Recent content by adrian_durham

I'm definitely not asking about how good of a calculus text it is. I certainly am not asking if this will prepare you for yet some other course. I'm asking about the nature of the material covered in it. For instance, "A student who made an A in his calculus class where they used Apostol...

Clearly the issue is the exercises and not the presentation. So, are you saying then that a typical student out of Apostol can do stuff like use the Archimedean Property to prove that a monotone function is integrable? Can they do epsilon-delta proofs? I really am just curious? It doesn't...

I don't have a copy of the Courant calculus text which I hear is a really good Calculus text, but have you guys seen A Course of Pure Mathematics by G H Hardy? That would really prepare you for real analysis, I think. At any rate, I just thought I would mention it. (I was not entirely happy...

The truth of a belief will never make the argument you used to arrive at it is any less spurious. And, knowledge isn't knowledge without correct justification. Rigor doesn't come with time and it doesn't suddenly emerge from years of heuristic rationalization. It is a completely separate...

With apostol? Well, that's the question. How much do I have? For instance, just because the author is rigorous in their presentation, that doesn't mean the student is actually expected to understand it. To what extent is the student expected to be rigorous (as opposed to something else that...

Well, much like sex and money, it only becomes important when you don't have enough.

Well, I think that your argument really drives home that it certainly cannot be said to be true about empty sets, in any case, whether it is false or just meaningless. However, I think I might agree with you, here. It is the same reason we tend to take "Let x be an element of E," as if it were...

Now that I think about it, just to elaborate on what I'm saying, "Let x be an element of E," is not actually an assertion -- a proposition that is either true or false. When someone says this in a proof we have to interpret it (and usually it is no big deal). But, in this case, it should be...

Or, equivalently, the transitivity proof that goes: "Easy proof: Let x be an element of E. a<=x<=b. Therefore a<=b." clearly doesn't work if there is no actual x in E. Maybe it isn't entirely obvious, but you really have to have an actual x, here. You aren't doing something like "IF x WERE...

Alrighty I'll take a look at that, then. Thanks!

I graduated early, myself. I think in your case with all that AP, you might do just fine with scholarships and all. I, personally, just couldn't stand high school, so that's why I got out. In my opinion, it really is largely a waste of time academically speaking, too, and certainly...

So, for instance, maybe Baby Rudin is the paradigm of "how to do it right" which includes proving stuff like Baire's Theorem. By "rigorous", I don't necessarily mean "Baby Rudin". On the other hand, Thomas and Finney does, in fact, have the formal definition of a limit, for instance, on p70 of...

Well, that probably isn't the equivalent, though, is it? It is more like a follow up to the Calculus book. And, does it really systematically hit classical mechanics, e&m, etc. like Halliday, Resnick and Walker -- perhaps the Thomas and Finney of physics -- would? I was also looking at the...

No one seems to be interested in my post in the Calc/Anal forum... I was wondering what would be the physics equivalent of the Courant Calculus text. Also, while we're at it, isn't Courant more rigorous than Apostol? I actually have the first volume of Apostol, and it's not bad at all. But...

Personally, I don't think that genius... ...has anything to do with following a formula or doing a calculation. It's you're ability justify your conclusions that matters. I'd be more impressed by someone that can actually prove that the derivative of cosx is -sinx than someone that can...