A Primer for Mathematical Analysis

This book presents a concise introduction to real and complex number systems and metric space theory. The goal is to help students bridge the gap between undergraduate courses in advanced calculus and graduate level material in analysis or related subjects such as differential geometry or probability. The unifying feature in all of these subject areas is the predominance of the limit, and metric space theory is the mathematical language in which limits are formulated. To understand analysis at a graduate level, students need to develop fluency in this language. To facilitate this development, exercises are incorporated into the main text, with many key results posed as problems. Solutions are provided to help readers fill in any gaps.

This book:

Covers the most crucial prerequisites for graduate level analysis, including metric space theory
Contains plentiful exercises to help develop proficiency in the key ideas and techniques, with solutions provided
Features a self-contained presentation designed for students to review or study on their own