I went to school in Glasgow, Scotland, and then to Glasgow University where I gained a Honours B.Sc. (Hons) in Mathematics and Natural Philosophy in 1964. I then studied at Imperial College, London, with Jim Clunie, gaining my PhD in 1967.
I then spent 1967-68 at the University of Maryland and Syracuse University, before obtaining a lectureship at Glasgow University (1968-70). I then moved to Queen Elizabeth College, London [now part of Kings College London] for 1970-78, before gaining a Chair at The Open University in Milton Keynes, UK. I was Head of the Pure Mathematics Department for 17 years, and then Dean of the Faculty of Mathematics and Computing for 10 years (1996-2006). I retired in 2007, and was then made Emeritus Professor.
I was Secretary of the Maclaurin Society, Glasgow University (1963-64) and Secretary of the Imperial College Mathematics Society (1965-67). Then I was Council and General Secretary of the London Mathematical Society (1981-91), Editor of the LMS Proceedings (1983-86), Publications Secretary of the LMS (1986-96), and Secretary of the European Mathematical Society (1999-2002). I also organised a range of conferences on Complex Analysis at Durham University in the 1970s and 1980s.
I served for many years as Reviewer for Mathematical Reviews (1966-2013) and Zentralblatt für Mathematik (1968-2013).
I was also External Examiner at around a dozen universities and Teaching Quality Assessor at around ten universities over the years.
Currently I am working on updating my textbooks on Geometry and Advanced Calculus, both published by CUP.
My PhD thesis On univalent polynomials and related classes of functions was written under the direction of Jim Clunie at Imperial College. Since then I have conducted research in univalent functions, complex polynomials, and planar harmonic functions.
Here are my publications:
- Coefficient regions for univalent polynomials of small degree, Mathematika 14 (1967), 165-169; MR 36 # 3971.
- On a conjecture of Ilieff, Proc. Camb. Phil. Soc. 64(1968), 83-85; MR 36 # 3958.
- On functions of bounded boundary rotation I, Proc. Edinburgh Math. Soc. 16 (1969), 339-347; MR 41 # 8642.
- On functions of boundary of bounded rotation II, Bull. London Math. Soc. 1. (1969), 321-322; MR 41 # 8643.
- (with R. R. Hornblower) Sums and products of functions in the MacLane class A, Mathematika 16 (1969), 86-87, MR 40 # 2871.
- (with Chr. Pommerenke) On the Bernstein-Szegö theorem for complex polynomials, Canadian J. Math. 21 (1969), 370-371; MR 38 # 6033.
- (with W. E. Kirwan) On some classes of bounded univalent functions, J. London Math. Soc. (2) 1 (1969), 431-443; MR 40 # 4439.
- (with W. E. Kirwan) A covering theorem for typically-real functions, Glasgow Math. J. 10 (1969), 153-155; MR 40 # 7431.
- On univalent polynomials, Glasgow Math. J. 11 (1970),102-107; MR43 # 2204.
- (with W. E. Kirwan) The Maclaurin coefficients of bounded convex functions, Bull. London Math. Soc. 2 (1970), 159-164; MR 42 # 6211.
- (with W. E. Kirwan & J. G. Clunie) Coefficient estimates for a class of starlike functions, Canadian J. Math. 22 (1970), 476-485; MR 41 # 5614.
- (with W. E. Kirwan) The growth of the maximum modulus of univalent functions, Duke Math. J. 38 (1971), 805-818; MR 45 # 5334.
- (with W. E. Kirwan & J. G. Clunie) On the coefficient problem for functions of bounded boundary rotation, Ann. Acad. Sci. Fenn Ser. A, No. 523 (1973), 18pp, MR 49 # 3108.
- On coefficient problems for certain power series, Proc. Symposium on Complex Analysis (1973), L.M.S. Lecture Notes Series, Vol. 12 (1974), 17-27; MR 54 # 537.
- (with L. Brickman) Coefficient regions for starlike polynomials, Ann. Univ. Mariae-Curie Skladowska Sect. A. 29 (1975), 15-21 (1977); MR 56 # 8819.
- (with W. K. Hayman, W. H. J. Fuchs and Ü. Kuran) A characterisation of harmonic polynomials in the plane, Proc. London Math. Soc., (3) 32 (1976), 213-229; MR 53 # 833.
- (with J. M. Anderson and K. F. Barth) Research problems in complex analysis, Bull. London Math. Soc. 9 (1977), 129-162; MR 55 # 12899.
- The Grunsky coefficients of meromorphic starlike and convex functions, Annals Univ. Mariae-Curie Skladowska, Sect. A 31 (1977), 45-48 (1980); MR 81c: 30054.
- Analytic mappings of the unit disk on a convex domain; Solution to Problem 6071, American Mathematical Monthly 84 (1977), 663.
