The size of Wiman–Valiron discs for subharmonic functions of a certain type

Wiman–Valiron theory and the results of Macintyre about “flat regions” describe the asymptotic behaviour of entire functions in certain discs around maximum points. We use a technique of Bergweiler, Rippon and Stallard to describe the asymptotic behaviour of a certain type of subharmonic function, and a technique of Bergweiler to estimate the size of its Wiman–Valiron discs from above and below. The results are extended to -subharmonic functions

A proactive collaborative workshop approach to supporting student preparation for graduate numerical reasoning tests

Numerical competency and reasoning skills are of high importance and high concern to graduate recruiters. The use of numerical reasoning tests in graduate recruitment is increasing. Many students are unaware of the prevalence of these tests, and the need for refreshment and practice of numerical skills. We describe a stand-alone workshop that is jointly run by the Maths Learning Centre and the Careers And Employability Service at De Montfort University. This workshop helps students to proactively prepare for these tests by providing test information, preparation tips and signposting to further maths and career support. The workshop’s main feature is a testing activity that is run individually and for small groups. Findings suggest that these workshops have been effective and are popular with students

On the derivatives of composite functions

Let g be a non-constant polynomial and let f be transcendental and meromorphic of sub-exponential growth in the plane. Then if k\geq 2 and Q is a polynomial the function (f\circ g)^{(k)}-Q has infinitely many zeros. The same conclusion holds for k \geq 0 and with Q a rational function if f has finitely many poles. We also show by example that this result is sharp

Research problems in function theory: fiftieth anniversary edition

In 1967 Walter K. Hayman published ‘Research Problems in Function Theory’, a list of 141 problems in seven areas of function theory. In the decades following, this list was extended to include two additional areas of complex analysis, updates on progress in solving existing problems, and over 520 research problems from mathematicians worldwide. It became known as ‘Hayman's List’. This Fiftieth Anniversary Edition contains the complete ‘Hayman's List’ for the first time in book form, along with 31 new problems by leading international mathematicians. This list has directed complex analysis research for the last half-century, and the new edition will help guide future research in the subject. The book contains up-to-date information on each problem, gathered from the international mathematics community, and where possible suggests directions for further investigation. Aimed at both early career and established researchers, this book provides the key problems and results needed to progress in the most important research questions in complex analysis, and documents the developments of the past 50 years