1: Preliminaries
2: Limit of a sequence, an idea, a definition, a tool
3: Interlude: different kinds of numbers
4: Up and down - increasing and decreasing sequences
5: Sampling a sequence - subsequences
6: Special (or specially awkward) examples
7: Endless sums - a first look at series
8: Continuous functions - the domain thinks that the graph is
unbroken
9: Limit of a function
10: Epsilontics and functions
11: Infinity and function limits
12: Differentiation - the slope of the graph
13: The Cauchy condition - sequences whose terms pack tightly
together
14: More about series
15: Uniform continuity - continuity's global cousin
16: Differentiation - mean value theorems, power series
17: Riemann integration - area under a graph
18: The elementary functions revisited
Brian McMaster studied at Queen's University Belfast, graduating
with a PhD in 1972, and has served his alma mater department in
various capacities including those of Adviser of Studies, Head of
Research and Associate Director of Education. His publication
profile covers over sixty refereed journal articles, mostly in the
area of analytic topology but incorporating a smattering of
applications in disciplines as diverse as probabilistic metric
spaces and decision
support theory. He has successfully supervised twelve individual
postgraduate programmes including eight PhDs. He is presently
formally retired but continues to deliver a full undergraduate
teaching load
on a voluntary basis, thus witnessing his lifelong commitment to
and passion for communicating mathematics to students. His teaching
interests focus around analysis (real and complex) and set theory
and their development into various fields especially that of
analytic topology. Aisling McCluskey graduated from Queens
University Belfast with a PhD in 1990 and subsequently was awarded
a postdoctoral fellowship in Toronto. She was appointed to a
permanent lectureship in Mathematics in NUI, Galway
in January 1992. Since then, she has established a meaningful and
rewarding academic career there, maintaining an active research
profile whilst holding the teaching and learning of mathematics
central
to her academic endeavour.
She has enjoyed numerous international visiting researcher
positions, and in like kind has hosted many eminent researchers at
NUI, Galway. She has received institutional and national awards for
excellence in teaching. In scholarly pursuit of her passion for and
commitment to mathematics education, she completed a postgraduate
certificate in teaching and learning in higher education (2009), a
postgraduate diploma (2010) and a Masters degree (2011) at NUI
Galway.
The clear, concise writing makes this book ideal for equipping
undergraduates with a solid conceptual framework for approaching
analysis rigorously and confidently.
*V.K. Chellamuthu, CHOICE*
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