Approaches for Including Discrete Mathematics in the Mathematics Curriculum
The basic problem is that mathematicians and various client disciplines
have diverse needs.
Potential physics and engineering majors: differentiation and
integration of functions of 1 variable, applications, techniques of
integration, sequences and series, vectors and vector motion, partial
differentiation, multiple integration, linear algebra, differential
equations
Potential biology, economics, other(?) majors: differentiation and
integration of functions of 1 variable, applications, statistics, partial
differentiation, multiple integration, [possibly linear algebra]
Potential computer science majors: introduction to logic and proofs
(with some emphasis on structural induction), Boolean algebra, functions,
relations, and sets, basic number theory and number systems, cardinality
and counting, introduction to graphs, basic properties of matrices,
basic order analysis, introduction to computability,
elementary probability and statistics
Potential mathematics majors: traditionally, same as potential
physics and engineering majors, although some options include statistics or
discrete mathematics
Three basic approaches
Realistically, there seem to be three curricular approaches to address the
needs of diverse audiences.
Integrate continuous and discrete mathematics in a common [2-year] sequence
Offer independent/disjoint courses in continuous mathematics, statistics,
and discrete mathematics
Organize separate courses in continuous mathematics, statistics, and
discrete mathematics to take advantage of common approaches [and topics]
Each approach seems to have its own advantages and disadvantages.
