An Introduction to Analysis

An Introduction to Analysis is an essential undergraduate textbook on algebra, topology, and calculus, designed for students considering advanced degrees in mathematics. It serves as an ideal primer, offering basic results in these subjects.

This unique textbook is perfect for a one-year course and introduces students to rigorous proofs and formal mathematical writing—skills necessary for excelling in the field. With a range of problems throughout, An Introduction to Analysis covers n-dimensional calculus from the beginning, including differentiation, the Riemann integral, series, and differential forms, as well as Stokes's theorem. This allows students serious about mathematics to progress swiftly to more challenging topics.

The book discusses fundamental material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It also covers linear algebra topics, 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 combine these topics in one easy-to-use and comprehensive volume. It provides a rigorous introduction to calculus in one and several variables, introduces students to basic topology, and addresses topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappings. Additionally, it discusses differential forms and Stokes's theorem in n dimensions, as well as the Riemann integral, integrability, improper integrals, and series expansions.