An Invitation to Mathematics: From Competitions to ResearchDierk Schleicher, Malte Lackmann This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, which 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. |
Contents
| 1 | |
How to Solve a Diophantine Equation | 8 |
From Sex to Quadratic Forms | 21 |
Number Theory in Dynamical Systems | 42 |
How do IMO Problems Compare with Research Problems? | 55 |
How do Research Problems Compare with IMO Problems? | 71 |
Graph Theory Over 45 Years | 84 |
Communication Complexity | 97 |
Ten Digit Problems | 118 |
The EverElusive Blowup in the Mathematical Description of Fluids | 137 |
About the Hardy Inequality | 165 |
The Lion and the Christian and Other Pursuit and Evasion Games | 181 |
Three Mathematics Competitions | 195 |
On Useless and Useful Mathematics | 206 |
Other editions - View all
An Invitation to Mathematics: From Competitions to Research Dierk Schleicher,Malte Lackmann No preview available - 2011 |
An Invitation to Mathematics: From Competitions to Research Dierk Schleicher,Malte Lackmann No preview available - 2013 |
Common terms and phrases
algorithm Alice and Bob answer assume Banach spaces Béla Bollobás blowup boundary called chess Christian class number coins colour communication complexity conjecture converge cubes defined denote differential equations digits Diophantine Diophantine equation disjoint dynamics edges Erdős Euler equations example finite flow fluid formula function f geometry graph theory grid Hardy inequality IMO problems incompressible infinite infinite-dimensional input integers Invitation to Mathematics irrational number iteration Julia set Lasker lattice linear Lion lower bound math mathematicians methods Navier-Stokes Navier-Stokes equations Newton map Newton's method number theory olympiads orbit plane positive prime number proof protocol prove quadratic forms quadratic polynomials question Ramsey theory random reader real number reduced triples root satisfy Schleicher sequence singular solution solve space structure subspace Terence Tao tetrahedra theorem Timothy Gowers tions triangle vector vertex vertices winning strategy zero Zn+1