Mastering the Skills of Analysis: Analysis Workbook

Another book for the first proof based analysis course: Why in the world should anyone care? Most books present the theory in the right order, with precision and in detail. This is essential because one point of the course is to learn the precise ideas and results of basic analysis. Doing analysis is also an essential skill for mastery and moving further in analysis. While texts contain exercises, the explanation of skills and a plan of organized practice is often missing. This book complements traditional books by explaining and illustrating the skills of a first course in analysis and giving a plan of organized practice to master them.

I am a mathematician working in many areas intersecting analysis. I've published about 200 papers, 9 mathematics books. I was fortunate to have excellent teachers, colleagues, collaborators, students and mentors. I've directed many undergraduate research projects, master's projects and 43 PhD students of high accomplishment. PhD students of my PhD students are directing their own PhD students! My own teachers stressed helping students achieve. Mathematics doesn't progress if our students are not better mathematicians that we are. I have been teaching introductory analysis since the 1980's and have a long-standing interest in how we learn new material, understand it, analyze, retain and forget.