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I am teaching Mathematical Economics for undergraduate students. Students have taken Mathematics I and II during their first year and they must take Mathematical Economics when they are third year students. I have two options for teaching: first, I can teach Mathematics Rules and proofs (such as derivatives and integrals), or, as a second option I can teach only Economical applications.

If I take the first option I must pay more time for reteaching basics that they had seen during first year, but I think they may relearn the basics of Mathematics, and Mathematical Economics too. On the other hand, with the second option I can focus on Economical usages of mathematics only and offer more application examples. But in this case students may lose their interest in math and maybe start to fear Mathematics.

Which option is better for my students?

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    $\begingroup$ It would be easier to answer this question with some more information.... Is this in Turkey? What course of study are your students following? Who said there are only two options? Can you show what the options look like with links or with examples? $\endgroup$ – user173 Sep 16 '14 at 11:42
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Forget the first option. If they didn't pick it up the first time, they won't this time either. The second option is far more likely to induce either fear or boredom with Math.

Your mission here is to make math useful to them. Teach the applications. Review the background material as needed for those applications.

As an aside I would expect an economics course would have far more use for linear algebra and statistics than in calculus.

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Why not try to do some of both: introduce a mathematical idea, and then spend time carefully developing economic applications. I would be inclined to spend the semester alternating between two weeks on theory and two weeks of applications.

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