I do not have any say about whether you are going to opt both of them or not, but the proposition that Engineering would not teach you purely mathematics is utterly baseless.

As for Engineering is concerned, we are taught the following:
1) Calculus 1 (30% of pure mathematics)
2) Calculus 2 (50% pure mathematics)
3) Linear Algebra ( 10% pure mathematics)
4) Differential Equations (20% ofApplied mathematics)
5) Introduction to mathematical Physics for Engineers (30% of Applied mathematics)
6) Numerical Analysis (20% of Applied mathematics)


Vector analysis is the part of advanced courses like Electricity and Magnetism etc.

All of he above six courses are taught in (good) Engineering universities as the 3-credit-hour course.


Rest 5-10% of each paper one can easily do at home.

Anyway, I found it necessary to make the myths regarding Engineering and less-mathematics more just-change-the-bulbs-of-a-home clear.

Best of luck for your optional subjects. I'm sure you will ace them if you are dedicated and have ample time at your disposal.

Regards.