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From the Preface:
introduces the elements of the theory
of real-valued functions of a real variable.
The book is aimed at young mathematicians and others who would like to see
a coherent account of basic analysis as a rigorous
mathematical theory. It aims to avoid various extremes:
(1) It does not brush any of the serious
difficulties in analysis proper under the
carpet. The reader is assumed to be
bright, and willing to work hard.
(2) It does not dwell on routine stuff. The reader
has probably already taken a non-rigorous calculus
course, and does not need to be led through that
Anthony G. O'Farrell was born in Dublin, Ireland,
and grew up in County Tipperary before returning to Dublin.
in the Irish Meteorological Service from 1964
to 1968. For most of that time he
was a student of
Mathematical Science at University College, Dublin, where he was
particularly influenced by
P.G. Gormley, who turned him decisively to analysis, particularly
complex analysis. Resigning from the Meteorological Service to devote
himself to Mathematics, he was further influenced by T. J. Laffey
and E. C. Schlesinger, and decided to
continue his studies in the United States.
At Brown University, his horizons were expanded by H. Federer, B. Harris,
A. Browder, J. Wermer, B. Cole, W. Fulton and A. Landman, among others,
and his subsequent work focussed mainly on algebraic and geometric aspects of
real and complex analysis. In 1975, after two years at the
University of California
at Los Angeles, he was appointed Professor of Mathematics at Maynooth College,
He was elected to the Royal Irish Academy in 1980. While engaged in
teaching, research and administration at Maynooth, he contributed to
the mathematical and scientific community in Ireland and abroad, and
visited research institutes and universities in Canada,
France, Germany, India, Israel, Japan, Russia, Sweden, Spain,
the UK and USA, as well as speaking at many international conferences
and collaborating with many researchers.
Now Professor Emeritus of Maynooth University, he devotes himself to
research, writing and pro-bono activities, as well as
a modicum of outdoor activity and cultural pursuits.
He is married, with three
surviving children and seven grandchildren.
Published in USA by Lulu.com for Logic Press
First published 2018. Reprinted with corrections 2019.
Hardcover 340+viii pages