**Siobhan Vernon**was given the name

**Siobhan O'Shea**and only after her marriage did she take her husband's name and became known as Siobhan Vernon. She was the daughter of Joseph J O'Shea and his wife M O'Shea, and the family lived in Main Street, Macroom. The 1921 Postal Directory County Cork lists Joseph J O'Shea as living in Main Street and gives his occupation as auctioneer.

Her primary education was at the Convent of Mercy in Macroom. There she studied and took her Primary Leaving Certificate examination at the end of the seventh grade which gave her entry to secondary education. She continued to study at the Convent of Mercy but she also attended the De La Salle, Macroom, a Catholic Voluntary secondary school for boys, for the higher level mathematics classes required for the Leaving Certificate.

She entered University College, Cork in 1949 and, after taking the examinations at the end of her first year of study in the summer of 1950, she was awarded a scholarship. She graduated in 1952 with First Class Honours in Mathematics and Mathematical Physics. Following the award of the B.Sc. she was appointed as a Demonstrator at University College, Cork, while she continued to study for higher degrees. The *Southern Star from Cork* reported on 29 November 1952 [4]:-

O'Shea's role as Demonstrator was part of a support scheme for post-graduate students. At this time the professor of mathematics was Henry St John Atkins and the professor of statics was Tadhg O Ciardha. O'Shea was awarded the degree of M.Sc. in Mathematics and Mathematical Statistics in 1954 and, following the award of the degree, she became a Senior Demonstrator. Henry St John Atkins (1896-1987) was professor of mathematics at Cork from 1936 to 1954 and, in addition, registrar while Alfred O'Rahilly was President of University College, Cork, from 1943 to 1954. Henry St John Atkins was appointed President in 1954 and, since this left mathematics short staffed, Patrick Brendan Kennedy was appointed as a lecturer in mathematics.Miss Siobhan O'Shea, B.Sc., daughter of Mr Joseph J O'Shea and Mrs O'Shea, Main Street, Macroom, was recently appointed a Demonstrator at University College, Cork.

At Cork, Kennedy encouraged O'Shea to undertake research in mathematics. On 17 December 1956 she submitted her paper *Note on an integrability theorem for sine series* to the *Quarterly Journal of Mathematics, Oxford*, and it was published in the following year. In the paper she writes:-

She was appointed to the new full-time post of Assistant in Mathematics at University College, Cork, in 1957 and submitted her second paperI wish to thank Professor P B Kennedy for suggesting the problem treated in this note.

*On a divergent trigonometrical series given by Steinhaus*to the

*Proceedings*of the American Mathematical Society on 28 May 1958. She acknowledged financial support:-

She again thanks Kennedy:-Research sponsored by the Research and Development Command, United States Air Force, through its European Office.

Her third paperI wish to thank Professor P B Kennedy for suggesting this problem to me.

*The absolute convergence of certain lacunary Fourier series*was published in the

*Proceedings*of the Royal Irish Academy in 1960-61. Kennedy suggested to O'Shea that she might benefit from taking study leave and supported her application for leave of absence in session 1962-63. She spent this session at Royal Holloway College, University of London, where she was a Visiting Lecturer for the year. Returning to Cork, she submitted her published papers for a Ph.D. and, in 1964, was awarded the degree by the National University of Ireland. Her thesis was entitled

*Some results in classical analysis*and it appears under the name Johanna (Siobhan) O'Shea. The

*Southern Star from Cork*reported on 7 November 1964 [5]:-

Although we have been unable to determine the precise date on which her father, Joseph O'Shea, died, it is evident from [4] and [5] that he died between 1952 and 1964. O'Shea was appointed as a lecturer at Cork in 1965. She continued to be encouraged by Kennedy and acknowledged this in her next paperAt the recent conferring of degrees at U.C.C., Miss Siobhan O'Shea M.Sc, daughter of Mrs M O'Shea and the late Mr J O'Shea, Main St., Macroom, received her Ph.D. degree in Mathematics. Dr O'Shea has been on the staff in the mathematics department at U.C.C. since she graduated some years ago.

*On power series with non-negative coefficients*(1966). This paper, sent in June 1964 and revised in March 1965, contains the note:-

Kennedy had left Cork in 1963 to take up an appointment at the University of York in England but died at the age of 36 in 1966.I wish to thank Professor P B Kennedy for suggesting the problem treated in this note and also the referee for his helpful comments.

O'Shea's next two publications were *Note on power series of a certain type* (1968) and *A class of power series with no real zeros* (1971). We quote from her obituary written by Paddy Barry concerning her teaching [1]:-

Peter Vernon was a geologist, famed for his paperHer publications were generally in the field of infinite series, in particular trigonometric series, which is mathematical analysis but in her teaching she had an inclination to algebra. For many years she taught the First Arts course and part of the Third Arts one, and gave supplementary lectures through the medium of Irish. Students, at various levels, profited greatly by her lectures; she was well known to the many who went into the teaching profession. If memory serves, she was one of just two women in this country at university level in pure or applied mathematics in the early days.

*Drumlins and Pleistocene ice flow over the Ards Peninsula/Strangford Lough area, County Down, Ireland*(1966). When he wrote this paper he was on the staff of The Queen's University of Belfast, but he was later appointed to the Geology Department of the University of Cork. There he met O'Shea and later the two married; they had four children. For ten years while she was bringing up the children, Siobhan Vernon reduced her teaching to half-time but after this she returned to full-time teaching. She retired in 1988.

Under her married name of Siobhan Vernon, she published the three papers *On power series with non-negative coefficients. II* (1975), *On the critical points of polynomials* (1978) and *On commutativity in certain classes of rings* (1983). The 1978 paper was reviewed by Wolfgang Luh who writes:-

Her 1983 paper is the only one she published on algebra, although as noted above, she liked teaching algebra. This paper gives theorems which generalise results of Des MacHale, one of her colleagues in Cork, which he had published in 1980. Her final publication was a chapter of the bookLetP(n)denote the class of polynomials of degree n ≥2which have all their zeros in the unit disk. The author proves that there exists a numberD=D(n) > 0such that the derivative of any polynomial p inP(n)withp(a) = 0, 0 ≤a≤D, has a zero in|z-^{a}/_{2}| ≤ 1 -^{a}/_{2}.An estimate for D is given.

*Creators of Mathematics: The Irish Connection*which she was invited to contribute by its editor Ken Houston. This chapter was a biography of Patrick Brendan Kennedy and Maebh Long writes in the review of the book [3]:-

In 1995 the Convent of Mercy in Macroom, the school she had attended when young, honoured her with the Catherine McAuley award, given to a "distinguished past pupil".Siobhán Vernon's account of Patrick Brendan Kennedy is well written and engaging, her personal acquaintance with the Professor of Mathematics in Cork and York leads to a moving portrayal of a warm and humorous yet tragic figure.

A Christmas Lunch for retired members of University College Cork staff was held in the Aula Maxima on 12 December 2001. Both Siobhan Vernon and her husband Peter Vernon attended. In the autumn of 2000 her daughter Maude Vernon graduated from Cork with a Bachelor of Business Studies.

**Article by:** *J J O'Connor* and *E F Robertson*