Proof Based Math Education in Economics One of the things I've experienced as a graduate student is really the lack of math being a main factor in holding me back from approaching more advanced materials in microeconomics and macroeconomics. Often I find myself playing a lot of catchup. I primarily express this with reference to the lack of training in proofs based mathematics.
My question is: as economics educators what is the rationale for not exposing students to proof based mathematics at the undergraduate or masters level? (a basic intro to proofs class can go a long way).
Note: this question excludes those programs that are specialized PhD stream feeders.
I believe there are different goals to undergraduate and (research-oriented) graduate programs.
Most undergraduate students will not pursue a career in research. For them, different proof techniques may not be of first-order importance. In my eyes, they should learn basic stuff like incentives matter; thinking in terms of marginal changes; supply and demand; market power can be bad; what can be done with OLS; although the market is great it can fail with externalities or public goods; why does inflation matter; how to model asymmetric information; correlation and causality; solving a dynamic game backwards and credible threats; and so on. All of that can be taught without using heavy mathematical machinery. There are enough important concepts to teach and you can only do so much. However, I agree that it should be made clear that taking a few math classes can be very helpful if a career in research is planned.
Moreover, I think that I would not have enjoyed pure math without economic applications as an undergraduate. Usually, I become interested in some economic problem which then incentivizes me to learn new mathematical techniques. My impression is that most undergraduate students have even stronger feelings about that. I fully understand that it is hard to catch up on basic mathematical ideas as a grad student, but it would not have been much easier as an undergrad without a conviction to do research.
Different institutions have different approaches. Therefore, most PhD programs have a mandatory first-year that is quite heavy on proofs and mathematical techniques. Often there is also an additional math camp. The idea is to get everyone on a similar level.