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.

我们的提案建立在剑桥分析中心 (CCA) 的成功基础上，该中心目前是 EPSRC 博士培训中心。我们建议在两个重要且快速发展的分析领域进一步发展我们的活动，即信息数学和复杂系统统计。从牛顿开始，对他来说，微积分的发展和对运动物体的数学理解紧密地交织在一起，用于描述真实现象的数学始终涉及连续性、变化率、平均值的概念以及离散对象和连续对象之间的关系等基本挑战。这是分析的领域，包括通过偏微分方程和随机过程进行建模，以及指导此类模型的有效计算的数学理论。连续的国际评论都承认数学分析在数学及其应用之间的关系中的中心地位数学，也需要提高英国博士分析培训的能力。数学分析及其应用是 EPSRC 的优先领域。除了分析在物理现象建模中的既定和重要用途之外，数字技术还创造了新的领域，数学分析在指导从大规模离散系统中提取知识方面发挥着至关重要的作用。这些包括高维统计和信息数学领域，包括压缩感知。在每一个领域，人们都在寻找一种可靠的方法来解释大量高维数据。已经有几位 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。统计和从数据到知识是 EPSRC 的优先领域。我们根据当前的成功模式提出了第一年的培训计划，现在又扩展了两门核心课程，一门是复杂系统统计，一门是信息数学。这些新课程将与现有剑桥硕士（MASt）的研究生水平课程配对，学生可以利用这些课程来巩固他们的理解。核心课程本身是基于受监督的学生团队作业并进行学生演示。第一年的其他主要组成部分是研究小型项目（通常是通往博士项目的途径）和行业研讨会。第二年到第四年主要致力于博士论文。第一年的培训在群体中建立了协作精神，并通过混合具有不同先前技能的学生，鼓励跨不同分析线索的思想交叉传播。在以后的几年里，这一点通过一系列研讨会、讲习班和可转移技能培训得以维持。学生们意识到，他们使用不同技能对给定问题的集体理解往往会超出每个人的理解。这使得基于队列的培训在分析中特别有价值。 我们已经让所有学生了解数学的作用以及数学家在工业和社会中的机会，我们鼓励通过小型项目、工业研讨会和学习周，以及对一些工业和社会的博士项目来亲身参与应用程序。合作伙伴。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中最困难和最关键的部分。这必然是我们的首要任务，我们从用户参与中寻求协同作用和灵感。在新的 CDT 中，我们的工业联系网络以及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得到进一步加强。