The first book surveying the history and ideas behind reverse mathematics
Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. In Reverse Mathematics, John Stillwell offers a historical and representative view, emphasizing basic analysis and giving a novel approach to logic. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.
John Stillwell is professor of mathematics at the University of San Francisco and an affiliate of the School of Mathematical Sciences at Monash University, Australia. His many books include Mathematics and Its History and Elements of Mathematics (Princeton).
Title: Reverse Mathematics
Author: Stillwell, John
ISBN: 9780691196411
Binding:
Publisher: Princeton University Press
Publication Date: 2019-09-24
Number of Pages: 200
Weight: 0.2981 kg
The field has been due for a general treatment accessible to undergraduates and to mathematicians in other areas. . . . With Reverse Mathematics, John Stillwell provides exactly that kind of introduction. -Carl Mummert, Notices of the American Mathematical Society
Stillwell carefully situates the field in the broader context of the history of mathematics and its foundations, and does a fine job of making the whole endeavor accessible to a general mathematical audience. -Jeremy Avigad, Carnegie Mellon University
Filling an important niche, this book gives readers a good picture of the basics of reverse mathematics while suggesting several directions for further reading and study. -Denis Hirschfeldt, University of Chicago
Stillwell's book is self-contained and includes much background material in analysis, mathematical logic, combinatorics, and computability. I heartily commend this very readable and accessible book. -Stephen Simpson, Vanderbilt University