适合人群
适合年级 (Grade): 高中生
适合专业 (Major): 应用数学、经济学、金融学、数据科学、统计、运筹学、管理学等相关专业学生或对以上领域感兴趣的学生；
建议选修: 离散数学及其应用
导师介绍
Patrick
牛津大学 University of Oxford
终身正教授
Patrick 导师现任牛津大学统计学系的终身正教授，荣获牛津大学杰出教学奖，毕业于普林斯顿大学运筹学与金融工程博士学位。之后，Patrick 加入了耶鲁大学的耶鲁网络科学研究所。并在电子工程系做了两年的博士后，任教于耶鲁大学计算机科学系。
Patrick 导师的多个研究获得了业内的一致认可。2016-2019年间，导师负责的项目：“Locality in Network Optimization”获得了美国国家科学基金会$450,000.00的奖金。导师经常受邀参加顶级的全球计算机和统计专业的学术会议和论坛并发表讲座。例如2021年的International Conference on Artificial Intelligence and Statistics (AISTATS) 人工智能与统计国际会议和2020年的Neural Information Processing Systems 神经信息处理系统国际峰会的讲座，并在业内引起了强烈的反响和热议。导师的学术成果也多次出现在顶级期刊和IEEE论文中，例如全球知名的机器学习期刊《Journal of Machine Learning Research》和《IEEE Transactions on Control of Network Systems》等。导师更是受邀为各所顶级世界名校的专业研讨讨论发表演讲，例如2020年Bernoulli-IMS One World Symposium世界研讨会和美国布朗大学，斯坦福大学的相关专业讲座。导师也凭借自身突出的研究成果，组织了多个专业论坛和研讨会，包括今年举办的第35届“Conference on Learning Theory”，导师作为区域主席组织了该论坛的活动。 Patrick 导师是多个IEEE论文的审稿人，也是多个科研机构的成员，包括Institute of Mathematical Statistics (IMS)、Bernoulli Society和European Laboratory for Learning & Intelligent Systems (ELLIS)。
他的研究兴趣集中在概率论、统计学和计算机科学。对高维概率、统计和优化的基本原理，为机器学习和人工智能提供高计算效率、统计最优的算法感兴趣。
Dr. Patrick is a Professor of Statistics and Machine Learning at the University of Oxford and holds a Ph.D. in Operations Research and Financial Engineering from Princeton University. After that, he joined the Yale Institute for Network Science at Yale University. He worked two years as a Postdoctoral Associate in the Electrical Engineering Department and was a lecturer in the Computer Science department at Yale University.
Multiple studies by Patrick have received unanimous recognition in the industry. “Locality in Network Optimization” received a $450,000.00 grant from the National Science Foundation (NSF) in 2016-2019. Patrick is often invited to attend and give lectures at top global computer and statistics conferences and forums. With his outstanding research achievements, he has also organized several professional forums and seminars, including the 35th “Conference on Learning Theory” held this year, for which Patrick organized this activity as the regional chairman.
His research interests lie at the intersection of probability, statistics, and computer science, and he is interested in the investigation of fundamental principles in high-dimensional probability, statistics and optimization to design computationally efficient and statistically optimal algorithms for machine learning.
项目背景
数理经济学是运用数学模型进行经济分析、解释经济现象、描述经济学理论的一门学科。主要目标是利用数学模型和技术来解决经济学中问题，包括资产配置、市场行为、经济增长、公共政策等。通过建立数学模型，数理经济学可以对经济系统进行定量分析，以预测经济变量的行为，评估政策效果等。数理经济学在许多经济学领域都有广泛的应用，例如宏观经济学、微观经济学、金融经济学等。
项目介绍
有效的经济分析广泛应用数理经济学，例如最优决策问题、市场供需关系，及资源分配问题、风险管理及投资组合优化问题等。数理经济学提供建立和分析经济模型的工具和方法，通过建立数学模型，可以推导出具有经济意义的理论结论，帮助我们更好的理解经济现象和经济决策。本项目将介绍集合、极限、微积分及性质、线性代数、微分方程等基本数学概念，结合经济模型及应用，强调对经济分析至关重要的数学原理及概念，还将介绍用于研究最优决策问题的优化理论。学生将在项目结束时，提交研究课题项目报告，进行成果展示。
Effective economic analysis is widely used in mathematical economics, such as optimal decision problems, market supply and demand, and resource allocation problems, risk management and portfolio optimization problems. Mathematical economics provides the tools and methods to establish and analyze economic models. By establishing mathematical models, theoretical conclusions of economic significance can be derived to help us better understand economic phenomena and make economic decisions. This program will introduce basic mathematical concepts such as sets, limits, calculus and properties, linear algebra, and differential equations. In conjunction with economic models and applications, it will emphasize mathematical principles and concepts that are essential to economic analysis. Professor will also introduces optimization theory for studying optimal decision problems. At the end of the program, students will submit a research project report and present their results.
项目大纲
经济模型简介 Introduction to economic models
集合、函数和序列 Set,Functions and Sequences
微积分与优化 Calculus and Optimization
凸凹性 Convexity and concavity
均值定理 Mean-value theorem
线性代数 Linear Algebra
积分与微分方程 Integration and differential equations
经济应用和最优控制 Economic applications and optimal control
项目回顾与成果展示 Program Review and Presentation
论文辅导 Project Deliverables Tutoring
项目收获
7周在线小组科研学习+5周不限时论文指导学习 共125课时
项目报告
优秀学员获主导师Reference Letter
EI/CPCI/Scopus/ProQuest/Crossref/EBSCO或同等级别索引国际会议全文投递与发表指导（可用于申请）
结业证书
成绩单
LASER Award in Research Skills for Academic Study官方证书并转换8 UCAS Tariff Points（可选）