A Contextual Introduction to Real Analysis: How we got from there to here is an innovative introduction to real analysis that presents the subject through the historical development of its key ideas. Rather than introducing rigorous definitions as isolated abstractions, the text shows how concepts such as limits, continuity, convergence, differentiation, and integration emerged in response to specific mathematical challenges. Historical context is woven into the structure of the book, helping students understand both the motivation and necessity behind modern analysis.
The second edition expands the book’s coverage with new material on the Fundamental Theorem of Calculus, the Cauchy, Riemann, and Darboux integrals, and an introduction to Cantor’s set-theoretic framework, measure theory, and the Lebesgue integral. Designed for undergraduate real analysis courses, the text combines historical narrative, guided proof development, and integrated exercises to help students transition from intuitive reasoning to rigorous mathematics. By connecting the evolution of mathematical ideas with modern theory, the book offers a distinctive and engaging pathway into one of mathematics’ most challenging subjects.
Robert Rogers is a SUNY Distinguished Teaching Professor of Mathematics at SUNY Fredonia where he has been on the faculty since 1987. He received his BS in Mathematics with Certification in Secondary Education from SUNY – Buffalo State, his MS in Mathematics from Syracuse University, and his PhD in Mathematics from the University at Buffalo. He is a past president of the Association of Mathematics Teachers of New York State and a former chair and governor of the Mathematical Association of America Seaway Section. He is a former editor of the New York State Mathematics Teachers’ Journal and is an MAA – Seaway Section Distinguished Lecturer. He is a recipient of the SUNY Fredonia President’s Award for Excellence in Teaching and the MAA Seaway Section’s Clarence Stephens Award for Teaching Excellence. He is a recipient of the MAA Distinguished Service Award – Seaway Section and is a member of the New York State Mathematics Educators’ Hall of Fame.
Eugene Boman is Professor, Emeritus at the Harrisburg campus of the Pennsylvania State University. He has taught college level mathematics since he began his graduate studies at the University of Connecticut in 1984. In 2008 he won the Carl B. Allendorfer Award for excellence in expository mathematical writing from the editors of Mathematics Magazine for the article “Mom! There’s an Astroid in My Closet” (Mathematics Magazine, Vol. 80 (2007), pp. 247-273). He earned his BA from Reed College in 1984. He earned his MA in 1986 and his Ph.D. in 1993, both from the University of Connecticut.
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