Curriculum Vitæ

Personal Details

Name: Dr. David Andrew WOOD

Address: Mathematics Institite, University of Warwick, Coventry, CV4 7AL.

Telephone (work): 024 7652 3592

Email (work): david.wood(at)warwick.ac.uk

Email (personal): dave(at)dave-wood.org

Fax (work): 024 7652 4182

Nationality: British

Education

1992 to 1995 University of Warwick, Coventry, CV4 7AL.

PhD. in Mathematics (graduated July 1996):

Thesis title “Coupled Oscillators With Internal Z2 Symmetry”. Main results using Equivariant Bifurcation theory to study a new class of coupled systems in the cases of both steady-state and Hopf bifurcations. Application to a biological system which is also of interest to roboticists. Supervised by Ian Stewart.

1991 to 1992 University of Warwick, Coventry, CV4 7AL.

MSc. in Mathematics:

Dissertation title “Towards Modelling an Insects Central Pattern Generator by Networks of Coupled Nonlinear Oscillators”. Courses taken include Manifolds, Dynamical Systems, Dynamical Systems with Symmetry and Mathematical Biology.

1988 to 1991 University of Warwick, Coventry, CV4 7AL.

BSc. (hons) in Applied Mathematics: First Class.

1982 to 1988 Dr. Challoners Grammar School, Amersham, Bucks.

4 GCE A’levels (Maths, Further Maths, Physics, History ), 1 GCE OA’level (Maths), 9 GCE O’levels grades A-C.

Work Experience

July 2006 to present Mathematics Institute, UNIVERSITY OF WARWICK, CV4 7AL.

Principal Teaching Fellow (FA 8), Director of Undergraduate Studies (see below for details).

July 1999 to 2006 Mathematics Institute, UNIVERSITY OF WARWICK, CV4 7AL.

Temporary Lecturer, Teaching Fellow: Teaching load equivalent to 2 ten week lecture courses, 23 undergraduate tutees and one MSc. student. In addition  responsible for ‘Mathstuff’, a Web based teaching and learning resource for the undergraduates in the department and increasing administrative duties (First year exam secretary, undergraduate support class organisation, etc.)

October 1997 to July 1999 OCIAM, Mathematical Institute, UNIVERSITY OF OXFORD, 24-29 St. Giles, Oxford, OX1 3LB.

Research Assistant funded by EPSRC

October 1998 to October 1999 Somerville College, OXFORD.

College Lecturer: Tutoring undergraduates at the college in Applied Mathematics.

October 1995 to October 1997 Mathematics Institute, UNIVERSITY OF WARWICK, Coventry, CV4 7AL.

Research Assistant: Working under Ian Stewart on a DTI funded project (Carrier Technology Initiative) on the dynamic control of a spring coiling machine (DYNACON) using traditional, fuzzy logic and chaos control techniques. The project also looked at quality control testing of strip using novel approaches.

October 1994 to October 1995 Mathematics Institute, UNIVERSITY OF WARWICK, Coventry, CV4 7AL.

Teaching Assistant

Details of Current Post

I have been in continuous employment by the Mathematics Institute, University of Warwick, since July 1999, and since 2006 as Director of Undergraduate Studies.

Teaching duties

• MA240 Modelling Natures Nonlinearity, which attempts to introduce the students to some quite deep mathematical concepts through their application to phenomena exhibited by nature. Second/Third year undergraduate level, 30 lectures, assessment: two assignments and a mini-project.
• MA133 Differential Equations: First year undergraduate module introducing first and second order differential equations, difference equations and 2×2 systems of ODEs. 30 lectures, assessment: 15% by assignments, 85% by 2 hour exam.
• I also act as personal tutor to 18 students and regularly take on 4th year projects.

Administrative duties as Director of Undergraduate Studies

• Responsible for all things undergraduate, including regulations, course transfers, unusual options, arranging teaching for support classes and supervisions, first year exam secretary.
• Currently sitting on various committees: in both the mathematics department (Teaching Committee, Staff Student Liaison Committee, Exam Boards for all years) and University (Sub Faculty of Science, Campus Life Committee, Faculty of Science, E-Learning Steering, IATL Management Committee).

Teaching Experience

• In academic year 2007/8 I was a “commendee” in the Warwick Awards for Teaching Excellence (WATE) after reaching the final shortlist of 10.
• I have taught the course MA240 Modelling Natures Nonlinearity at Warwick most years since 1995 apart from when I was at Oxford. This is a course primarily for second year undergraduates which introduces some deep ideas about nonlinear mathematics to students without the necessary background for a rigorous approach. The course is 100% assessed, through 2 assessments, which includes ‘walk-through’ exam-style questions, sometimes a small amount of computer simulation and a small but significant compulsory project. The project in particular has proved extremely popular with students in the past and often shows a lot of originality and insight. I have put together a complete set of printed lecture notes for the course and in the three years I have been teaching this course I have received very positive feedback from the students.
• Since 2006 I have taught MA133 Differential Equations (350 students) introducing first and second order differential equations, difference equations and 2×2 systems of ODEs.
• For two years (99/00, 00/01) I taught the first year course “3D Geometry and Motion II”, a core 15 lecture course for the first year mathematicians (220 students) essentially covering the various extensions of integration of single variables to higher dimensions.
• I have also taught the first year core module Foundations (now module code MA132) for a number of years both to students from the Mathematics Department and those on joint degrees. This is a first term module introducing students to the idea of proof, set theory, functions, logic, equivalence relations and a little group theory.
• While a Lecturer at Somerville College I taught Applied Mathematics, mainly to the colleges first year mathematicians. This consisted of holding small group tutorials every week during term time and setting and marking weekly assignments and termly College exams.
• For two years at Oxford University I assisted with examples classes for the third year course ‘b10 Nonlinear Systems’.
• For four years from 1992 to 1995, as a graduate student, I helped supervise the first year course Experimental Maths, at Warwick University; a mixture of simple experimental observation followed by rigorous mathematical modelling and ran for five weeks each year. During the same period I also acted as a ‘supervisor’ to first and second year undergraduates which involved giving support to small groups of students on a weekly basis. In 1996 and 1997 I continued with these, with, in addition, acting as personal tutor to some first, second and third year undergraduates.
• I am developing a module on Bifurcations, Symmetry and Catastophes aimed at 3rd/4th year students to possibly be introduced for 2010/11 academic year.

