The goal of the NUMTA2013 Conference is to create a multidisciplinary round table for an open discussion on numerical modeling nature by using traditional and emerging computational paradigms. The Conference will discuss all aspects of numerical computations and modeling from foundations and philosophy to advanced numerical techniques. New technological challenges and fundamental ideas from theoretical computer science, linguistic, logic, set theory, and philosophy will meet requirements and new fresh applications from physics, chemistry, biology, and economy. The NUMTA2013 Conference is organized jointly by the University of Calabria, Department of Computer Engineering, Modelling, Electronics and Systems Science, Italy, and by the N.I. Lobachevsky State University of Nizhni Novgorod, Russia, in cooperation with the Society for Industrial and Applied Mathematics (SIAM), USA. Researchers from both theoretical and applied sciences are very welcome to submit their papers and to use this excellent possibility to exchange ideas with leading scientists from different research fields. Papers discussing new computational paradigms, relations with foundations of mathematics, and their impact on natural sciences are particularly solicited. A special attention will be also dedicated to numerical optimization and different issues related to theory and practice of the usage of infinities and infinitesimals in numerical computations. Together with regular presentations at the Conference there will be the Summer School offering tutorials and discussion sections covering the topics of the Conference. Participants at the Summer School can submit either regular papers or participate at the poster session that will be also organized. English is the working language both at the Conference and the Summer School.