麻豆社madou

Dr Thomas Britz

Dr Thomas Britz

Senior Lecturer

Education

Science
School of Mathematics & Statistics

I am part of the at the here at 麻豆社madou Sydney.

PROFESSIONAL AFFILIATIONS AND SERVICE POSITIONS

President of the (CMSA) (December 2021 鈥)
Friend of the Australian Council of Heads of Mathematical Sciences (December 2021 鈥 )
Chief Editor of (November 2015 鈥)
Managing Editor for the (August 2011 鈥 )
Area Editor for the (April 2014 鈥揙ctober 2023)
Referee for 61 journals and 2 conference proceedings (> 175 reports)
Reviewer for Mathematical Reviews and Zentralblatt MATH (> 250 reviews)
Grant proposal assessor for ARC DP, NISDRG, FRP, Vidi (32 reports)
PhD Opponent/Assessor (2 times)

Member of the Hybrid Learning and Teaching Community of Practice, 麻豆社madou (May 2023 鈥 )
Member of 麻豆社madou Student Wellbeing Community of Practice, 麻豆社madou (January 2022 鈥撎)
Academic Mentor, 麻豆社madou (2019听鈥 )
First Responder, 麻豆社madou (July 2018听鈥 )
Academic Advisor, MATH, 麻豆社madou (August 2010听鈥 )

Member of the Education Excellence Committee, Science Faculty, 麻豆社madou (March 2018 鈥撎)
Member of (uDASH), 麻豆社madou (August 2021 鈥 2024)
Member of the Sustainability Committee, MATH, 麻豆社madou (February 2020 鈥 2023)
Co-organiser of the 42th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, 麻豆社madou, December 2019听(March 2018听鈥撎鼶ecember 2019)
School liaison for the 麻豆社madou MathSoc, MATH, 麻豆社madou (Jan 2012 鈥 2018)
Chair of the Publicity Committee, MATH, 麻豆社madou (July 2014 鈥撎齋eptember 2018)
Lecturer's Representative for the School Standing Committee, 麻豆社madou (June 2011 鈥 2018)
Manager of Web and Social Media, MATH, 麻豆社madou (November 2017 鈥 August 2018)
Member of the Computing Committee, MATH, 麻豆社madou (February 2018 鈥 August 2018)
Member of the Research Committee, MATH, 麻豆社madou (October 2015 鈥 July 2017)
Pure Representative on the Postgraduate Committee, MATH, 麻豆社madou (September 2013 鈥 September 2017)
Chair of the School Standing Committee, MATH, 麻豆社madou (February 2014 鈥 April 2015)
Member of the Policy and Resources Committee, MATH, 麻豆社madou (February 鈥 December 2014)
Organiser of Pure Departmental Seminar, School of Mathematics & Statistics, 麻豆社madou (Aug 2010 鈥 Jan 2013)
Co-organiser of the Joint Colloquium, School of Mathematics and Statistics, 麻豆社madou (Aug 2010 鈥 Jan 2013)
Co-organiser of the 36th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, 麻豆社madou, December 2012 (March 2011 鈥撎鼶ecember 2012)

Member of the (August 2018 鈥 )
Life member of the (CMSA)

I also enjoy a range of outreach activities, to promote mathematical thinking, learning and enjoyment.

