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Mathematical Challenges from Theoretical/Computational Chemistry
BOX 5.1American Chemical Society Curriculum Standards for Mathematical Course Work
"Students should emerge from an ACS-approved program in chemistry with:
A firm foundation in the fundamentals and applications of calculus, including knowledge of differential equations and proficiency with partial derivatives.
An understanding of the basic principles of linear algebra and practical knowledge of statistics with applications to such problems as experimental design, validation of data, and optimization procedures.
Experience with computers, including programming, numerical and non-numerical algorithms, simulations, data acquisition, and use of databases for information handling and retrieval."
SOURCE: Undergraduate Professional Education in Chemistry: Guidelines and Evaluation Procedures, American Chemical Society, Washington, D.C., 1992, p. 11.
numerical analyst and subsequently becomes interested in chemical statistical mechanics, should this be viewed as a loss or a gain?
For academic chemistry departments, analogous principles of departmental autonomy can affect chemists seeking to work with mathematicians. Because theoretical/computational chemists must often demonstrate the applications of their work to experimental areas of chemistry, fundamental work of a mathematical nature—for example, algorithm development or identification of problem features amenable to mathematical attack—may be undervalued. On balance, chemistry departments have more experience in evaluating multidisciplinary research, soliciting judgments as needed from a variety of scientists both inside and outside the department. A further positive effect on interdisciplinary work is that chemistry departments tend to value research that has a significant impact on thinking, research, and practice in chemistry and other areas.
For both fields, the difficulty of interdisciplinary collaboration is exacerbated by the lack of a well-established network of contacts between mathematicians and chemists. On most university campuses, chemistry and mathematics departments are physically separate, so casual daily contact does not occur. An effort is typically required for faculty to attend all the seminars in their own department, let alone in other departments. This reality aggravates the difficulty not only of initiating a collaboration, but also of developing an appreciation of the other discipline's challenges. Faculty members are not immune to misperceptions and stereotypes: chemists may regard mathematicians as unapproachable or uninterested in chemistry problems; mathematicians may not realize that chemistry problems contain interesting and novel mathematics.
There are, however, exceptions. For instance, in the United Kingdom there is a long fruitful history of productive mathematical research being initiated by theoretical scientists ("natural philosophers") employed as faculty members of mathematics departments. This goes back to Newton, but the tradition continues to modern times. D.R. Hartree and P.A.M. Dirac are recent examples at Cambridge, and C.A. Coulson spent most of his career as a professor of mathematics at Oxford. Some departments in the United States also have established atmospheres that are conducive to collaborative work.
Outside of academia (e.g., pharmaceutical companies), cross-disciplinary work between chemists and mathematicians has succeeded because the problems of disciplinary boundaries are less pervasive in many instances, and team efforts are often the norm. Issues of tenure, grants, and promotion are nonexistent or less important. These settings should provide models for collaborative research.