The Mathematical Sciences: A Report -- Copyright -- Foreword -- Contents -- I Summary -- 1 Mathematics and Society -- THE MATHEMATIZATION OF CULTURE -- THE NEED FOR MATHEMATICALLY TRAINED PEOPLE -- APPLIED MATHEMATICAL SCIENCES -- CORE MATHEMATICS -- THE POSITION OF THE UNITED STATES IN MATHEMATICS -- 2 Recommendations -- RESEARCH -- Growth and Level -- The Special Situation of Computer Science -- Basic Research in Applied Mathematics -- Sources of Support -- Forms of Support -- Peer Evaluation -- EDUCATION -- Research Apprenticeship -- Early Graduate Education -- Faculty Improvement -- Undergraduate Education in Applied Mathematical Sciences -- SURVEYS AND STUDIES -- Continuing Survey Activities in the Mathematical Sciences -- Mathematical Sciences in Government Research and Development Establishments -- New National Goals -- IMPLICATIONS FOR PROGRAM AND RESOURCES PLANNING -- The Staffing of the Colleges -- Research and Research Education -- Undergraduate and Early Graduate Education -- Applied Research -- Sources and Forms -- Cautionary Remarks -- II The State of the Mathematical Sciences -- 3 The Community of Mathematics -- HISTORICAL PERSPECTIVES -- THE NATURE OF MATHEMATICS -- CORE AND APPLICATIONS -- CRITICISMS AND TENSIONS -- IMPROVING COMMUNICATIONS -- 4 Core Mathematics -- MATHEMATICAL LOGIC -- NUMBER THEORY -- COMBINATORIAL ANALYSIS -- ALGEBRA -- Field Theory -- Ring Theory -- Linear Algebra -- Algebras -- Group Theory -- Homological Algebra and Category Theory -- ANALYSIS -- Functions of Complex Variables -- Harmonic Analysis -- Functional Analysis -- Differential Equations -- Probability Theory -- GEOMETRY -- Algebraic Geometry -- Differential Geometry -- Point Set Topology -- Algebraic Topology -- Differential Topology -- Lie Groups -- 5 Applied Mathematical Sciences -- FLUID DYNAMICS: AN EXAMPLE OF PHYSICAL MATHEMATICS -- STATISTICS.

COMPUTER SCIENCE -- OPTIMIZED ALLOCATION, CONTROL, AND DECISIONS -- OTHER AREAS -- 6 Examples of Mathematics in Use -- MATHEMATICS AND PHYSICS -- MATHEMATICAL SCIENCES IN ENGINEERING -- AN EXAMPLE FROM THE ENVIRONMENTAL SCIENCES: NUMERICAL WEATHER PREDICTION -- MATHEMATICAL SCIENCES IN ECONOMICS -- MATHEMATICS IN FINANCE AND INSURANCE -- MATHEMATICS IN MANAGEMENT AND OPERATIONS -- CONCLUDING REMARKS -- III The Mathematical Sciences in Education -- 7 Undergraduate Education -- THE INCREASE IN MATHEMATICS MAJORS -- TOTAL ENROLLMENTS IN THE MATHEMATICAL SCIENCES -- QUALITY AND DISTRIBUTION OF MATHEMATICAL-SCIENCE FACULTY -- THE JUNIOR COLLEGES -- THE MATHEMATICS FACULTY IN JUNIOR COLLEGES -- 8 Graduate Education -- THE MASTER'S DEGREE -- THE DOCTORATE IN THE MATHEMATICAL SCIENCES -- THE DOCTORATE OF PHILOSOPHY AND INTERMEDIATE DEGREES -- GRADUATE-STUDENT PARTICIPATION IN UNDERGRADUATE TEACHING -- 9 Special Educational Issues -- THE COLLEGE TEACHER -- APPLIED MATHEMATICS -- COMPUTER SCIENCE -- STATISTICS -- RESEARCH VERSUS TEACHING -- WASTED MATHEMATICAL TALENT -- IV Level and Forms of Support -- 10 Federal Support of Research -- LEVEL AND SOURCES OF SUPPORT -- THE ROLE OF THE MISSION-ORIENTED AGENCIES -- FORMS OF SUPPORT -- The Project System -- Departmental Grants -- Developmental Block and Area Grants -- TIME AND EFFORT REPORTING -- 11 Federal Support of Education -- GRADUATE EDUCATION -- POSTDOCTORAL RESEARCH EDUCATION -- CONTINUING EDUCATION FOR COLLEGE TEACHERS -- 12 Private Foundations -- GRANTS BY PRIVATE FOUNDATIONS -- COMMENTS -- 13 Industrial and Government Laboratories -- ACTIVITIES AT SOME MAJOR LABORATORIES -- THE GENERAL SITUATION AND ITS PROBLEMS -- COMMENTS -- V Conclusions -- 14 Tasks and Needs -- THE CORE -- PHYSICAL MATHEMATICS -- STATISTICS -- COMPUTER SCIENCE -- OPERATIONS RESEARCH AND MANAGEMENT SCIENCE -- OTHER AREAS.

15 The Mathematical Sciences in Society's Service -- THE MATHEMATICAL POPULATION -- MATHEMATICAL STRATEGY -- TRANSFER TIMES -- EMERGENCIES -- THE LEVEL OF INVESTMENT -- GROWTH CANNOT BE FOREVER -- THE NONUTILITARIAN VIEW -- References -- Appendixes -- Appendix A Individuals Who Contributed to the Work of COSRIMS -- COSRIMS -- PANEL ON APPLIED MATHEMATICS -- PANEL ON GRADUATE EDUCATION -- PANEL ON LEVEL AND FORMS OF SUPPORT -- PANEL ON NEW CENTERS -- PANEL ON PURE MATHEMATICS -- PANEL ON UNDERGRADUATE EDUCATION -- COSRIMS-CBMS SURVEY PANEL ON THE MATHEMATICAL SCIENCES IN INDUSTRY AND GOVERNMENT -- AUTHORS OF COSRIMS ESSAYS -- CONFERENCE BOARD OF MATHEMATICAL SCIENCES (CBMS) SURVEY COMMITTEE -- CBMS SURVEY PANEL ON GRADUATE EDUCATION -- CBMS SURVEY PANEL ON INFORMATION SCIENCE -- CBMS SURVEY PANEL ON MATHEMATICS EDUCATION -- CBMS SURVEY PANEL ON PROBABILITY AND STATISTICS -- OTHER CONTRIBUTORS -- Appendix B Final Report of the American Mathematical Society's Committee on Information Exchange and Publication in… -- Appendix C The Role of the Private Foundations in the Support of Mathematics -- A Report by L. H. Farinholt to the COSRIMS Panel on Level and Forms of Support -- GENERAL STATEMENT ABOUT FOUNDATIONS -- WHAT FOUNDATIONS HAVE DONE FOR MATHEMATICS -- Alfred P. Sloan Foundation (10,422,078) -- Ford Foundation (3,326,000) -- Carnegie Corporation of New York (3,181,000) -- Rockefeller Foundation (1,160,000) -- Louis W. and Maud Hill Family Foundation (590,464) -- John Simon Guggenheim Foundation (356,000) -- Research Corporation (211,500) -- THE FUTURE OF FOUNDATION SUPPORT -- Appendix D The Support of Computer Use in Higher Education -- A Statement by E. A. Feigenbaum, Director, Stanford Computation Center -- A Statement by Courtney S. Jones, Assistant to the Controller, Stanford University.

Appendix E PhD Origins of Mathematicians in Certain Categories -- A Study Made for the COSRIMS Panel on New Centers.