Phone
9385 7115
Location
Room RC-5111, School of Mathematics and Statistics Anita B. Lawrence Centre 麻豆社madou Sydney Sydney NSW 2052
  • Books | 2024
    Angell D; Britz T, 2024, Parabolic Problems 60 Years of Mathematical Puzzles in Parabola, CRC Press
  • Book Chapters | 2022
    Britz T; Cameron PJ, 2022, 'Codes', in Ellis-Monaghan JA; Moffatt I (ed.), Handbook of the Tutte Polynomial, Chapman & Hall/CRC, pp. 328 - 344,
    Book Chapters | 2001
    Britz T; Mainetti M; Pezzoli L, 2001, 'Some operations on the family of equivalence relations', in Crapo H; Senato D (ed.), Algebraic Combinatorics and Computer Science. A Tribute To Gian-Carlo Rota, Springer-Verlag Italia, Milan, pp. 445 - 460
  • Journal articles | 2025
    Wang C; Abel RJR; Britz T; Bunjamin YA; Combe D, 2025, 'Group divisible designs with block size 4 and group sizes 4 and 10 and some other 4-GDDs', Discrete Mathematics, 348, pp. 114254,
    Journal articles | 2024
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2024, 'Group divisible designs with block size 4 and group sizes 4 and 7', Journal of Combinatorial Designs, 32, pp. 328 - 346,
    Journal articles | 2024
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2024, 'Group divisible designs with block size 4 and group sizes 4 and 7', Journal of Combinatorial Designs, 32, pp. 328 - 346,
    Journal articles | 2024
    Britz T; Chakraborty HS; Ishikawa R; Miezaki T; Tang HC, 2024, 'Harmonic Tutte polynomials of matroids II', Designs, Codes, and Cryptography, 92, pp. 1279 - 1297,
    Journal articles | 2024
    Britz T, 2024, 'Book review of Vector: A Surprising Story of Space, Time, and Mathematical Transformation', Parabola, 60,
    Journal articles | 2024
    Chng ZY; Britz T; Tan TS; Wong KB, 2024, 'The Ramsey Numbers for Trees of Large Maximum Degree Versus the Wheel Graph W8', Bulletin of the Malaysian Mathematical Sciences Society, 47, pp. 134,
    Journal articles | 2024
    Li NZ; Britz T, 2024, 'ON THE SCALE-FREENESS OF RANDOM COLORED SUBSTITUTION NETWORKS', Proceedings of the American Mathematical Society, 152, pp. 1377 - 1389,
    Journal articles | 2023
    Abel RJR; Britz T; Bunjamin YA; Combe D; Feng T, 2023, 'Group divisible designs with block size 4 where the group sizes are congruent to 1 mod 3', Discrete Mathematics, 346, pp. 113277,
    Journal articles | 2023
    Gilmore N; Britz T; Maartensson E; Orbegoso-Jordan C; Schroder S; Malerba M, 2023, 'Continental-scale assessment of micro-pumped hydro energy storage using agricultural reservoirs', Applied Energy, 349, pp. 121715,
    Journal articles | 2022
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2022, 'Group divisible designs with block size 4 and group sizes 2 and 5', Journal of Combinatorial Designs, 30, pp. 367 - 383,
    Journal articles | 2022
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2022, 'Group divisible designs with block size 4 where the group sizes are congruent to 2 mod 3', Discrete Mathematics, 345, pp. 112740,
    Journal articles | 2022
    Britz T, 2022, 'The beauty of the Golden Ratio', Parabola, 58,
    Journal articles | 2020
    Britz T; Carey A; Gesztesy F; Nichols R; Sukochev F; Zanin D, 2020, 'The product formula for regularized Fredholm determinants', Proceedings of the American Mathematical Society, Series B, 8, pp. 42 - 51,
    Journal articles | 2020
    Britz T; Cavenagh NJ; Mammoliti A; Wanless IM, 2020, 'Mutually orthogonal binary frequency squares', Electronic Journal of Combinatorics, 27, pp. 1 - 26,
    Journal articles | 2020
    Britz T; Co-author I, 2020, 'How to write a Parabola article', Parabola, 56,
    Journal articles | 2020
    Britz T; Mammoliti A; Shiromoto K, 2020, 'Wei-type duality theorems for rank metric codes', Designs, Codes, and Cryptography, 88, pp. 1503 - 1519,
    Journal articles | 2020
    Britz T, 2020, 'Fibonacci numbers: Brief history and counting problems', Parabola, 56,
    Journal articles | 2018
    Britz T, 2018, 'On the betweenness centrality of trees, forests and cycles', Sustainable Forestry, 1, pp. 1 - 5,
    Journal articles | 2018
    Mammoliti A; Britz T, 2018, 'On mubayi's conjecture and conditionally intersecting sets', SIAM Journal on Discrete Mathematics, 32, pp. 2361 - 2380,
    Journal articles | 2018
    Tran B; Straka P; Falster MO; Douglas KA; Britz T; Jorm LR, 2018, 'Overcoming the data drought: Exploring general practice in Australia by network analysis of big data', Medical Journal of Australia, 209, pp. 68 - 73,
