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The 17th-century calculus of Newton and Leibniz was built on shaky foundations, and it wasn't until the 18th and 19th centuries that mathematicians – especially Bolzano, Cauchy, and Weierstrass – began to establish a rigorous basis for the subject. The resulting discipline is now known to mathematicians as analysis. This book, aimed at readers with some grounding in mathematics, describes the nascent evolution of mathematical analysis, its development as a subject in its own right, and its wide-ranging applications in mathematics and science, modelling reality from acoustics to fluid dynamics, from biological systems to quantum theory.
Acknowledgements
1. Taming Infinity
2. All change...
3. Should I believe my computer?
4. Dimensions aplenty
5. I'll name that tune in...
6. Putting the i in analysis
7. But there's more...
Appendix
Historical timeline
References
Further Reading
Index
Richard Earl is a Departmental Lecturer in the Mathematical Institute, University of Oxford, and the Ben Delo Fellow in Mathematics at Worcester College, Oxford. From 2003-13, he was Admissions Coordinator and Schools Liaison Officer in the department, roles which included promoting mathematics within schools and colleges. From 2013-22, he was Director of Undergraduate Studies. He has won several teaching awards within the University for his teaching and lecturing. He is the author of Towards Higher Mathematics: A Companion (2017), Topology: A Very Short Introduction (OUP, 2019), and editor of the current edition of The Concise Oxford Dictionary of Mathematics (OUP, 2021).
