Applied mathematics research laboratory

一般的应用数学和特定的学科，如微分方程、统计学、优化、数值分析和随机过程，使人类在许多领域的知识得以进步。如今，不仅需要将这些工具有效地应用于现实生活中的问题，而且还需要进行日常的研究项目和论文。特别是，Escobar教授、Ferrando教授和Rohlf教授的研究兴趣涉及各种计算密集型主题，如高维分布的评估、多维过程的离散化、降维技术的比较、信号处理、求解高维线性和非线性偏微分方程。执行这些主题的复杂程序以及使用最先进的数学软件需要一个深思熟虑的计算环境和专门设计的计算机，这些计算机可以在合理的时间内执行任务。该提案的目的是为瑞尔森大学的“应用数学研究实验室（RAMLab）”的学习和研究环境获取计算资源。申请的资金将用于为RAMLab购买高性能计算机。该设备旨在供数学系的教职员工（主要是上述教授）及其来自瑞尔森几个系（经济学、计算机科学、医学、工程和物理）以及其他大学（多伦多、滑铁卢、慕尼黑）的未来本科生和研究生使用。我们的大多数研究项目都是高度合作的，因此这个设备对我们来说至关重要，以便为我们研究领域的同事和学生提供支持。

Applied mathematics in general, and specific disciplines such as Differential Equations, Statistics, Optimization, Numerical Analysis and Stochastic Processes have allowed for advancement of human knowledge in a large number of areas. Nowadays, a high level of sophistication of the equipment is required not only to apply these tools effectively to real-life problems but also to carry out day- to-day research projects and papers. In particular, the research interest of Prof. Escobar, Prof. Ferrando and Prof. Rohlf involve a variety of computationally-intensive topics such as evaluation of high dimensional distributions, discretization of multidimensional processes, comparison of dimension reduction techniques, signal processing, solving highly dimensional linear and non-linear Partial differential equations. The execution of complex programs on those topics as well as the use of state-of-the-art mathematical software requires a well thought out computing environment and specially designed computers that can perform the tasks in a reasonable amount of time.               The aim of this proposal is to obtain computational resources for an environment for learning and research, called "Applied Mathematics Research Laboratory (RAMLab)" at Ryerson University. The requested funds will be used to purchase high performance computers for RAMLab. This equipment is intended to be used by faculty members of the department of mathematics (mainly the aforementioned professors) and their prospective undergraduate and graduate students from several departments at Ryerson (Economics, Computer Sciences, Medicine, Engineering and Physics) as well as from other universities (Toronto, Waterloo, Munich). Most of our research projects are highly collaborative, therefore this equipment will be vital for us in order to provide support to colleagues and students working in our areas of research.