The courses in the various disciplines vary somewhat within each field depending on the area of specialty. For example, there is a significant difference in the requirements of electrical, mechanical and civil engineering and a civil engineer may not require a lot of knowledge in the use of Fourier transforms. Also, general economics would not require the rigorous courses in topology or functional analysis required of those studying mathematical economics.
The table below displays the titles of the courses that are traditionally studied in these respective areas but the intensity and focus differ significantly, depending on the field. For examples, athematical economics and theoretical physics require a high level of mathematical rigor, while some of the other sub-fields of these subjects are less demanding. The table summarizes the courses taken in each subject area in the undergraduate and graduate years of study.
The amount of mathematics required in a subject is roughly approximate to the level of abstraction that is involved. Concepts in fields like quantum physics and field theory are highly abstract, as they model the physical laws in curved space, requiring a knowledge of tensors and topology. Mathematical economics deals with complex models that include dynamic systems involving what is referred to as the “mathematics of chaors.” So, theoretical physics and mathematical economics require a substantial amount of mathematical sophistication. Fields like civil engineering, on the other hand, deal with more “concrete” entities that require substantial mathematics, but their models are less abstract and the orientation is practical rather than theoretical.
Scottish statistician George Udny Yule argued that the economist faced a bigger problem than the physicist because mathematical economics has to deal with so many elusive variables. He stated:
The investigation of causal relations between economic phenomena presents many problems of peculiar difficulty, and offers many opportunities for fallacious conclusions. Since the statistician can seldom or never make experiments for himself, he has to accept the data of daily experience, and discuss as best he can the relations of a whole group of changes; he cannot, like the physicist, narrow down the issue to the effect of one variation at a time. The problems of statistics are in this sense far more complex than the problems of physics.
