As this is primarily a text on point-set topology, I recommend reading this article on the Texas Topology approach, which was taught to me when I was in undergrad
Basically the idea is for the students to discover and prove the key theorems themselves -- with the instructor giving them hints and some feedback. No cheating and no textbooks -- the founder, R.L. Moore, would screen students to his classes to weed out those who already knew too much.
This approach was quite tough, and lasted from the about 1970 to the 1980s, at which point there was a bit of a revolution -- according to the story told me, the younger professors moved all the furniture of the older professors onto the lawn, and declared they would go back to a more standard approach to teaching topology.
At the same time, it's incredibly rewarding to discover and prove something like the Baire category theorem all by yourself. No matter how clumsy and inefficient your approach ends up being. It's a bit of a shame that no university does this anymore, but I think an enterprising student can still persuade a professor to work with them like this.
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As this is primarily a text on point-set topology, I recommend reading this article on the Texas Topology approach, which was taught to me when I was in undergrad
https://www.sciencedirect.com/science/article/pii/S031508600...
Basically the idea is for the students to discover and prove the key theorems themselves -- with the instructor giving them hints and some feedback. No cheating and no textbooks -- the founder, R.L. Moore, would screen students to his classes to weed out those who already knew too much.
This approach was quite tough, and lasted from the about 1970 to the 1980s, at which point there was a bit of a revolution -- according to the story told me, the younger professors moved all the furniture of the older professors onto the lawn, and declared they would go back to a more standard approach to teaching topology.
At the same time, it's incredibly rewarding to discover and prove something like the Baire category theorem all by yourself. No matter how clumsy and inefficient your approach ends up being. It's a bit of a shame that no university does this anymore, but I think an enterprising student can still persuade a professor to work with them like this.