This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, that introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research.
The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is about. We hope that it will also be of interest to teachers or more advanced mathematicians who would like to learn about exciting aspects of mathematics outside of their own work or specialization.
Together with a team of young ``test readers'', editors and authors have taken great care, through a substantial ``active editing'' process, to make the contributions understandable by the intended readership.
Author(s): Terence Tao (auth.), Dierk Schleicher, Malte Lackmann (eds.)
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2011
Language: English
Pages: 220
Tags: Mathematics, general
Front Matter....Pages I-XIV
Structure and Randomness in the Prime Numbers....Pages 1-7
How to Solve a Diophantine Equation....Pages 9-19
From Sex to Quadratic Forms....Pages 21-41
Small Divisors: Number Theory in Dynamical Systems....Pages 43-54
How do IMO Problems Compare with Research Problems?....Pages 55-69
How do Research Problems Compare with IMO Problems?....Pages 71-83
Graph Theory Over 45 Years....Pages 85-95
Communication Complexity....Pages 97-117
Ten Digit Problems....Pages 119-136
The Ever-Elusive Blowup in the Mathematical Description of Fluids....Pages 137-164
About the Hardy Inequality....Pages 165-180
The Lion and the Christian, and Other Pursuit and Evasion Games....Pages 181-193
Three Mathematics Competitions....Pages 195-205
Complex Dynamics, the Mandelbrot Set, and Newton’s Method — or: On Useless and Useful Mathematics....Pages 207-220
