EPSRC Centre for Doctoral Training in Analysis (Cambridge Centre for Analysis)

EPSRC 分析博士培训中心（剑桥分析中心）

• 批准号: EP/L016516/1
• 金额: $ 412.82万
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Training Grant
• 财政年份: 2014
• 资助国家: 英国
• 起止时间: 2014 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FL016516%2F1
• 关键词: EPSRC; Centre; Doctoral; Training; Analysis

Our proposal builds on the successful start made by Cambridge Centre for Analysis (CCA), a current EPSRC Centre for Doctoral Training. We propose to develop further our activity in two important and rapidly evolving areas of analysis, namely mathematics of information and statistics of complex systems.Beginning with Newton, for whom the development of calculus and the mathematical understanding of bodies in motion were closely intertwined, the mathematics used to describe real phenomena consistently involves notions of continuity, rate of change, average value, and basic challenges such as the relationship between discrete and continuum objects. This is the domain of analysis, encompassing modelling by partial differential equations and by random processes, and the mathematical theory which guides effective computation for such models.The centrality of mathematical analysis in the relationship between mathematics and its applications has been acknowledged by successive International Reviews of Mathematics, as has the need to increase the capacity of UK PhD training in analysis. Mathematical Analysis and its Applications is an EPSRC Priority Area.Beyond the established and important uses of analysis in modelling physical phenomena, digital technology has created new areas where mathematical analysis, in guiding the extraction of knowledge from massive discrete systems, plays an essential role. These include the fields of high-dimensional statistics and the mathematics of information, including compressed sensing. In each of these, one is looking for a reliable means to interpret massive high-dimensional data. Already several CCA students are working in these areas. Big Data is one of the Eight Great Technologies championed by the Minister for Universities and Science. Statistics and Data to Knowledge are EPSRC Priority Areas.We propose a first year training programme based on our current successful model, now expanded by two further core courses, one in Statistics of Complex Systems and one in Mathematics of Information. These new courses will be paired with postgraduate level courses from the existing Cambridge Masters' (MASt), which students can use to consolidate their understanding. The core courses themselves are based on supervised student team assignments leading to student presentations. The other main components of the first year are research mini-projects (often the route to a PhD project) and an industry workshop. Years two to four are devoted mainly to the PhD thesis.First year training establishes a collaborative ethos in the cohort and, by mixing students with different prior skills, encourages cross-fertilization of ideas across the different threads of analysis. This is sustained in later years through a programme of seminars, workshops and training in transferable skills. The students appreciate that their collective understanding of a given problem using different skills will often exceed each individual's understanding. This makes cohort-based training especially valuable in analysis. We already expose all our students to the role of mathematics and the opportunities for mathematicians in industry and society, and we encourage first-hand engagement with applications through mini-projects, industrial seminars and study weeks, and, for some, PhD projects with industrial partners. The development of core skills and eventually the ability to generate new ideas is the hardest and crucial part of training as a research mathematician. This is necessarily our overriding task, in which we seek synergy and inspiration from user engagement. In the new CDT, our network of industrial connections will be further enhanced, along with our collaborations with Cambridge engineering colleagues, and our links with the Smith Institute for Industrial Mathematics.

我们的建议基于剑桥分析中心（CCA）的成功开始，这是当前的EPSRC博士培训中心。我们建议在两个重要和快速发展的分析领域，即对复杂系统的信息和统计数据的数学进行进一步的活动。与牛顿的发展，微积分的发展以及对运动中身体的数学理解是紧密相互交织的，这些数学是一致地始终如一地描述了持续性的现象始终如一地描述了持续性的依赖性，构成质疑和基本质疑，基本质疑和基本的质疑和基本的质疑和基本的价值，并构成了基本的质疑和基本的价值，并且是有价值和基本的价值。这是分析的领域，涵盖了部分微分方程和随机过程的建模，以及指导此类模型有效计算的数学理论。由于需要增加数学评论，因此数学及其应用之间的数学分析的中心性已确认，因为需要提高UK PHD培训的能力。数学分析及其应用是EPSRC的优先领域。构成分析在建模物理现象中的建立和重要用途，数字技术创造了新的领域，在该领域中，数学分析在指导从大规模离散系统中提取知识的数学分析起着至关重要的作用。这些包括高维统计的领域和信息的数学，包括压缩感应。在这些中，每个人都在寻找一种可靠的手段来解释大量的高维数据。已经有几个CCA学生在这些领域工作。大数据是大学和科学部长倡导的八项伟大技术之一。统计数据和知识的数据是EPSRC优先领域。我们根据我们当前的成功模型提出了一年的培训计划，现在由两个进一步的核心课程扩展，一个是复杂系统的统计数据，一个是在信息数学中。这些新课程将与现有的剑桥大师赛（MAST）的研究生级课程配对，学生可以用来巩固他们的理解。核心课程本身是基于有监督的学生团体作业，导致学生演讲。第一年的另一个主要组成部分是研究迷你项目（通常是博士项目的途径）和行业研讨会。二至四年主要专门致力于博士学位论文。第一年的培训在队列中建立了一种协作精神，并通过混合具有不同先验技能的学生来鼓励在不同分析线索中对思想进行交叉施肥。这是通过研讨会，讲习班和可转移技能的培训的计划来维持的。学生们对使用不同技能对给定问题的集体理解通常会超过每个人的理解。这使得基于队列的培训在分析中特别有价值。 我们已经使所有学生都接触了数学和数学家在工业和社会中的机会，我们鼓励通过微型项目，工业研讨会和研究周进行第一手互动，以及对于与工业合作伙伴的一些博士学位项目。核心技能的发展以及最终产生新想法的能力是研究数学家培训的最难和关键部分。这必然是我们的压倒性任务，在其中我们从用户参与度中寻求协同作用和灵感。在新的CDT中，我们与剑桥工程同事的合作以及与史密斯工业数学研究所的联系将进一步增强我们的工业联系网络。