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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.

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    $\begingroup$ Do you consider real analysis and abstract linear algebra as proofs based math courses? A number of universities do cover these in masters. $\endgroup$ – Dayne Nov 21 at 1:52
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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.

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    $\begingroup$ +1. To add to this, I have found that many students from non economics undergrad (I am also one such) who directly study advanced macro or applied economics using economic techniques have relatively poorer understanding of fundamental economics concepts (I have witnessed this a lot in applied researchers in central banks). This has made me believe that not focussing too much on maths in undergrad is. in some ways, also a good thing and preserves the 'social science' side of the economics discipline. It encourages broader thinking. $\endgroup$ – Dayne Nov 21 at 18:01
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I'm an undergraduate from India studying in an university controlled by the Central government. I've experienced the same longing for a proofs class now that we are starting advanced microeconomics,a lot of doubts especially on the abstract calculus used to define certain slopes and moulding that mathematical definition into statements relating to decisions, and back and forth again and again for a new topic will most probably give more doubts than what people consider normal. That doesn't mean one is not intelligent enough, that only means that one is questioning the entire foundation of the theory and starting from the ground up. This quest will require one to familiarize himself/herself with proof making and establishing rigorous mathematical statements that act as stepping stones to extract results. So in my view, the reason why such an exposure isn't given early on is to instill a certain clarity in the student. Knowing what to prove is a pre-requisite to proving something. Learning what theories have to offer and accepting or rejecting them with whatever reasons you might have will enable you to look at the final result that is being established here so when you touched and felt enough theory, tools to prove/disprove them are provided to you to use as per your imagination.

A significant level of familiarity with theoretical concepts happens at mid-masters or late undergraduate level.

Another reason is the eligibility to join the course, if you've spent your high school exploring literature, you will be strongly advised to not take a math major. Here, in India, you won't be allowed to, because the eligibility criteria for joining a math course dictates that you must have passed your high school math with a specific percentage that is deemed enough by the university(it differs from uni to uni).

For Economics, we allow anyone with any specialisation in high school to join the course. The ones who end up joining are usually those who don't have a strong math background, and thus the professors take more time to familiarize them with the study of economics before giving them access to tools that create new theories.

"You get the keys when you learn how to drive"

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