Gifted and Talented

In 2002 I was the course leader for mathematics at the inaugural Summer School of the National Academy for Gifted and Talented Youth (NAGTY). The main focus of this was the three week summer school held at Warwick University (residential for the students attending) for which I had to provide and teach material for 20 children, ranging from ages 11 to 16 who had a range of different backgrounds. I continued to be a course leader at the Warwick Summer Schools for the duration of NAGTY which came to an end in 2007. I also ran three online projects based on population modelling, called “Gaia Island”. These project were a mixture of online work using forums and a web site along with a small number of outreach sessions at the University. There were typically 70-80 students registered for each of these projects, running over 8 to 12 weeks. In addition I was involved in several strategy events and at one stage as a
consultant.

NAGTY has now been replaced at Warwick by IGGY (International Gateway for Gifted Youth) which aims to use our experience of gifted education to bring together exceptional children from all over the world. So far there have been Summer and Winter schools in Warwick, Singapore and Botswana for which I have been a course leader again (Mathematics through the eyes of an ant).

From March 2011the strategic decision was made by the University to concentrate more on the online provision as part of the University’s strategy, and I am currently the Academic Leader in this process, with my duties shared between encouraging fellow academics to contribute exciting content and leading the Junior Commission, “Energy 2025″ (as well as providing content myself).

Research Interests and Activities

My research interests are two-fold, although the two are not necessarily unrelated. Firstly I am interest in issues in Equivariant Bifurcation Theory, in particular its application to systems of coupled cells/oscillators with some inherent symmetry properties. There are still many unanswered questions to consider in such systems, especially when one allows an ‘internal symmetry’ to exist within each cell when uncoupled. The current state of research in this area suggests that there are many interesting phenomena to study, for both the abstract side and applications. Of particular interest are systems where the coupling leads to a ‘wreath product’ of the global and internal symmetries (essentially a semi-direct product). Applications with which I am specifically involved include

• The modelling of an insects ‘Central Pattern Generator’ (essentially the network of neurons controlling inter-limb coordination during locomotion) using networks of coupled oscillators. Such a problem is of interest to both biologists, industrialists and roboticists and has lead from the study of a relatively low number of oscillators (six) to consideration of coupled rings of a large number of cells (typically 20) due to evolutionary considerations. Recent work by others have made this problem a little more tractable and has also led to some other possible implications to my models.
• Using the symmetry properties of a derived performance measure to optimize the placement of an array of hydrophones (a network of typically 15-20 underwater microphones). The performance measure is a in some sense a function of the success of such an array detecting the direction of a plane wave in an isotropic noise field. The results of this analysis appeared in the European Journal of Applied Mathematics and essentially they show that a numerical optimization problem in R^{2n} where n is of the order of 20 or so, can be reduced to a series of numerical optimizations in R or R².

The latter problem in particular has led to more theoretical work of bifurcation analysis in O(2)xSn-equivariant functions. It turns out that the branches of solutions that are interesting are those joining two branches from a primary bifurcation which are created through secondary bifurcations. The analysis, which must be done for a fifth-order truncation in 2n dimensions, can be simplified due to the symmetries present, but is still turning out to be rather complicated. The patterns of solution observed however are rather nice, and in addition to the hydro phone problem detailed above there is potential for some other interesting applications.

In addition there are some other research problems with which I am interested, which I intend to pursue in the future when time allows.

Maths in Industry

I have been involved in mathematical probelms in industry for many years, including my first post-doc working on control in the spring making industry, and my two years at Oxford where one of my main duties was writing reports for the OCIAM Friday Workshops with Industry. I have attended nearly all of the UK European Study Groups with Industry since 1998, and several Danish meetings, and in 2010 was the organiser for ESGI 73 held at Warwick.

Selected Publications

• D. Wood, Making Better Springs Using Aspects of Chaos Theory, Journal of Mechanical Engineering Science 220, pp 253-269 2006.
• D. Wood, D. Allwright, Optimisation Of Hydrophone Placement: A Dynamical Systems Approach, European Journal of Applied Mathematics 14, pp369-386, 2003.
• D. Wood, A Cautionary Tale Of Coupling Cells With Internal Symmetries, International Journal of Bifurcation and Chaos 11, pp 123-132, 2001.
• M. Bayliss, R. Morris, M. Muldoon, M. Readman, L. Reynolds, I. Stewart, D. Wood, Control Of Free Length When Coiling A Helical Spring, IEE Control Theory and Applications, 148, 2001
• D. Wood, D. Allwright, Symmetries And Mode Interactions In The Optimisation Of Hydrophone Placement In Acoustic Arrays, Equadiff 99 Proceedings, World Scientific, Vol 1, 2000.
• D. Wood, Hopf Bifurcations In Three Coupled Oscillators With Internal Z2 Symmetries, Dynamics and Stability of Systems 13, pp 54-93, 1998.