Enhancing Economic Understanding through Advanced Mathematical Tools
This document addresses the necessity for sophisticated mathematical tools in social sciences, particularly economics, as they study complex phenomena unlike the simpler models in physics. It highlights the intimidation faced by students when introduced to advanced concepts like convexity, continuity, and optimization in courses such as ECON 404 and MOFI 401. Additionally, it emphasizes the paradox that while these mathematical tools are essential for deepening understanding, they can deter acceptance among social scientists, widening the knowledge gap. Student feedback reflects the need for more foundational exposure and confidence in handling these concepts.
Enhancing Economic Understanding through Advanced Mathematical Tools
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Presentation Transcript
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Bits of motivation J-P Aubin (Dynamic Economic Theory) • If we accept that physics studies much simpler phenomena than the ones investigated by social (and biological) sciences and that for this purpose they motivated and used more and more complex mathematical apparatus, we have to accept also that social sciences require a [..] dedicated arsenal, which goes beyond what is presently available. • It has been said that physics could be defined as the part of the environment, which can be understood through mathematical metaphors. So, how we try and understand economics without mathematical metaphors [JK]? • Paradoxically, the very fact that the mathematical tools useful for social sciences are and have to be quite sophisticated impairs their acceptance by many social scientists and the gap menaces to widen.
Bits of motivation Student says… • 90% of the material covered was new • students feel highly intimidiated by the implication that they are supposed to have covered and be familiar with much of the material - I know I felt this way
Bits of motivation Lecturers say… ECON 404 Micro and MOFI 401 Options Math Extentions --- students benefited from the exposure to concepts such asconvexity, continuity, basic set notation, etc.; the realplus they had seen the terms before we covered them in class.The students in MOFI 401 actually get their hands dirty;would benefit from being reminded about the chainand quotient rules, and even basic probability theory. ECON 405 • optimisation – both constrained and unconstrained (lagrangeans). • implicit function theorem • supermodularity • what it is to invert a matrix • concavity • quasi concavity • fixed point theorems
