What are the benefits or losses of learning real analysis through a constructivist approach instead of a standard apporach?

Question

Recently I've found some courses on real analysis that use the constructivist approach and I got curious on some aspects:

• What are the benefits of learning through this approach?
• Is it ok to learn through a constructivist approach instead of a standard approach?

• How different the teaching on these approaches would be?

  1. Here I'm presuming a student who haven't taken real analysis lectures.

  2. I'm presuming that constructivist approaches to real analysis are not a standard practice in analysis courses but I'm not sure about that.

Answer 1

The main benefit I can see (apart from possible personal preferences in favor of constructive mathematics) is that people who learn "classical" methods first can find it challenging to learn to work constructively later. So, if someone is planning to do constructive math later, learning it constructively from the outset might be a benefit. On the other hand, if one is planning to do classical mathematics later, it may make more sense to learn it classically in the first place.

Teaching constructive math has the same variations as teaching classical math - some professors will use a detailed lecture-style approach, while some will use an inquiry-based approach where the student discovers more on her own. Books on constructive mathematics read basically the same as books on classical mathematics.