Richard Miles

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Dr Richard Miles BSc, PGCE, PhD, SFHEA

Senior Lecturer in Mathematics and Secondary Education

Summary

I am a Senior Lecturer in Mathematics and Secondary Education.  I have previously worked as a teacher, lecturer and researcher in schools and universities in both the UK and Sweden.  My mathematics research background is in the field of Algebraic Dynamical Systems.

About

I am Senior Lecturer in Mathematics and Secondary Education at the Sheffield Institute of Education.

My teaching career began in secondary schools in the UK before pursuing a PhD in the field of Algebraic Dynamical Systems.  I subsequently taught and researched at the University of East Anglia before moving to Sweden to research at the Royal Technical Institute in Stockholm.  Whilst living in Stockholm, I returned to school teaching for several years at the Internationella Engelska Gymnasiet and developed a deeper interest in pedagogy and comparative educational practices in Sweden and the UK.  I also taught mathematics in my second language of Swedish as a Senior Lecturer at Uppsala University before returning to the UK

I teach on the BSc (Hons) Mathematics with Education and QTS degree, Mathematics Subject Knowledge Enhancement for PGCE and PGDE for Teach First

Teaching

Department of Teacher Education

College of Social Sciences and Arts

I teach on 20th and 21st Century Applications of Mathematics, Development of Geometric ideas, Infinite Processes, Mathematics for Meaning A, Problem Solving through Modelling, Emerging Philosophy of Teaching and Learning, Mathematics Subject Knowledge Enhancement.

Mathematics

Research

Publications

Journal articles

Miles, R. (2020). An alternative route to the Mandelbrot set: connecting idiosyncratic digital representations for undergraduates. Teaching Mathematics and Its Applications. http://doi.org/10.1093/teamat/hraa003

Miles, R. (2018). The taxicab locus of Apollonius: promoting exploratory routes to the punchline using rich undergraduate tasks. International Journal of Mathematical Education in Science and Technology, 1-9. http://doi.org/10.1080/0020739x.2018.1555725

Miles, R., & Ward, T. (2018). The dynamical zeta function for commuting automorphisms of zero-dimensional groups. Ergodic Theory and Dynamical Systems, 38 (4), 1564-1587. http://doi.org/10.1017/etds.2016.77

Miles, R. (2017). A dynamical zeta function for group actions. Monatshefte für Mathematik, 182 (3), 683-708. http://doi.org/10.1007/s00605-016-0909-x

Miles, R., & Ward, T. (2015). Directional uniformities, periodic points, and entropy. Discrete and Continuous Dynamical Systems - Series B, 20 (10), 3525-3545. http://doi.org/10.3934/dcdsb.2015.20.3525

Miles, R. (2015). A natural boundary for the dynamical zeta function for commuting group automorphisms. Proceedings of the American Mathematical Society (PROC), 143 (7), 2927-2933. http://doi.org/10.1090/S0002-9939-2015-12515-4

Miles, R. (2015). Orbit growth for algebraic flip systems. Ergodic Theory and Dynamical Systems, 35 (8), 2613-2631. http://doi.org/10.1017/etds.2014.38

Bell, J., Miles, R., & Ward, T. (2014). Towards a Pólya-Carlson dichotomy for algebraic dynamics. Indagationes Mathematicae, 25 (4), 652-668. http://doi.org/10.1016/j.indag.2014.04.005

Miles, R. (2013). Synchronization points and associated dynamical invariants. Transactions of the American Mathematical Society (TRAN), 365, 5503-5524. http://doi.org/10.1090/S0002-9947-2013-05829-1

Miles, R. (2010). Finitely represented closed orbit subdynamics for commuting automorphisms. Ergodic Theory and Dynamical Systems, 30 (6), 1787-1802. http://doi.org/10.1017/50143385709000741

Everest, G., Miles, R., Stevens, S., & Ward, T. (2010). Dirichlet series for finite combinatorial rank dynamics. Transactions of the American Mathematical Society (TRAN), 362 (1), 199-227. http://doi.org/10.1090/S0002-9947-09-04962-9

