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美国研究生运筹学硕士申请解析！

马天娇

2023-02-15 09:10:33

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运筹学作为一门新兴学科，是数学的一个分支。美国运筹学是要是用统计学、数学模型和算法等方法，去寻找复杂问题的解答。近几年，因为其本身 “量化万金油”的属性，加上非常不错的就业选择和就业率，成为了不少出国留学生主要考虑就读的专业之一。

Part 1. 什么是运筹学？

运筹学(Operations Research，简称OR)是一门应用数学学科，利用统计学和数学模型等方法，去寻找复杂问题中的最佳或近似最佳解，帮助人们更好的做决策。它起源于Research on military operations，在二战期间，英美两国为有效地配置各项资源，因而召集科学家针对军事作业规划进行研究。20世纪50年代初，美国运筹学会创始人之一P.M.Morse定义运筹学:“运筹学是为领导机构对其控制下的业务活动作决策时提供定量依据的科学方法”。

Part 2. 开设运筹学的项目

美国大学一般把运筹学开设在工程学院或商学院下，也有学校专门设立了运筹研究中心。选择运筹项目时，可以首先考虑偏好商科，工程，数学，还是计算机下的运筹项目。考虑知名度小的地方项目时，可以考虑毕业生流向，当地的大公司招聘需求。运筹学的研究方向与学校周围的资源环境有很大的关系。比如康奈尔大学、哥大和普林斯顿大学比较倾向金融、风险管理方向，亚利桑那州立大学偏向电子器材制造、质量控制和供应链领域的运筹。另外密歇根大学、威斯康星大学、匹兹堡大学由于都有附属的医学中心，所以研究也更偏向healthcare。运筹学顶级的项目往往是那些引领新研究和理论发展的项目。

U.S. News 全美大学综排Top50里，开设在商学院下的运筹学项目：

#2 Harvard University, Business School: Technology and Operations Management
#3 Massachusetts Institute of Technology, Operations Research Center
#9 Northwestern University, Industrial Engineering and Management Sciences
#6 Stanford University, Management Science and Engineering
#6 University of Pennsylvania, The Wharton School (Business): Operations and Information Management
#10 Duke University, Fuqua School of Business
#20 University of California at Los Angeles, The Anderson School (Business): Decisions, Operations, and Technology Management
#22 University of California, Berkeley, Haas School of Business: Manufacturing and Information Technology
#25 Carnegie Mellon University, Tepper School of Business: Operations Research
#25 Carnegie Mellon University, The Heinz School of Public Policy and Management
#34 University of Florida, Warrington College of Business: Decision and Information Sciences
#36 University of California at Irvine, Graduate School of Management: Operations and Decision Technologies
#40 Case Western Reserve University, Weatherhead School of Management: Operations
#40 College of William and Mary, School of Business Administration: Operations and Information Technology
#40 Boston University, School of Management
#46 University of Wisconsin, Madison, School of Business:
Operations and Information Management
#48 University of Texas at Austin, McCombs School of Business: Management Science and Information Systems

US. News 全美大学综排Top50里，工科/计算机/数学相关的运筹学项目(部分与上表重合)：

#1 Princeton University, Operations Research and Financial Engineering#3 Columbia University, Industrial Engineering and Operations Research
#3 Massachusetts Institute of Technology, Operations Research Center
#3 Stanford University, Management Science and Engineering
#9 Northwestern University, Industrial Engineering and Management Sciences
#10 Johns Hopkins University, applied Mathematics and statistics: operations research
#10 Johns Hopkins University, systems science and engineering: operations research
#16 University of Pennsylvania, Electrical and Systems Engineering
#17 Cornell Tech, Master in Operations Research and Information Engineering
#17 Cornell University, Operations Research and Industrial Engineering
#17 Rice University, Computational and Applied Mathematics
#17 Rice University Industrial Engineering
#20 University of California at Los Angeles, Computer Network Modeling and Analysis
#20 University of California at Los Angeles, Engineering Optimization/Operations Research
#22 University of Southern California, Industrial and Systems Engineering
#22 University of California, Berkeley, Industrial Engineering and Operations Research
#25 Carnegie Mellon University, Algorithms and Computational Complexity
#25 University of Michigan, Industrial and Operations Engineering
#25 Carnegie Mellon University, Tepper School of Business: Operations Research
#28 University of Virginia, Systems Engineering
#29 Georgia Institute of Technology, Algorithms, Combinatorics, and Optimization
#29 Georgia Institute of Technology, Industrial and Systems Engineering
#34 University of Florida, Industrial and Systems Engineering
#40 Boston University, Division of Systems Engineering
#40 Northeastern University, Operations Research
#40 College of William and Mary, Operations Research
#46 University of Wisconsin, Madison, Industrial Engineering
#46 University of Wisconsin, Madison, Optimization
#48 University of Texas at Austin, Operations Research and Industrial Engineering
#48 University of Illinois at Urbana-Champaign, Mechanical and Industrial Engineering
#50 Rensselaer Polytechnic Institute, Decision Sciences and Engineering Systems
#50 Lehigh University, Industrial and Manufacturing Systems Engineering
申请中的先修课要求

运筹学项目对申请者的专业限制较小。不论是来自理科(数学、统计)、工科(工业工程、自动化、电子工程、计算机)还是经济学及商科背景的同学都可以申请。但一般来讲，数学背景越强，申请者会越受欢迎。除此之外，编程能力、相关学科 (如经济学)知识等也属于加分项。对于商学院的申请者来说，沟通能力和英语口语能力也非常重要。

除了绩点和排名、申请者的院校和专业背景，因为运筹学在实际学习和项目中对数理和编程要求较高，最好注意修读些高级的数学和计算机课程：

如实分析(Real Analysis)

优化(Optimization)

随机(Stochastics)

博弈论(Game Theory)

机器学习(Machine Learning)等等。

以康奈尔运筹与工业工程(Ithaca, M.ENG) 项目为例，我们来看通常的入学前的先修课要求:
1. 微积分系列，包括线性代数和矢量微积分
2. 入门概率统计
3. 通用编程语言（例如C，C ++，Java或Python）编写的中级计算机编程课程。(仅是包含编程语言, 没有大量使用的不算, R/SAS 也不算)
注意金融工程分支的额外的要求：(入学前满足)：

1.两个学期的基于微积分的概率，统计和/或随机过程理论课程 (仅使用了概率和统计方法，但理论不是课程重点的不算，专业考试证书如CFA，FRM也不能替代)。

2.金融入门课程。经济学和会计学课程不能替代

3.强烈建议：微分方程课程

4.强烈建议：熟练使用R和/或Python

数据分析学分支的额外要求 (入学前满足):

两个学期的基于微积分的概率论和统计理论课程(仅使用了概率和统计方法，但理论不是课程重点的不算，专业考试证书如CFA，FRM也不能替代)。