Once you're fully ensconced in the major, it pivots into type B. And it turns out that I hate type B but slogged through it with medium-good grades.
looking back on it now, I've come to like type B and wish I could go retake those classes with my current perspective.
I think my original distaste was largely due to what felt like a bait-n-switch: start out majoring in something you like and are good at, but then pull the rug out and switch to something completely different
The fact that intro math classes don't do proofs (Type B) is because of the same pressure from people who only want to do Type A.
Due to internal changes in my uni, for the first time, my freshmen year, the math department taught proper proof-based Calculus 101 (from Apostle of all books) to all majors. Then the engineers and biologists complained so much, they had to cut out a lot of proofs from Calculus 102. There were even more complaints, so by second year, there were hardly any proofs in the core math courses. In a few years, the calculus courses had become devoid of proofs.
Some unis have separate intro courses for math majors, but it's very difficult to offer them in the current economic climate.
I think Proof vs non-proof is part of it, but it’s mostly related to level of abstraction.
You can do proofs for calculus, probability, or logic and still feel like you’re working with the types of problems you do in type A math.
But once you start doing proofs in modern algebra or topology you’re doing things with abstract objects that seem to exist for the amusement of mathematicians that look down on “applied math”
The real problem is that "type B", despite being much more important of an activity to learn (for mathematics or any other kind of technical problem solving) is almost entirely ignored in primary/secondary education.
Once you're fully ensconced in the major, it pivots into type B. And it turns out that I hate type B but slogged through it with medium-good grades.
looking back on it now, I've come to like type B and wish I could go retake those classes with my current perspective.
I think my original distaste was largely due to what felt like a bait-n-switch: start out majoring in something you like and are good at, but then pull the rug out and switch to something completely different