The role of mathematics in the college curriculum and applications of mathematics in society are examined in this pamphlet produced by the NRC's Ad Hoc Committee on Applied Mathematics Training. It is suggested that the growing need for mathematicians in the physical, biological, and social sciences has changed the constituency of potential mathematics majors and requires a corresponding adjustment on the part of the mathematics departments. The departments need to be more aware of contributions they can make to other fields and need to publicize these areas to establish contact within the institution and with other occupational fields. Curriculum and department-wide recommendations are made emphasizing the need to improve these relations, increase student motivation, and offer a wider choice of careers to mathematics majors. Nontraditional education programs in mathematics that would provide experiential learning opportunities are recommended. Societal aspects that influence the field of mathematics and mathematics education are also discussed. Fourteen recommendations compiled by the committee (including those dealing with recognition of faculty interest and with industry and government campus participation) are presented as well as the summary proposal submitted to the Sloan Foundation for the formation of the Committee. (SF)