    Journal articles | 2017
    Bright D; Greenhill C; Britz T; Ritter A; Morselli C, 2017, 'Criminal network vulnerabilities and adaptations', Global Crime, 18, pp. 424 - 441,
    Journal articles | 2017
    Britz T, 2017, 'Geoffrey Marnell: Mathematical Doodlings - Curiosities, Conjectures and Challenges', Parabola, 53,
    Journal articles | 2016
    Britz T; Shiromoto K, 2016, 'On the Covering Dimension of a Linear Code', IEEE Transactions on Information Theory, 62, pp. 2694 - 2701,
    Journal articles | 2016
    Hunter DO; Britz T; Jones M; Letnic M, 2016, 'Reintroduction of Tasmanian devils to mainland Australia can restore top-down control in ecosystems where dingoes have been extirpated: A response to Baker et al. 2016 and Fancourt & Mooney 2016', Biological Conservation, 196, pp. 20 - 21,
    Journal articles | 2015
    Britz T; Cavenagh NJ; S酶rensen HK, 2015, 'Maximal partial Latin cubes', Electronic Journal of Combinatorics, 22,
    Journal articles | 2015
    Britz T; Shiromoto K; Westerb盲ck T, 2015, 'Demi-matroids from codes over finite Frobenius rings', Designs, Codes, and Cryptography, 75, pp. 97 - 107,
    Journal articles | 2015
    Hunter DO; Britz T; Jones M; Letnic MI, 2015, 'Reintroduction of Tasmanian devils to mainland Australia can restore top-down control in ecosystems where dingoes have been extirpated', Biological Conservation,
    Journal articles | 2014
    Britz T; Johnsen T; Martin J, 2014, 'Chains, demi-matroids, and profiles', IEEE Transactions on Information Theory, 60, pp. 986 - 991,
    Journal articles | 2014
    Britz T; Mammoliti A; S酶rensen HK, 2014, 'Proof by picture: A selection of nice picture proofs', Parabola, 3, pp. 5 - 15,
    Journal articles | 2013
    Chan TH; Grant A; Britz T, 2013, 'Quasi-uniform codes and their applications', IEEE Transactions on Information Theory, 59, pp. 7915 - 7926,
    Journal articles | 2012
    Britz T; Johnsen T; Mayhew D; Shiromoto K, 2012, 'Wei-type duality theorems for matroids', Designs Codes and Cryptography, 62, pp. 331 - 341,
    Journal articles | 2010
    Britz T, 2010, 'Code enumerators and Tutte polynomials', IEEE Transactions on Information Theory, 56, pp. 4350 - 4358,
    Journal articles | 2009
    Britz T; Royle G; Shiromoto K, 2009, 'Designs from matroids', SIAM Journal on Discrete Mathematics, 23, pp. 1082 - 1099
    Journal articles | 2008
    Britz T; Shiromoto K, 2008, 'A MacWilliams type identity for matroids', Discrete Mathematics, 308, pp. 4551 - 4559,
    Journal articles | 2008
    Britz T; Shiromoto K, 2008, 'Designs from subcode supports of linear codes', Designs Codes and Cryptography, 46, pp. 175 - 189
    Journal articles | 2007
    Britz D; Britz T; Shiromoto K, 2007, 'The higher weight enumerators of the doubly-even self-dual [48,24,12] code', IEEE Transactions on Information Theory, 53, pp. 2567 - 2571
    Journal articles | 2007
    Britz T, 2007, 'Higher support matroids', Discrete Mathematics, 307, pp. 2300 - 2308
    Journal articles | 2007
    Britz T, 2007, 'The Moore-Penrose inverse of a free matrix', Electronic Journal of Linear Algebra, 16, pp. 208 - 215
    Journal articles | 2006
    Britz T, 2006, 'On P-weight and P-distance inequalities', Discrete Mathematics, 306, pp. 598 - 599
    Journal articles | 2005
    Britz T; Olesky DD; van den Driessche P, 2005, 'Schur complements of matrices with acyclic bipartite graphs', Electronic Journal of Linear Algebra, 14, pp. 2 - 11
    Journal articles | 2005
    Britz T; Rutherford CG, 2005, 'Covering radii are not matroid invariants', Discrete Mathematics, 296, pp. 117 - 120
    Journal articles | 2005
    Britz T, 2005, 'Extensions of the Critical Theorem', Discrete Mathematics, 305, pp. 55 - 73
    Journal articles | 2004
    Britz T; Mcdonald JJ; Olesky DD; van den Driessche P, 2004, 'Minimal spectrally arbitrary sign patterns', SIAM Journal on Matrix Analysis and Applications, 26, pp. 257 - 271
    Journal articles | 2004
    Britz T; Olesky DD; van den Driessche P, 2004, 'Matrix inversion and digraphs: the one factor case', Electronic Journal of Linear Algebra, 11, pp. 115 - 131
    Journal articles | 2004
    Britz T; Olesky DD; van den Driessche P, 2004, 'The Moore-Penrose inverse of matrices with an acyclic bipartite graph', Linear Algebra and its Applications, 390, pp. 47 - 60,
