Mathematics: A Very Short IntroductionOUP Oxford, 22 août 2002 - 143 pages The aim of this book is to explain, carefully but not technically, the differences between advanced, research-level mathematics, and the sort of mathematics we learn at school. The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understanding of paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questions about the mathematical community (such as "Is it true that mathematicians burn out at the age of 25?") ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. |
Table des matières
Numbers and abstraction | 17 |
Proofs | 35 |
Limits and infinity | 56 |
Dimension | 70 |
Geometry | 86 |
Estimates and approximations | 112 |
Some frequently asked questions | 126 |
Further reading | 139 |
Autres éditions - Tout afficher
Expressions et termes fréquents
180 degrees abstract method angles answer argument axioms become calculations Chapter chess circle complicated concept coordinates cube curved defined definition dimensional distance divided edges equation Estimates and approximations Euclid's exactly example fact Figure follows four-dimensional four-dimensional sphere give golden ratio graph grid hyperbolic geometry idea infinite decimal Koch snowflake large number Limits and infinity line segment logarithm manifold mathematical proof mathematicians mathematics means molecules multiply natural logarithm negative numbers number of digits number system Numbers and abstraction objects obvious parallel postulate pentagons polygon possible prime number prime number theorem problem proof properties Pythagoras question real numbers rectangle rules sequence shape side lengths simple smaller sort space speed sphere spherical geometry square root statement straight line surface theorem three-dimensional Timothy Gowers trefoil knot triangle two-dimensional understand vertices visualize whole number words