Related papers: MadeinMath. A Math Exhibition out of Many Threads
These notes are based on the mini-course given in June 2004 in Cetraro, Italy, in the frame of a C.I.M.E. school. Of course, they contain much more material that I could present in the 6 hours course. The main goal is to give an idea of the…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
In this article, I discuss the relationship of mathematics to the physical world, and to other spheres of human knowledge. In particular, I argue that Mathematics is created by human beings, and the number $\pi$ can not be said to have…
The purpose of this note is to raise two different questions, which are rarely if ever considered, and to which, it seems, we lack convincing, systematic answers. These questions can be posed as: - Why do we compute? - What do we compute?…
In recent years dynamical systems (of deterministic and stochastic nature), describing many models in mathematics, physics, engineering and finances, become more and more complex. Numerical analysis narrowed only to deterministic algorithms…
In this paper, we introduce a mathematical method to extract similarities between paintings and musical tracks. Our approach is based on the digitalization of both paintings and musical tracks by means of finite expansions in terms of…
Mathematics can serve many functions in physics. It can provide a computational system, reflect a physical idea, conveniently encode a rule, and so forth. A physics student thus has many different options for using mathematics in his…
These notes are an exposition and synthesis of various "jet space" constructions in complex analytic geometry. They are written primarily for model-theorists interested in the results of Campana and Fujiki (whose model-theoretic…
Talk 1: Open problems in knot theory that everyone can try to solve. Knot theory is more than two hundred years old; the first scientists who considered knots as mathematical objects were A.Vandermonde (1771) and C.F.Gauss (1794). However,…
This is a survey of results on definability and undefinability in models of arithmetic. The goal is to present a stark difference between undefinability results in the standard model and much stronger versions about expansions of…
A perplexing problem in understanding physical reality is why the universe seems comprehensible, and correspondingly why there should exist physical systems capable of comprehending it. In this essay I explore the possibility that rather…
Economic growth, people's health, and urban development face challenges in the post-epidemic era. How to promote high-quality and sustainable urban development, improve citizens' sense of happiness, and solve problems in city management…
This contribution covers the topics presented by the authors at the {\it ``Fundamental Problems of Turbulence, 50 Years after the Marseille Conference 1961"} meeting that took place in Marseille in 2011. It focuses on some of the…
Matchings were among the earliest motivations for graph theory. They subsequently remained a central goal, inspiring the development of new tools that went well beyond problems directly concerning matchings. These tools proved widely…
This is an expanded version of a three-hour minicourse given at the winterschool Winterbraids IV held in Dijon in February 2014. The aim of these lectures was to present some aspects of the dimer model to a geometrically minded audience. We…
The current and upcoming generation of Very Large Volume Neutrino Telescopes---collecting unprecedented quantities of neutrino events---can be used to explore subtle effects in oscillation physics, such as (but not restricted to) the…
This paper describes the use of weighted Monte Carlo events to accurately approximate integrals of functions of the experimentally measured kinematical vectors and their dependence on physical parameters. This technique is demonstrated in…
In these notes of lectures at the 2004 Summer School of Mathematical Physics in Ravello, Italy, the author develops an approach to calculus in which more efficient choices of limits are taken at key points of the development. For example,…
Did migrants make Paris a Mecca for the arts and Vienna a beacon of classical music? Or was their rise a pure consequence of local actors? Here, we use data on more than 22,000 historical individuals born between the years 1000 and 2000 to…
This volume contains the proceedings of the Eighth Workshop on Model-Based Testing (MBT 2013), which was held on March 17, 2013 in Rome, Italy, as a satellite event of the European Joint Conferences on Theory and Practice of Software, ETAPS…