    Journal articles | 2003
    Britz T; Britz D, 2003, 'Mathematical proof of the consistency of Feldberg鈥檚 simple BDF start in electrochemical digital simulation', Journal of Electroanalytical Chemistry, 546, pp. 123 - 125
    Journal articles | 2002
    Britz T, 2002, 'MacWilliams identities and matroid polynomials', Electronic Journal of Combinatorics, R9, pp. 1 - 19,
    Journal articles | 2001
    Britz T; Fomin S, 2001, 'Finite posets and Ferrers shapes', Advances in Mathematics, 158, pp. 86 - 127
    Journal articles | 2001
    Britz T, 2001, 'The inverse of a non-singular free matrix', Linear Algebra and its Applications, 338, pp. 245 - 249,
    Journal articles | 1988
    Britz T; Britz D, 1988, 'Transform (Type-In)', Amstrad Action, 32
  • Preprints | 2024
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2024, Direct constructions of some group divisible designs with block size $4$ and up to $50$ points,
    Preprints | 2024
    Britz T; Chakraborty HS; Miezaki T, 2024, Harmonic Tutte polynomials of matroids III,
    Preprints | 2023
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2023, Group divisible designs with block size 4 and group sizes 4 and 7, ,
    Preprints | 2022
    Britz T; Chakraborty HS; Ishikawa R; Miezaki T; Tang HC, 2022, Harmonic Tutte polynomials of matroids II, ,
    Preprints | 2022
    Britz T; Hu X; Islam A; Tang HC, 2022, Bounds on the closeness centrality of a graph, ,
    Recorded / Rendered Creative Works | 2022
    Britz T, 2022, How to create a supportive learning community, 麻豆社madou eLearning, Editor(s): Britz T, Published: 07 March 2022, Duration: 00:13:39, Recorded / Rendered Creative Works,
    Preprints | 2021
    Abel RJR; Britz T; Bunjamin YA; Combe D, 2021, Group divisible designs with block size 4 and group sizes 2 and 5, ,
    Preprints | 2021
    Li NZ; Britz T, 2021, On the scale-freeness of random colored substitution networks, ,
    Preprints | 2020
    Britz T; Carey A; Gesztesy F; Nichols R; Sukochev F; Zanin D, 2020, The product formula for regularized Fredholm determinants, ,
    Software / Code | 2019
    Britz T; Bright D; Snoyman R, 2019, Criminal Networks, Published: 2019, Software / Code,
    Preprints | 2019
    Britz T; Cavenagh NJ; Mammoliti A; Wanless IM, 2019, Mutually orthogonal binary frequency squares, ,
    Recorded / Rendered Creative Works | 2019
    Britz T, 2019, The Emotions of Mathematics, TEDx Talks, YouTube, Editor(s): TEDx麻豆社madou , Published: 12 April 2019, Duration: 00:14:31, Recorded / Rendered Creative Works,
    Other | 2018
    Henry B; Britz T; Schumacher E; Marschalek R; Zacarelli Denke R; Bojanic Helbingen C; Zayas Claure CD; Humenberger H; Fallas-Monge JJ; Dur谩n Silva R; Jupri A; Kageyama K; Ishibashi I; 脕vila Pozos O; Rivera I; Voss P; Panduro Urrelo HE; Karas S; Ruminska M; Sulitsa | O; Romanchuck V; Tolmachev Y, 2018, MATHBRIDGES Calendar, University of M眉nster,
    Conference Papers | 2010
    Chan TH; Grant A; Britz T, 2010, 'Properties of quasi-uniform codes', in 2010 IEEE International Symposium on Information Theory Proceedings, Austin, Texas, presented at 2010 IEEE International Symposium on Information Theory, Austin, Texas, 13 June 2010 - 18 June 2010
    Preprints | 2009
    Britz T; Heiseldel B; Johnsen T; Mayhew D; Shiromoto K, 2009, Generalizations of Wei's Duality Theorem, ,
    Software / Code | 2007
    Britz T; Britz D; S酶rensen HK, 2007, Fast Tutte polynomial calculator, Maple, C++, Fortran, Published: 22 August 2007, Software / Code,
    Theses / Dissertations | 2003
    Britz T, 2003, Matroids, Codes and Relations, University of Aarhus
  • Media | 2023
    Britz T; Gilmore N; Malerba M, 2023, Farmers are famously self-reliant. Why not use farm dams as mini-hydro plants?, The Conversation Media Group Ltd,
    Media | 2023
    Britz T, 2023, The beauty of the Golden Ratio, Faculti Media Limited, ,
    Media | 2023
    Britz T, 2023, What is combinatorics?, Faculti Media Limited,
    Media | 2022
    Britz T, 2022, Does Amber Heard really have the world鈥檚 most beautiful face? An expert explains why the Golden Ratio test is bogus, The Conversation Media Group Ltd,
    Media | 2022
    Britz T, 2022, The history and mystery of Tangram, the children's puzzle game that harbours a mathematical paradox or two, The Conversation Media Group Ltd,

