I hope to expand this page to something similar to my informal thoughts on geometry page. At the moment, all I have is the following.
A dialogue concerning the existence of the square root of two.
What is wrong with thinking of real numbers as infinite decimals?
Why isn't it just obvious that the integers form an unbounded subset of R?
How to solve basic analysis exercises without thinking.
Proving that continuous functions on the interval [0,1] are bounded
What is the point of the mean value theorem?
Why study finite-dimensional vector spaces in the abstract when they are all isomorphic to Rn?
The relationship between theory and computation in linear algebra.