A Passage to Modern Analysis is an exceptionally well-written and reader-friendly introduction to real analysis, making it an ideal resource for students of mathematics and its applications at the advanced undergraduate and beginning graduate levels. The text strikes an excellent balance between providing in-depth coverage and maintaining accessible exposition, ensuring that students can develop both intuition and understanding.
The book features a rich array of examples, problems, and clear explanations that help open up a student's intuition while still covering deep areas of real analysis. A yearlong course based on this text offers a solid foundation for further study or application of real analysis at the graduate level. While primarily grounded in the analysis of R and Rn, the book also introduces and discusses more general settings such as inner product spaces, normed spaces, and metric spaces at appropriate points.
The final five chapters serve as a bridge to advanced topics, including ordinary differential equations, Fourier series and partial differential equations, Lebesgue measure and the Lebesgue integral, and Hilbert space. This structure allows the book to introduce interesting and useful developments beyond Euclidean space, highlighting the important roles that analysis concepts play in these areas. Overall, A Passage to Modern Analysis prepares readers for further exploration of advanced mathematical topics and applications.