Research Grants

$525,115 total awarded by grants, including the following:

  • Discovery Grant: T. Britz, "Chromatic polynomials, random graphs, and error-correcting codes: a unified approach to graph colouring problems鈥, $242,066, 2007鈥2009
  • PIMS Postdoctoral Fellowship, 20,000CAD, 2003鈥2004
  • Villum Kann Rasmussen Postdoctoral Fellowship, 350.000DKK (2004鈥2005)
  • Carlsberg Foundation Postdoctoral Fellowship, 350.000DKK, 2006
  • , T. Britz,听$25,000, 2013
  • 麻豆社madou Light Digital Uplift of MATH3411: $15,000, 2019.

Vice-Chancellor鈥檚 Award for Outstanding Contributions to Student Wellbeing, 麻豆社madou, 2021.
Science Dean's Award for Excellence in Student Wellbeing, 麻豆社madou, 2021.
Vice-Chancellor's Award for Contributions to Student Learning, 麻豆社madou, 2015.

I am interested in most areas of discrete mathematics and combinatorics. Most of my research has been so far in graph theory, matroid theory, coding theory, combinatorial polynomials, combinatorial matrix theory, design theory, partially ordered sets, matching theory, flow theory, and enumerative combinatorics. Most of my research is highly foundational and theoretical but I also enjoy applying combinatorial methods and results to other areas, so far including big data in medicine, bioinformatics, criminology, ecology, electrochemistry, energy-storage, law, linear algebra, oceanography, psycholinguistics, quantum mechanics and renewable energy. I also very much welcome the opportunity to solve tangible real-life problems and have consulted for a variety of companies and government.
If you have any problem that might benefit from some math- or problem-solving skills, then please email me!

My Research Supervision

Supervision:

PhD students:
听 Hopein Christofen Tang, 麻豆社madou, 2023鈥
听 John Fitzgerald, 麻豆社madou (joint supervision with Lyria Bennet Moses, 麻豆社madou Law, and Ben Hachey, USyd), 2015鈥
听 Zhi Yee Chng, 麻豆社madou (joint supervision with Tan Ta Sheng and Wong Kok Bin, University of Malaya), 2024
听 Adam Mammoliti, 麻豆社madou, 2019
听 James Ross, 麻豆社madou (secondary supervisor; primary supervisor: Catherine Greenhill), 2023
听 Haya Saeed Aldosari, 麻豆社madou (secondary supervisor; primary supervisor: Catherine Greenhill), 2020
听 Vicki Likourezos, 麻豆社madou (secondary supervisor; primary supervisor: Slava Kalyuga, 麻豆社madou Arts), 2016-2017
听 Peter Ayre, 麻豆社madou (secondary supervisor; primary supervisor:听 Catherine Greenhill), 2019
听 Ali Hussian Alkhaldi, 麻豆社madou (secondary supervisor; primary supervisor:听 Norman Wildberger), 2014

