Contents 1 Wave equations and First-order hyperbolic systems 4 1.

Introducing a new hobby for other people may inspire them to join with you. Reading, as one of mutual hobby, is considered as the very easy hobby to do. But, many people are not interested in this hobby. Why? Boring is the reason of why. However, this feel actually can deal with the book and time of you reading. Yeah, one that we will refer to break the boredom in reading is choosing semantics ...

Preface These lecture notes, part of a course given in Aarhus, August 1999, treat the classical empirical process defined in terms of empirical distribution functions. A proof, expanding on os-Major-Tusnóne in a 1989 paper by Bretagnolle and Massart, is given for the Komlády result on the speed of convergence of the empirical process to a Brownian bridge in the supremum norm. Herein " A := B " ...

We present an overview of the development of the irrational numbers due to Karl Weierstrass. This construction was first presented during lectures in the 1860s in Berlin. Weierstrass never published his construction. Several of his students (Kossak, Horwitz, von Dantscher and Pincherle, to name a few) gave accounts in lecture notes from the courses. However, these notes were not published under...

These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of such equations. The main incentive for this study was its potential application to the tangential Hilbert 16th problem on zeros of complete Abelian integrals. The exposition consists mostly of examples ill...

1 2 These lecture notes are based on my book [1]. Please see that book for more information, including references to the literature.

These are lecture notes from the summer school on Geometry, Topology and Dynamics of Character Varieties at the Institute for Mathematical Sciences, National University of Singapore in July of 2010. The objective is to give an introduction to some of the tools used in studying the degeneration of hyperbolic structures on surfaces as developed by Thurston, and in particular to describe his const...