn
2017 Osborn JH, 'Guttmann 2015: 70 and counting', Gazette of the Australian Mathematical Society, 44 18-25 (2017)
Co-authors Judy-Anne Osborn
2016 Brent RP, Osborn JAH, Smith WD, 'Probabilistic lower bounds on maximal determinants of binary matrices', Australasian Journal of Combinatorics, 66 350-364 (2016) [C1]

Let D(n) be the maximal determinant for n × n {±1}-matrices, and R(n) = D(n)/n be the ratio of D(n) to the Hadamard upper bound. Using the probabilistic method, we prove new lowe... [more]

Let D(n) be the maximal determinant for n × n {±1}-matrices, and R(n) = D(n)/n 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 /h ¿ 0 as n ¿ 8, so the second bound is close to (pe/2) for large n. Previous lower bounds tended to zero as n¿8with d fixed, except in the cases d ¿ {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) > 0.1133. n/2 2 1/2 -d/2 -3/2

Co-authors Judy-Anne Osborn
2016 Brent RP, Ohtsuka H, Osborn JAH, Prodinger H, 'Some binomial sums involving absolute values', Journal of Integer Sequences, 19 (2016) [C1]

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... [more]

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.

Citations Scopus - 2Web of Science - 2
Co-authors Judy-Anne Osborn
2015 Brent RP, Osborn J-AH, Smith WD, 'Note on best possible bounds for determinants of matrices close to the identity matrix', LINEAR ALGEBRA AND ITS APPLICATIONS, 466 21-26 (2015) [C1]
DOI 10.1016/j.laa.2014.09.041
Citations Scopus - 8Web of Science - 9
Co-authors Judy-Anne Osborn
2015 Prieto-Rodriguez 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 98-110 (2015) [C1]
Co-authors Judy-Anne Osborn, Elena Prieto, Andrew Kepert, Peter Howley
2013 Brent RP, Osborn J-AH, 'On minors of maximal determinant matrices', Journal of Integer Sequences, 16 (2013) [C1]
Citations Scopus - 3
Co-authors Judy-Anne Osborn
2013 Brent RP, Osborn JAH, 'Bounds on minors of binary matrices', Bulletin of the Australian Mathematical Society, 88 280-285 (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 near-extremal properties', SIAM J. Discrete Math. 23(2009), 1422-1440], but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices. Copyright © 2012 Australian Mathematical Publishing Association Inc.

DOI 10.1017/S000497271200086X
Co-authors Judy-Anne Osborn
2013 Brent RP, Osborn J-AH, 'General lower bounds on maximal determinants of binary matrices', ELECTRONIC JOURNAL OF COMBINATORICS, 20 (2013) [C1]
Citations Scopus - 3Web of Science - 2
Co-authors Judy-Anne Osborn
2012 Borwein JM, Osborn J-AH, '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, 15 138-143 (2012) [C3]
DOI 10.1007/978-94-007-2129-6
Co-authors Judy-Anne Osborn
2011 Borwein JM, Osborn J-AH, 'Loving and Hating Mathematics by Reuben Hersh and Vera John-Steiner [Book Review]', The Mathematical Intelligencer, 33 63-69 (2011) [C3]
DOI 10.1007/s00283-011-9260-1.
Citations Scopus - 1
Co-authors Judy-Anne Osborn
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 non-zero 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 re-entrance 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 re-entrance phenomenon vanishes under certain pulling angles, with details depending on how the three-dimensional polymer is modeled. © 2010 IOP Publishing Ltd and SISSA.

DOI 10.1088/1742-5468/2010/09/P09018
Citations Scopus - 33Web of Science - 28
Co-authors Judy-Anne Osborn
2010 Osborn J-AH, 'Bi-banded paths, a bijection and the Narayana numbers', Australasian Journal of Combinatorics, 48 243-252 (2010) [C1]
Citations Scopus - 3Web of Science - 2
Co-authors Judy-Anne Osborn
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 non-classical. Hence, we also present an efficient method for finding explicit closed-form polynomial expressions for these non-classical orthogonal polynomials. Our method for finding the closed-form 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. © 2009 IOP Publishing Ltd.

DOI 10.1088/1751-8113/42/44/445201
Co-authors Judy-Anne Osborn
2006 Brak R, Essam J, Osborn J, Owczarek AL, Rechnitzer A, 'Lattice Paths and the Constant Term', J Phys Conf Ser, 47-58 (2006)
Co-authors Judy-Anne Osborn
Show 15 more journal articles

Conference (3 outputs)

Year Citation Altmetrics Link
2020 Borwein NS, Osborn JAH, 'On the educational legacies of Jonathan M. Borwein', Springer Proceedings in Mathematics & Statistics, Newcastle, NSW (2020) [E1]
DOI 10.1007/978-3-030-36568-4_7
Co-authors Judy-Anne Osborn
2020 Bailey DH, Borwein NS, Brent RP, Burachik RS, Osborn JAH, Sims B, Zhu QJ, 'Preface', Springer Proceedings in Mathematics and Statistics (2020)
Co-authors Brailey Sims, Judy-Anne Osborn
2020 Brent RP, 'The Borwein brothers, Pi and the AGM', Springer Proceedings in Mathematics and Statistics, Callaghan, Australia (2020) [E1]
DOI 10.1007/978-3-030-36568-4_21
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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 Judy-Anne Osborn, Associate Professor Kathryn Holmes, Associate Professor Elena Prieto-Rodriguez, 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
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Research Supervision

Number of supervisions

Completed1
Current0

Past Supervision

Year Level of Study Research Title Program Supervisor Type
2020 PhD Modelling Diversity in Abstract Algebra Textbooks PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle Co-Supervisor
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News

Tipping the balance towards humanity in World War Z

June 20, 2013

Could a dire new infection sweep the world in a matter of weeks? Might the disease be so strange that it alters the behaviour of people beyond recognition, maki

Dr Judy-Anne Osborn

Position

Lecturer
CARMA
School of Mathematical and Physical Sciences
College of Engineering, Science and Environment

Focus area

Mathematics

Contact Details

Email judy-anne.osborn@newcastle.edu.au
Phone 02 4921 5543
Mobile 0438 944 021
Fax 02 4921 6898

Office

Room SR272
Building SR - Building (Social Sciences Building)
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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