RE: Can I just say, and I'm just being honest...
October 24, 2017 at 10:09 pm
(This post was last modified: October 24, 2017 at 10:10 pm by Kernel Sohcahtoa.)
CIJS,
I've been reading Lara Alcock's How to Think about Analysis, and IMO, it's been a nice, informative read: I liked her commentary about gaining an understanding of what a math theorem is actually saying before one attempts to prove it. In particular, I found the following passage to be interesting:
"Once you understand what the theorem says, you are in a position to study the proof. But how should you do this? How will you know when something is proved? For many undergraduate students, the obvious answer is that you know something is proved when your lecturer or textbook says it is. Obviously you have no reason to doubt a presented proof: it's entirely reasonable to believe something on the basis that someone in authority tells you it's valid. It's not very intellectually satisfying, though--much better to understand something in detail than just to believe it." (Alcock, 38)
Reference
Alcock, Lara (2014). How to Think about Analysis. USA: Oxford University Press.
I've been reading Lara Alcock's How to Think about Analysis, and IMO, it's been a nice, informative read: I liked her commentary about gaining an understanding of what a math theorem is actually saying before one attempts to prove it. In particular, I found the following passage to be interesting:
"Once you understand what the theorem says, you are in a position to study the proof. But how should you do this? How will you know when something is proved? For many undergraduate students, the obvious answer is that you know something is proved when your lecturer or textbook says it is. Obviously you have no reason to doubt a presented proof: it's entirely reasonable to believe something on the basis that someone in authority tells you it's valid. It's not very intellectually satisfying, though--much better to understand something in detail than just to believe it." (Alcock, 38)
Reference
Alcock, Lara (2014). How to Think about Analysis. USA: Oxford University Press.