The book covers the set of real numbers, elementary point-set topology
, sequences and series of real numbers, limits and continuity, differentiation, the Riemann integral, sequences and series of functions, functions of several real variables, the Lebesgue integral, and many other related subjects over nine chapters.
It is meant to precede his 2010 An Epsilon of Room, Volume 1, which introduces the analysis of Hilbert and Banach spaces, point-set topology
, and related topics.
These approaches continue through the canon and are employed in subsequent courses such as Linear Algebra, Probability and Statistics, Real Analysis, Point-Set Topology
Readers should understand basics of point-set topology
and differential topology.
There is also content revision in the following areas: Introducing point-set topology
before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.