<p>Which is more math intensive and requires higher level reasoning?</p>
<p>I heard Economics as an undergrad involves little to no math at all but once you get into Gradschool you are bombarded with an unbelievable amount of math. Then theres Engineering majors which obviously involves math but Grad school isnt essential.</p>
<p>Economics majors can be rather light on math (a year of “calculus for business majors” and introductory statistics) or very heavy on math (freshman and sophomore math that is the same as what math and engineering majors take, plus junior and senior level math courses like real analysis, intermediate / advanced differential equations, intermediate / advanced statistics).</p>
<p>The only hard math for an economics major is advanced statistics and econometrics. Which are usually optional to take anyways. </p>
<p>Also I find that statistics/econometrics is significantly easier to understand than the math involved engineering classes. </p>
<p>Another thing about economics is that the electives that you choose to take don’t have to involve math at all. However with engineering, you will be facing tough math in almost every single class you take.</p>
<p>Of course when you get to something like financial engineering, the math is significantly more sophisticated than what a typical engineer will ever encounter.</p>
<p>If you want to investigate the math involved with advanced economics, take a look at the work done by some Nobel prize laureates in Economics. For example, look at the Black-Scholes formula and ways of valuing derivatives and pricing options.</p>
<p>One example comes to mind, although I don’t know how good it is. I’d generally consider game theory to be “harder” than differential equations, and economists do game theory whereas engineers do differential equations. This is academic, though, in the sense that you can do a very cursory treatment of game theory in an economics program and a very rigorous treatment of differential equations in an engineering program, and vice versa.</p>
<p>I would offer, though, that the “hardest” part of both economics and engineering programs is the mathematical component, though, and as such, the difficulty (real or artificial) of the programs - which can be inferred from graduation/retention rates - should correlate fairly well with how rigorously the programs do the mathematics. In other words, see which programs have higher drop-out rates, and maybe even see whether you have more economics -> engineering or engineering -> economics (normalized for the sake of comparison) transfers.</p>
<p>Also, the difficulty of the mathematics involved will very across engineering disciplines, somewhat at least. The variation is greater if you count software engineering & computer science as “engineering”, in which case, I’d be of the opinion that these involve the hardest mathematics… surpassed only by mathematics or rigorous statistics degree programs. Of course, as a math guy working in software, you might take this with a grain of salt.</p>
<p>However, this is confounded by the fact that switching into engineering is logistically difficult unless one has been planning it from freshman year, due to the prerequisite chains in math, physics, etc. that are needed. Trying to switch into engineering having not followed the engineering course schedule previously will typically result in delayed graduation, while switching into economics can probably be done up to a later stage.</p>
<p>Most economics majors take lightweight math (“calculus for business majors” and introductory statistics) and do not go to graduate school in economics. Those few intending to go to graduate school in economics take junior level math and statistics courses, possibly double majoring in math or statistics. So the answer to the title question depends on which economics majors are being referred to – the former do much less math than engineering majors, while the latter do much more math than engineering majors.</p>
<p>In fairness, the question is about which involves higher-level, harder mathematics… not which one requires more mathematics. You could clearly take 20 introductory courses in different subjects and not have to do much hard thinking, whereas a sequence of 10 consecutive (and meaningfully distinct) courses in e.g. discrete mathematics will probably take you from knowing nothing to knowing approximately as much as most PhD mathematicians do about logic, graph theory and the theory of computation.</p>