Many students acquire knowledge of a large number of theorems and
methods of calculus without being able to say how they work
together. This book provides those students with the coherent
account that they need. ""A Companion to Analysis"" explains the
problems that must be resolved in order to procure a rigorous
development of the calculus and shows the student how to deal with
those problems. Starting with the real line, the book moves on to
finite-dimensional spaces and then to metric spaces. Readers who
work through this text will be ready for courses such as measure
theory, functional analysis, complex analysis, and differential
geometry.Moreover, they will be well on the road that leads from
mathematics student to mathematician. With this book, well-known
author Thomas Korner provides able and hard-working students a
great text for independent study or for an advanced undergraduate
or first-level graduate course. It includes many stimulating
exercises. An appendix contains a large number of accessible but
non-routine problems that will help students advance their
knowledge and improve their technique.
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