Professor Chris Good BA, MA (Oxon), DPhil (Oxon)

Professor Chris Good, Head of School

School of Mathematics
Head of School
Professor of Mathematics

Contact details

Telephone
+44 (0) 121 414 6201
Email
c.good@bham.ac.uk
View my research portal
Address
School of Mathematics
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Chris Good is Professor of Mathematics at the University of Birmingham. He is the author of over 50 research articles in general topology, set-theoretic topology, topological dynamics and mathematical education.  He regularly collaborates with mathematicians around the world, including colleagues from Mexico, New Zealand, Poland and the US, as well as from Oxford, and has organised conferences in Birmingham, Oxford and Cambridge.  Chris has worked with several postdoctoral fellows and supervised a number of graduate students.  If you are interested in working with him, he would be interested in hearing from you.

Chris has a long standing interest in teaching and was awarded the first Head of School’s Excellence in Teaching Award.  He played a leading role in the development of the School’s new curriculum, championing the introduction of problem based learning and core skills.

Chris is a Fellow of the Institute of Mathematics and its Applications and Senior Fellow of the Higher Education Academy.  He has an Erdos number of 3 and an Erdos-Bacon number of 7. Since April 2019, Chris has been Deputy Dean of the Jinan University – University of Birmingham Joint Institute and in August 2020 he became Head of School for the School of Mathematics.

For more information, visit Chris’ School webpage.

Qualifications

  • DPhil in Mathematics (Oxon) 1992
  • MA (Oxon) 1991
  • BA in Mathematics (Oxon) 1988

Teaching

Chris has taught over 18 different modules at all levels, ranging from Foundation Year Mathematics, through First Year Probability and Statistics, to advanced topics in pure mathematics such as General Topology, Complex Analysis and Discrete Dynamics.  He has supervised many undergraduate projects as well as undergraduate Summer research projects.  He introduced the First Year enquiry based learning modules ‘Developing Mathematical Reasoning’ (based on the influential Moore Method, with the aid of a grant from the Educational Advancement Foundation) and ‘Mathematical Modelling and Problem Solving’ and the Second Year problem solving and skills module ‘Mathematics in Industry’ (with the aid of a grant from the HE STEM Programme).

Postgraduate supervision

Chris Good’s early research was in the construction of counterexamples (often using set-theoretic methods) especially around the Dowker space question and the behaviour of normality in product spaces. More recently he has become interested in dynamical systems, in particular symbolic dynamics and the structure of invariant sets, and abstract topological dynamics. He is able to supervise doctoral research in these areas, as well as in:

The structure of ω-limit sets of tent maps and shifts of finite type using a mixture of analytic and symbolic techniques
The relationship between shadowing and expansivity of maps on compact metric spaces
The role of periodic points in chaos
Abstract dynamical systems modelled by compact Hausdorff spaces, separable metric spaces, the space of rational numbers and continua
Characterisations of ordinals

Other activities

Chris is Deputy Head of School.

Publications

Recent publications

Article

Good, C, Greenwood, S & Uresin, N 2020, 'Abstract topological dynamics involving set-valued functions', Topology and its Applications, vol. 279, 107240. https://doi.org/10.1016/j.topol.2020.107240

Good, C, Leek, R & Mitchell, J 2020, 'Equicontinuity, transitivity and sensitivity: the Auslander-Yorke dichotomy revisited', Discrete and Continuous Dynamical Systems, vol. 40, no. 4, pp. 2441-2474. https://doi.org/10.3934/dcds.2020121

Good, C, Macias, S, Meddaugh, J, Mitchell, J & Thomas, J 2020, 'Expansivity and unique shadowing', Proceedings of the American Mathematical Society, vol. 2020, pp. 1-15. https://doi.org/10.1090/proc/15204

Good, C, Macías, S, Meddaugh, J, Mitchell, J & Thomas, J 2020, 'Expansivity and unique shadowing', Proceedings of the American Mathematical Society, vol. 149, no. 2, pp. 671-685. https://doi.org/10.1090/proc/15204

Good, C, Mitchell, J & Thomas, J 2020, 'On inverse shadowing', Dynamical Systems. https://doi.org/10.1080/14689367.2020.1739228

Good, C, Mitchell, J & Thomas, J 2020, 'Preservation of shadowing in discrete dynamical systems', Journal of Mathematical Analysis and Applications, vol. 485, no. 1, 123767, pp. 1-39. https://doi.org/10.1016/j.jmaa.2019.123767

Good, C, Mitchell, J & Meddaugh, J 2020, 'Shadowing, internal chain transitivity and α-limit sets', Journal of Mathematical Analysis and Applications, vol. 491, no. 1, 124291. https://doi.org/10.1016/j.jmaa.2020.124291

Grove, M & Good, C 2019, 'Approaches to feedback in the mathematical sciences: just what do students really think?', Teaching Mathematics and its Applications. https://doi.org/10.1093/teamat/hrz013

Henze, R, Mu, C, Puljiz, M, Kamaleson, N, Huwald, J, Haslegrave, J, di Fenizio, PS, Parker, D, Good, C, Rowe, JE, Ibrahim, B & Dittrich, P 2019, 'Multi-scale stochastic organization-oriented coarse-graining exemplified on the human mitotic checkpoint', Scientific Reports, vol. 9, no. 1, 3902. https://doi.org/10.1038/s41598-019-40648-w

Good, C, Oprocha, P & Puljiz, M 2019, 'Shadowing, asymptotic shadowing and s-limit shadowing', Fundamenta Mathematicae, vol. 244, no. 3, pp. 287-312. https://doi.org/10.4064/fm492-5-2018

Good, C & Meddaugh, J 2019, 'Shifts of finite type as fundamental objects in the theory of shadowing', Inventiones Mathematicae, vol. 220, pp. 715–736. https://doi.org/10.1007/s00222-019-00936-8

Fernández, L, Good, C & Puljiz, M 2018, 'Almost minimal systems and periodicity in hyperspaces', Ergodic Theory and Dynamical Systems, vol. 38, no. 6, pp. 2158-2179. https://doi.org/10.1017/etds.2016.123

Good, C & Macias, S 2018, 'What is Topological about Topological Dynamics?', Discrete and Continuous Dynamical Systems, vol. 38, no. 3, pp. 1007-1031. https://doi.org/10.3934/dcds.2018043

Good, C & Meddaugh, J 2016, 'Orbital shadowing, internal chain transitivity and omega-limit sets', Ergodic Theory and Dynamical Systems. https://doi.org/10.1017/etds.2016.30

Good, C & Fernández, L 2016, 'Shadowing for induced maps of hyperspaces', Fundamenta Mathematicae, vol. 235, pp. 277-286. https://doi.org/10.4064/fm136-2-2016

View all publications in research portal

Media experience

Expertise: Mathematics

Experience:  Chris has worked on a number of videos for the School.  He has given public talks and has appeared in videos on YouTube for Meet the Mathematicians.