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Mathematical Modeling for the MCM/ICM Co

样章
作者：
Jay Belanger 王杰 等
定价：
45.00元
ISBN：
978-7-04-044965-5
版面字数：
240千字
开本：
16开
全书页数：
186页
装帧形式：
平装
重点项目：
暂无
出版时间：
2016-03-28
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
数学应用

本系列丛书是以美国大学生数学建模竞赛（MCM/ICM）赛题为主要研究对象，结合竞赛特等奖的优秀论文，对相关的问题进行解析与研究。本辑针对2015年MCM/ICM竞赛的4个题目：Control Ebola virus outbreak、Search for a missing aircraft lost in the open sea、Manage human capital in organizations以及Create a sustainable world进行了解析与研究。本书由美国资深建模教师编写，由于参赛论文需要用英语书写，同时考虑到不同层次读者的需要，故本书为英文呈现。读者在学习建模方法的同时，可以了解美国建模教师对问题的理解。

本书内容新颖、实用性强，可作为指导学生参加美国大学生数学建模竞赛的主讲教材，也可作为本科生、研究生学习和准备全国大学生、研究生数学建模竞赛的参考书，同时也可供研究相关问题的教师和研究生参考使用。

  • Front Matter
  • 1 Eradicating Ebola
    • 1.1 Problem Description
    • 1.2 Outstanding Winners
    • 1.3 Previous Work
      • 1.3.1 The SIR model
      • 1.3.2 Clustering
      • 1.3.3 Technique for order of preference by similarity to ideal solution
    • 1.4 Modeling the Situation
      • 1.4.1 Approaching the problem
      • 1.4.2 Assumptions
      • 1.4.3 Modeling the spread of Ebola
      • 1.4.4 Amount of medicine
      • 1.4.5 Delivering the medicine
      • 1.4.6 Manufacturing the medicine
      • 1.4.7 Other factors
    • 1.5 Sensitivity Analysis
    • 1.6 Strengths and Weaknesses
    • 1.7 Comments
    • Exercises
    • References
  • 2 Searching for A Lost Plane
    • 2.1 Problem Description
    • 2.2 Outstanding Winners
    • 2.3 Previous Work
      • 2.3.1 Air France Flight 447
      • 2.3.2 Searching for AF447
      • 2.3.3 Finding AF447
    • 2.4 Modeling the Situation
      • 2.4.1 Approaching the problem
      • 2.4.2 Assumptions
      • 2.4.3 Determining a search region
      • 2.4.4 Determining an initial PDF
      • 2.4.5 Search probabilities
      • 2.4.6 Search strategy
      • 2.4.7 Search time
    • 2.5 Sensitivity Analysis
    • 2.6 Strengths and Weaknesses
    • 2.7 Comments
    • Exercises
    • References
  • 3 Using Networks to Model Human Capital Within Organizations
    • 3.1 Problem Description
    • 3.2 How to Approach the Problem
      • 3.2.1 Building a network model
      • 3.2.2 Dynamic processes
      • 3.2.3 Measurements and metrics
    • 3.3 Outstanding Winners
    • 3.4 Static Modeling of the Human Capital Network
      • 3.4.1 Assumptions
      • 3.4.2 Approach 1: Rule-driven assignment
      • 3.4.3 Approach 2: Multi-layer connected networks
      • 3.4.4 Approach 3: Using genetic algorithms to assign people to positions
    • 3.5 Dynamic Human Capital Network Modeling
      • 3.5.1 Assumptions
      • 3.5.2 Developing attributes for nodes
      • 3.5.3 Modeling churn
      • 3.5.4 Modeling promotion and recruitment
    • 3.6 Metrics and Results
    • 3.7 Sensitivity Analysis
    • 3.8 Strengths and Weaknesses
    • 3.9 Comments
    • Exercises
    • References
  • 4 Sustainable Society
    • 4.1 Problem Description
    • 4.2 How to Approach the Problem
    • 4.3 Outstanding Winners
    • 4.4 Approach 1: Ecological-Economic Tradeoff Model
      • 4.4.1 Sustainability model
      • 4.4.2 A 20-year plan for Zambia
      • 4.4.3 Evaluating the 20-year plan
      • 4.4.4 Sensitivity analysis
    • 4.5 Approach 2: Entropy-GE Matrix Model
      • 4.5.1 Sustainability model
      • 4.5.2 Forecast model
      • 4.5.3 Modified forecast model with control
      • 4.5.4 Sustainable development activities
      • 4.5.5 Congo 20-year sustainability plan
      • 4.5.6 External effects
      • 4.5.7 Stability analysis
    • 4.6 Comments
    • Exercises
    • References
  • 5 Math Modeling in Cutting-Edge Research Problems
    • 5.1 Problem Description
    • 5.2 Problem Formulation
    • 5.3 Modeling of Topic Discovery
      • 5.3.1 The simplest model
      • 5.3.2 A simple model with latent distributions
      • 5.3.3 A mixture model
      • 5.3.4 Latent semantic analysis
      • 5.3.5 Probabilistic LSA
      • 5.3.6 Latent Dirichlet Allocation
    • 5.4 Application of Labeled LDA: News Classifications
      • 5.4.1 Labeled LDA
      • 5.4.2 LLDA news classifiers
      • 5.4.3 Experiments
    • 5.5 Closing Remarks
    • Exercises
    • References
  • Appendix Dirichlet Distribution
    • 1 Beta distribution
    • 2 Beta is conjugate prior to binomial
    • 3 Dirichlet Distribution
    • 4 Dirichlet is conjugate prior to multinomial
    • Exercises
  • Index
  • 图书清单

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