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OCR for page R11
Contents ~ SUMMARY 1 MATHEMATICS AND SOCIETY 3 The Mathematization of Culture 3 The Need for Mathematically Trained People Applied Mathematical Sciences 6 Core Mathematics ~ The Position of the United States in Mathematics REcoMMENDAT~oNs 1 3 10 Research 15 Education 24 Surveys and Studies 31 Implications for Program and Resources Planning 32 T] THE STATE OF THE MATHEMATICAL SCIENCES 3 THE COMMUNITY OF MATHEMATICS 45 Historical Perspectives 45 The Nature of Mathematics 48 Core and Applications 51 Criticisms and Tensions 53 Improving Communications 55 X1

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4 CORE MATHEMATICS 57 Mathematical Logic 57 Number Theory 60 Combinatorial Analysis 62 Algebra Analysis Geometry 62 68 77 5 APPLIED MATHEMATICAL SCIENCES 84 Fluid Dynamics: An Example of PhYsica1 Mathema~ Statistics SS Computer Science 92 Optimized Allocation, Control, and Decisions Other Areas 99 6 EXAMPLES OF MATHEMATICS IN USE 1 0 1 Mathematics and Physics 102 Mathematical Sciences in Engineering 104 An Example from the Environmental Sciences: Numerical Weather Prediction 108 ~ iCS 85 97 Mathematical Sciences ir1 Economics 110 Mathematics in Finance and Insurance 111 Mathematics in Management and Operations 113 Concluding Remarks 114 III THE MATHEMATICAL SCIENCES IN EDUCATION 7 . X11 ~ A_ _ ~ U 1~GKADUATE EDUCATION 121 The Increase in Mathematics Majors 122 Total Enrollments in the Mathematical Sciences Quality and Distribution of Mathematical-Science Faculty 1 27 The Junior Colleges 130 The Mathematics Faculty in Junior Colleges 124 133

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GRADUATE EDUCATION 1 35 The hIaster's Degree 136 The Doctorate in the Mathematical Sciences 138 The Doctorate of Philosophy and Intermediate Degrees Graduate-Student Participation in Undergraduate Teaching 145 9 SPECIAL EDUCATIONAL ISSUES 1 47 The College Teacher Applied Mathematics Computer Science 152 Statistics 156 Research versus Teaching 158 Wasted Mathematical Talent 159 147 149 IV LEVEL AND FORMS OF SUPPORT 10 FEDERALS SUPPORT OF RESEARCH 163 Level and Sources of Support 163 The Role o:E the NIission-Oriented Agencies 167 Forms of Support 170 Time and Effort Reporting 177 1 1 FEDERAL SUPPORT OF EDUCATION 179 Graduate Education 179 Postdoctoral Research Education 182 Continuing Education for College Teachers 12 PRIVATE FOUNDATIONS 187 Grants by Private Foundations 187 Comments 1 88 184 1 3 INDUSTRIAL AND GOVERNMENT LABORATORIES 1 90 Activities at Some Major Laboratories The General Situation and Its Problems Comments 193 141 191 192 . . . x~

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V CONCLUSIONS 14 TASKS AND NEEDS 197 The Core 197 Physical Mathematics 201 Statistics 203 Computer Science 205 Operations Research and Management Science 207 Other Areas 208 15 XIV THE MATHEMATICAL SCIENCES IN SOCIETY S SERVICE 2 1 1 The Mathematical Population Mathematical Strategy 214 Transfer Times 215 Emergencies 217 The Level of Investment Growth Cannot Be Forever The Nonutilitarian View REFERENCES 221 APPENDIXES APPENDIX A 227 211 217 218 220 Individuals Who Contributed to the Work of COSRIMS APPENDIX B 233 Final Report of the American Mathematical Society's Committee on Information Exchange and Publication in Mathematics APPENDIX C 243 The llole of the Private Foundations in the Support of Mathematics APPENDIX D 249 The Support of Computer Use in Higher Education APPENDIX E 253 PhD Origins of Mathematicians in Certain Categories