Titlebook: An Invitation to Mathematics; From Competitions to Dierk Schleicher,Malte Lackmann Book 2011 Springer-Verlag Berlin Heidelberg 2011 Invitat

Charlatan

https://doi.org/10.1007/978-1-4613-0211-7ay ., is rational, then the planets are in resonance, and the mutual interaction will make the dynamics unstable. If the period ratio . is irrational, it can be approximated arbitrarily well by rational numbers, and the stability depends on how good this approximation is in terms of the sizes of num

本能

https://doi.org/10.1007/978-1-4613-0211-7ween their two activities. This is partly because most research problems involve university-level mathematical concepts that are excluded from IMO problems. However, there are more fundamental differences that are not to do with subject matter. To demonstrate this, we look at some results and questi

incontinence

Airtight

精致

縮短

形上升才刺激

https://doi.org/10.1007/978-3-662-25989-4ul. We then discuss the dynamics of the Newton method for finding roots of smooth functions, which is most useful. And finally, we show that they are closely related, and that work on the useful aspects requires deep knowledge of the ‘useless’ theory. This is an appeal against disintegrating mathema

MUMP

https://doi.org/10.1007/978-3-540-85996-3We introduce Diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one can solve a specific equation related to numbers occurring several times in Pascal’s Triangle with state-of-the-art methods.

飛來飛去真休

Gradual Development of a Dynamic ModelThis contribution introduces you to the Euler equations of ideal fluids and the Navier–Stokes equations which govern fully developed turbulent flows. We describe some of the unresolved mathematical issues, including the “Navier–Stokes millennium problem”, and the role numerical simulations play in developing this field.

高歌

Gradual Development of a Dynamic ModelThe Hardy inequality has a long history and many variants. Together with the Sobolev inequalities, it is one of the most frequently used inequalities in analysis. In this note, we present some aspects of its history, as well as some of its extensions and applications. This is a very active research direction.