Master by Research students:
听 Nero Ziyu Li, 麻豆社madou, 2021
听 Sin Keong Tong, 麻豆社madou, 2019
听 Zhi Yee Chng, 麻豆社madou, 2017
听 Maria Fischer, 麻豆社madou, 2015
听 Marie-Louise Hoejlund Rasmussen, Technical University of Denmark, 2005

Honours students:
听 Phillip Tzioumis 听麻豆社madou, 2024-
听 Hayden McLean, 麻豆社madou, 2023
听 Zhan Wei, 麻豆社madou, 2023
听 Rickey Wu, 麻豆社madou, 2023
听 Edmond Gao, 麻豆社madou, 2021
听 Ryan Snoyman, 麻豆社madou, 2020
听 David Morris, 麻豆社madou, 2020
听 Michael Libman, 麻豆社madou, 2019
听 Nelson Chen, 麻豆社madou, 2019
听 Daniel Tanios, 麻豆社madou, 2019
听 Jessica Dai, 麻豆社madou, 2018
听 Tyson Churcher, 麻豆社madou, 2016
听 Duncan Crowley, 麻豆社madou, 2016
听 Adam Mammoliti, 麻豆社madou, 2014
听 Elizabeth Alford, 麻豆社madou, 2012

Master by Coursework students:
听 Demetra Siountris, 麻豆社madou, 2020
听 Xin Hu, 麻豆社madou, 2019
听 Salha Ahmed Alshaikey, 麻豆社madou, 2012
听 Dalal Alanazi, 麻豆社madou, 2012
听 Saad Althobaiti, 麻豆社madou, 2012
听 Doug Han Yang, 麻豆社madou, 2009
听 Ali Alkhaldi,听 麻豆社madou, 2009

Research Course Project:
听 Jovana Kolar, 麻豆社madou, 2021
听听Abdellah Islam, 麻豆社madou, 2020
听 Iker Carrera, 麻豆社madou, 2020
听 James Ross, 麻豆社madou, 2014

AMSI Summer Research Project:
听 Ariana Liu, 麻豆社madou, 2023
听 Jovana Kolar, 麻豆社madou, 2022
听 Tiana Tsung Ung, 麻豆社madou, 2021

Summer Research Project:
听 Tiana Tsung Ung, 麻豆社madou, 2020
听 Abdellah Islam, 麻豆社madou, 2020
听 Charlie Stinson, 麻豆社madou, 2019
听 Zijian Gao, 麻豆社madou, 2019
听 Rui Tong, 麻豆社madou, 2018
听 Jacky Huang, 麻豆社madou, 2018
听 Gary Liang, 麻豆社madou, 2015
听 Adam Mammoliti, 麻豆社madou, 2014
听 Steve Sui, 麻豆社madou, 2013
听 Kirsten Vo-Phuoc, 麻豆社madou, 2012
听 Sen Lin, 麻豆社madou, 2011

My Teaching

I have designed, created and lectured the HDR/Honours courses

Aspects of Combinatorial Optimisation (at Kumamoto University, 2011)
Combinatorial Enumeration and Optimisation (AMSI Summer School 2012, with Prof. Ian Wanless).
MATH5505 - Combinatorics (麻豆社madou 2016, 2018)
An Introduction to Combinatorics (Aalto University, 2017)

and听written course material for, and lectured, the courses

MATH151 - Finite Mathematics (University of Victoria, BC, Canada)
MATH1081 - Discrete Mathematics
MATH1131 - Mathematics 1A
MATH1241 - Higher Mathematics 1B
MATH3411 - Information, Codes and Ciphers
MATH3521 - Algebraic Techniques in Number Theory

In total, I have lectured semester courses for 8,000 students.
I have also tutored numerous courses, for 2,000 students.

Here is quick access to some of my .