Miles, R., & Ward, T. (2010). A dichotomy in orbit-growth for commuting automorphisms. Journal of the London Mathematical Society, 81 (3), 715-726. http://doi.org/10.1112/jlms/jdq010

Miles, R., & Ward, T. (2010). A directional uniformity of periodic point distribution and mixing. Discrete and Continuous Dynamical Systems - Series A, 30 (4), 1181-1189. http://doi.org/10.3934/dcds.2011.30.1181

Miles, R., & Björklund, M. (2009). Entropy range problems and actions of locally normal groups. Discrete and Continuous Dynamical Systems - Series A, 25 (3), 981-989. http://doi.org/10.3934/dcds.2009.25.981

Miles, R. (2008). The entropy of algebraic actions of countable torsion-free abelian groups. Fundamenta Mathematicae, 201, 261-282. http://doi.org/10.4064/fm201-3-4

Miles, R. (2008). Homoclinic points of non-expansive automorphisms. Aequationes Mathematicae, 26 (1-2), 1-18. http://doi.org/10.1007/s00010-007-2919-1

Miles, R. (2008). Periodic points of endomorphisms on solenoids and related groups. Bulletin of the London Mathematical Society, 40 (4), 696-704. http://doi.org/10.1112/blms/bdn052

Miles, R., & Ward, T. (2008). Orbit-counting for nilpotent group shifts. Proceedings of the American Mathematical Society (PROC), 137, 1499-1507. http://doi.org/10.1090/S0002-9939-08-09649-4

Miles, R., & Ward, T. (2008). Uniform periodic point growth in entropy rank one. Proceedings of the American Mathematical Society (PROC), 136 (1), 359-365. http://doi.org/10.1090/S0002-9939-07-09018-1

Everest, G., Miles, R., Stevens, S., & Ward, T. (2007). Orbit-counting in non-hyperbolic dynamical systems. Journal für die reine und angewandte Mathematik, 608, 155-182. http://doi.org/10.1515/CRELLE.2007.056

Miles, R. (2007). Zeta functions for elements of entropy rank one actions. Ergodic Theory and Dynamical Systems, 27 (2), 567-582. http://doi.org/10.1017/50143385706000794

Miles, R., & Ward, T. (2006). Periodic point data detects subdynamics in entropy rank one. Ergodic Theory and Dynamical Systems, 26 (6), 1913-1930. http://doi.org/10.1017/5014338570600054x

Miles, R., & Ward, T. (2006). Mixing actions of the rationals. Ergodic Theory and Dynamical Systems, 26 (6), 1905-1911. http://doi.org/10.1017/50143385706000356

Miles, R. (2006). Expansive algebraic actions of countable abelian groups. Monatshefte für Mathematik, 147 (2), 155-164. http://doi.org/10.1007/s00605-005-

Miles, R. (2001). Dynamical systems arising from units in Krull rings. Aequationes Mathematicae, 61 (1-2), 113-127. http://doi.org/10.1007/s000100050

Einsiedler, M., Lind, D., Miles, R., & Ward, T. (2001). Expansive subdynamics for algebraic Z^d-actions. Ergodic Theory and Dynamical Systems, 21 (6), 1695-1729. http://doi.org/10.1017/S014338570100181X

D'Ambros, P., Everest, G., Miles, R., & Ward, T. (2000). Dynamical systems arising from elliptic curves. Colloquium Mathematicum, 84-85 (1), 95-107.

Book chapters

Miles, R., Staines, M., & Ward, T. (2015). Dynamical invariants for group automorphisms. In Bhattacharya, S., Das, T., Ghosh, A., & Shah, R. (Eds.) Recent trends in ergodic theory and dynamical systems : international conference in honor of S.G. Dani's 65th birthday, December 26-29, 2012, Vadodara, India. (pp. 231-258). American Mathematical Society: http://doi.org/10.1090/conm/631

Other activities

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