- (with K. F. Barth and W. K. Hayman) The growth of plane harmonic functions along an asymptotic path, Proc. London Math. Soc. (3) 37 (1978), 363-384; MR 80b: 31001.
- (with W. E. Kirwan) Some covering theorems for analytic functions, J. London Math. Soc. (2) 19 (1979); 93-101; MR 80d: 30011.
- (with J. G. Clunie, Joint Eds.) Aspects of Contemporary Complex Analysis, Academic Press (1980), 527pp; ISBN 0-12-125950-1; MR82f: 30001.
- The Lowner Differential Equation, Aspects of Contemporary Complex Analysis, Academic Press (1980), 79-95; MR 82i: 30029.
- (joint Editor) Collected Papers of J. E. Littlewood, Vols. I and II, Oxford University Press, Oxford (1982); MR84m: 01046.
- (with K. F. Barth and W. K. Hayman) Research Problems in complex analysis, Bull. London Math. Soc. 16 (1984), 490-517; MR86b: 30004.
- (with J. G. Clunie) The extreme points of some classes of polynomials, Math. Proc. Roy. Soc. Edinburgh, 101A (1985), 99-110; MR87c: 30005.
- On the behaviour of continuous functions near infinity, Complex Variables, 5 (1985), 221-228; MR87i: 30060.
- (with T. S. Taha) On some classes of bi-univalent functions, Mathematical Analysis and its Applications, Proceedings of the International Conference on Mathematical Analysis and its Applications, (eds. S. M. Mazhar, A. Hamoui and N. S. Faour), Pergamon Press (1988); 53-60; MR 90a: 30022; & in Studia Univ. Babes-Bolyai Math. 31 (1986), no. 2, 70-77; MR 88k: 30012.
- (with K. F. Barth) Asymptotic tracts of harmonic functions I, Ann. Acad. Sci. Fenn. Series AI Mathematics, 11 (1986), 215-232; MR87k: 31001.
- Growth rates of subharmonic functions in the plane, J. Ramanujan Math. Soc., 1 (1986), 1-7; MR 89g: 31002.
- (with A. K. Lyzzaik) Some covering properties of locally-univalent functions, Ann. Acad. Sci. Fenn. Series AI Mathematics, 13 (1988), 3-23; MR 90c: 30005.
- (with W. K. Hayman) Research problems in complex analysis, Bull. London Math. Soc., (1989) 21 (1989), 1-35; MR 89m: 30001.
- Some covering properties of locally univalent functions, Analysis and Related Mathematical Fields (ed. D. Skordev), Ser. Pliska, Studia Mathematica Bulgarica 11 (1991), 11-14; MR 92m: 30034.
- (with K. F. Barth) Asymptotic tracts of harmonic functions II, Proc. Edinburgh Math. Soc., 38 (1995), 35-52; MR 96h: 31001.
- (with K. F. Barth) Asymptotic tracts of harmonic functions III, International Journal of Mathematics and Mathematical Sciences, 19, no. 4 (1996), 633-636; MR 97k: 31001.
- On univalence, multivalence and infinite-valence, Complex Variables, 33 (1997), 63-74; MR 99a: 30010.
I have also supervised the research students: Peter Jelinski, Paul Hide and Taha S. Taha.
I have also been awareded the Lomonosoff Medal of the Russian Academy of Sciences, for services to mathematics research publishing.
Over the years I taught a wide range of undergraduate and postgraduate pure mathematics courses in a face-to-face situation in Glasgow, London, Maryland and Syracuse universities.
I have also written material for distance learning courses for the (UK) Open University in Complex Analysis, Differential Geometry, Metric and Topological Spaces, Advanced Calculus, Lebesgue Integration, Linear Algebra, Group Theory and Geometry. Associated with this I have made a good number of audio-cassettes and TV programmes, mostly on Advanced Calculus, Geometry and Group Theory.
Externally I have been an External Examiner at around a dozen universities in UK, Ireland and Malaysia; and been a Teaching Quality Assessor at around ten universities in UK.
I have also written two successful textbooks:
Geometry (with M. F. Esplen and J. J. Gray), Cambridge University Press (1999), 514pp; ISBN 0-521-59193-7 (hbk) & 0-521-59787-0 (pbk). MR 2000c: 51001.
Arabic translation: Arab Centre for Arabization, Translation, Authorship and Publication (ACATAP - ALESCO) (2001).
This has now had a second edition:
Geometry (2nd edition) (with M. F. Esplen and J. J. Gray), Cambridge University Press (2012), 587pp; ISBN: 978-1-107-64783-1 (pbk).
Instructors Manual: Geometry (with M. F. Esplen and J. J. Gray), Cambridge University Press (2012); www.cambridge.org/9781107647831;
A First Course in Mathematical Analysis, Cambridge University Press (2006), 453pp; ISBN 0-521-86439-9 (hbk) & 0-521-68424-2 (pbk). Reprinted with corrections, 2012.