An essential undergraduate textbook on algebra, topology, and
calculus An Introduction to Analysis is an essential primer on
basic results in algebra, topology, and calculus for undergraduate
students considering advanced degrees in mathematics. Ideal for use
in a one-year course, this unique textbook also introduces students
to rigorous proofs and formal mathematical writing--skills they
need to excel. With a range of problems throughout, An Introduction
to Analysis treats n-dimensional calculus from the
beginning-differentiation, the Riemann integral, series, and
differential forms and Stokes's theorem-enabling students who are
serious about mathematics to progress quickly to more challenging
topics. The book discusses basic material on point set topology,
such as normed and metric spaces, topological spaces, compact sets,
and the Baire category theorem. It covers linear algebra as well,
including vector spaces, linear mappings, Jordan normal form,
bilinear mappings, and normal mappings. Proven in the classroom, An
Introduction to Analysis is the first textbook to bring these
topics together in one easy-to-use and comprehensive volume.
Provides a rigorous introduction to calculus in one and several
variables Introduces students to basic topology Covers topics in
linear algebra, including matrices, determinants, Jordan normal
form, and bilinear and normal mappings Discusses differential forms
and Stokes's theorem in n dimensions Also covers the Riemann
integral, integrability, improper integrals, and series expansions
General
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