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,
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,
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
dimensions
Also covers the Riemann integral, integrability, improper integrals, and series expansions