Three infinities in mathematics : projective geometry, infinitesimal analysis, set theory / Marco Panza, Daniele C. Struppa.
| Author/creator | Panza, Marco author. |
| Other author | Struppa, Daniele Carlo, 1955- author. |
| Format | Book |
| Publication | Cham : Springer International Publishing, 2026. |
| Copyright Date | ©2026 |
| Description | xv, 431 pages : illustrations ; 24 cm. |
| Subjects |
| Series | Undergraduate texts in mathematics. Readings in mathematics Undergraduate texts in mathematics. Readings in mathematics. |
| Contents | Introduction -- Part 1. Infinity in Projective Geometry -- The Geometry of the Painters -- Appendices to Chapter 1. Projective Geometry -- Part 2. Infinitesimal Analysis -- Inklings of Infinity in Greek Mathematics -- Appendices to Chapter 3 -- The Birth and Development of Calculus -- Appendices to Chapter 4 -- Part 3. Set Theory and Infinity -- Naive Set Theory -- Appendice to Chapter 5 -- Axiomatic Set Theory -- Appendices to Chapter 6 -- Conclusions: Three Infinities or Just One? |
| Abstract | This book is intended as conceptual introduction to three mathematical theories arising from the attempt to understand (actual) infinity. Though the treatment does not avoid technical aspects, it tries to explain their origins and purposes. The book is divided into three parts, each composed of two chapters and a few appendices. Each part presents in detail one of three moments in which mathematicians made a concerted effort to control the idea of infinity: Projective Geometry, Infinitesimal Calculus, and Set Theory. The text includes exercises and philosophical and/or historical remarks. It is written both for non-mathematicians interested in understanding the most relevant ideas that govern these theories, and for professional mathematicians interested in exploring the possibility of a conceptually-engaged presentation of mathematical contents. The book can be used for advanced undergraduate students, as well as for beginning graduate students. |
| Bibliography note | Includes bibliographical references (pages 426-431). |
| ISBN | 9783032002761 (hardback) |
| ISBN | 3032002761 |
| ISBN | electronic book |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Joyner | General Stacks | QA9 .P26 2026 | ✔ Available | Place Hold |