re: Which is harder? Engineering, Med School, or Law School

Undergrad Engineering isn't the hardest.

In terms of "hard" i would imagine a PHD in applied mathematics of physics would be the "hardest" degree to get for most people. Abstract theorems and ideas which don't have an algorithm for an answer.

I took two grad school level math classes as an undergrad (we had a mix of grad students and then like 5-10 undergrad students in the classes as electives) and was sort of just passed in one of them because I tried somewhat hard but the work was just insane and I hadn't realized what I was getting in to.

The hardest one was called "asymptotic expansions and perturbation techniques" and they combined stuff I learned in Diff EQ 2, Fourier Series and Complex analysis as the stepping blocks "algebra" would be when you took calculus.

The chapter would be called something like "solve the duffing equation using (some set conditions) and you would end up with an integral that was technically "impossible to solve" based on the classes we had taken up to that point. But if you look at a closed circle in the complex plane (complex analysis course info) you could find a solution to the other parts of that closed loop using Fourier Series info, Diff Eq 2 info or some other upper level course and find the actual answer because the integral over the real plane portion had to be equal to the negative of the integral over the imaginary / complex portion due to some theorem.

^ that was one chapter / problem, then we got into something called "solve the boundary layer problem" using some sort of order of magnitude approximations summed together for the two sides of the boundary layer and then solve for some constant so you can combine the two to a single solution over the whole system. Didn't really ever quite understand what the frick was going on but I had made good friends with a grad school asian girl that I worked with that helped me pass.

- the fricked up thing is I still want to go back and pursue a masters / potentially a phd because even though I know it will be a total bitch I think I can do it.