Most Math Major Math is Taught Backwards

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When you’re a math major in undergrad and you get up to those junior and senior level courses you know, real analysis, Abstract algebra, topology you start to realize that a lot of the stuff is really taught backwards: theorem proof, theorem proof but you don’t even have a concrete grasp of what’s going on.

You’re just pushing all these symbols around. Maybe you can follow the rules, but you don’t really understand the subject.

That’s because you need the concrete examples first. You gotta work through the computations with actual numbers, see how it plays out, get a feeling for the process, and then you do the abstraction.

Skipping that concrete stage with actual numbers and test cases that can help you build some experience and intuition. Skipping that doesn’t make the course rigorous.

It just makes it inefficient.

Further reading:

• The Necessity of Grinding Through Concrete Examples Before Jumping Up a Level of Abstraction
• It’s Incredible How Poor Math Instruction Can Be

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