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. The most crucial prerequisites for graduate level analysis are given a self-contained presentation within the book. To facilitate self-study and promote the development of fluency, exercises are incorporated into the main text, with many key results posed as problems. Solutions are provided to help the reader fill in any gaps.