《MCM/ICM数学建模竞赛(第1卷，英文版)》
1 Introduction 1
1.1 A Brief History of Math Contests 1
1.2 The MCM 2
1.3 The ICM 4
1.4 Classifications of the MCM/ICM Papers 5
2 Preparation and Participation 7
2.1 Judging 7
2.2 Triage 7
2.3 Further Evaluations 8
2.4 Modeling for the MCM and ICM 9
2.4.1 Things to pay attention to 9
2.4.2 Reading and restating the problem 10
2.4.3 Give exact mathematical meanings to keywords 13
2.4.4 Models are for solving problems 14
2.4.5 Literature search 16
2.4.6 Assumptions 21
2.4.7 Creating models 22
2.4.8 Finding solutions 31
2.4.9 Stability and sensitivity 34
2.4.10 Writing up the solution 37
2.5 Before the Contest 38
2.5.1 Form the best team 38
2.5.2 Practice 39
2.6 Task Scheduling During the Contest 40
2.7 Exercises 43
3 The Keep-Right-Except-To-Pass Rule 45
3.1 Problem Description 45
3.2 How to Approach the Problem 46
3.2.1 Previous work on traffic flow 47
3.2.2 A general approach 47
3.2.3 The Nagel-Schreckenberg model 48
3.3 Outstanding Winners 48
3.4 Approach 1: Traffic and Cellular Automata 49
3.4.1 Models 49
3.4.2 Running the model 56
3.4.3 Comparing the rules 67
3.4.4 Improved rules 73
3.4.5 Sensitivity testing 74
3.4.6 Further questions 76
3.5 Approach 2: Traffic and Continuous Models 80
3.5.1 A one-lane model 81
3.5.2 A two-lane model 81
3.5.3 Steady state solutions 82
3.5.4 Traffic density 84
3.6 Comments 86
3.7 Exercises 86
4 College Coaching Legends 87
4.1 Problem Description 87
4.2 How to Approach the Problem 88
4.2.1 How to begin 88
4.2.2 The Analytic Hierarchy Process 90
4.3 Outstanding Winners 94
4.4 Approach 1: Ranking by Weighted Average of Selected Criteria 95
4.4.1 Select a sport and coaches 95
4.4.2 Set up ranking criteria 96
4.4.3 Method 1: Analytic Hierarchy Process 97
4.4.4 Method 2: Entropy 98
4.4.5 Evaluations 100
4.4.6 Combining the models 101
4.4.7 Gender 102
4.4.8 Time line 102
4.4.9 Sensitivity testing 104
4.5 Approach 2: Ranking by Eigenvector Centrality of WinningGraphs 106
4.5.1 How to start 107
4.5.2 Assumptions 107
4.5.3 Winning graphs 107
4.5.4 Coach ranking 109
4.5.5 Sensitivity analysis 111
4.6 Comments 111
4.7 Exercises 112
5 Using Networks to Measure Influence and Impact 113
5.1 Problem Description 114
5.2 How to Approach the Problem 118
5.2.1 Measurements 118
5.2.2 Common numerical measures 119
5.3 Outstanding Winners 124
5.4 Modeling Influence in the Co-author Network 124
5.4.1 The structure of the co-author network 125
5.4.2 Assumptions 127
5.4.3 Model 1: a basic model 128
5.4.4 Model 2: relational distance 129
5.4.5 Model 3: a model measuring node importance 131
5.4.6 Model 4: a multi-layer model based on centrality,clustering, and PageRank 133
5.5 Modeling Influence in the Citation Network 137
5.5.1 Assumptions 138
5.5.2 PageRank model 1: extended citation networks 138
5.5.3 PageRank model 2: authority and popularity 141
5.5.4 PageRank model 3: Analytic Hierarchy Process 143
5.5.5 Model 4: energy transfers 145
5.6 Model Applicability to Other Networks 147
5.7 Sensitivity Testing 150
5.8 Strengths and Weaknesses 151
5.9 Comments 153
5.10 Exercises 153
Index 155
References 159
