Recent content by ivanos

Are you quoting Henri Poincaré's definition of intuition? Do you think Klein possesses "higher plane of intelligence" than Hermite? xD

Graduate texts are always dry and dense and their style are not like Spivak's, conversational and informal. You're right: Spivak's is not that precise. So it may better suit college freshmen. College freshmen (excluding serious and budding mathematician-to-be) always need motivation on...

I've provided examples in my response to deluks917.

1. "If you are already certain of something, why start a thread on it?" Why not? 2. "The way you have developed this conversation is not the optimal way to stimulate debate over the topic." I doubt that.

I do have pre-decided opinion (who doesn't?). But that does not mean no discussions are allowed. Do you see in every discussion people without "pre-decided opinions"?

One more thing: Spivak likes to lists out a lot of theorems and then proves them directly in his conversational/informal texts while Apostol highlights them as theorems in another section and then let's the readers to prove most of them by themselves. Really serious mathematician-to-be shall...

The problem is in the foundational part, Spivak's assumes something but doesn't explicitly state it. For example, he assumes some elementary algebraic rules, such as if a=b, a+c=b+c, and then use them to proceed his proof. That's not rigorous enough compared with Apsotol's. As to the logical...

Heard many people say that there are three good cal textbooks: the ones by Apostol, Spivak, and Courant. I own Apostol's and Spivak's. The major difference between the two is the degree of rigor and logical order, in which Apostol's apparently beats Spivak's, although Spivak's is far better than...