Must admit being surprised that you and Graham thought analysis was simple. I didn't attend the tutorial either so I don't know about the reaction of the tutorial group. Ok so far and I still have 1 question to go I'll admit the TMA questions are straightforward (perhaps delibrately so) routine tests of convergence of sequences and series. However can you remember the proofs and reproduce them.
The real stuff will hit us in block II, When we get onto epsilon delta and for example the continuity but non differentiability of the blancmage function probably the hardest thing on the course. (OK you don't have to do this to get a good mark on the TMA or pass the exam). I do feel that M208 is in danger of lulling people into a false sense of security. There is always Cambridge to bring us back to a false sense of security.
Still if you find it genuinely easy I take my hat off to you
I don't think that either of us think that it's easy. It's [groping for words here] just that it all seems a bit obvious. [Not the right way to put it!]
What I was trying to get across is that this, superficially obvious thing, is, when you look at it properly, with the minds we are now building, a slippery customer.
Not having thought about analysis for a week did me good—when I came back there were a lot of, "wait a minute..." moments. That's a good sign, I think.
Yes fair enough, I guess the point of analysis is to make us realise just how unobvious the obvious is and just how difficult it is to make precise of just why what seems obvious at first sight isn't obvious. As you righthly point out on your blog Zeno's paradox being a prime example.
Ok those who haven't grasped the point will just dismiss analysis as mere pedantry and often it seems that way and even the answers in M208 aren't pedantic enough.
For example the proof's of something being a least upper bound of something usually involve sqrt(a/(b-m')) which is only real if b > m' So you can only appeal to the Archimedean principle if b > m'.
Or trigonometric functions are only bounded if the argument of the trigonometric function is an element of R.
Gosh becoming more pedantic than the answers in M208 must be learning something Once again good luck with the TMA. Only the last part of question 4 to go. Woo hoo I can have a break from maths tomorrow
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Whoops, terrible mess has been made.
;0
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Must admit being surprised that you and Graham thought analysis was simple. I didn't attend the tutorial either so I don't know about the reaction of the tutorial group. Ok so far and I still have 1 question to go I'll admit the TMA questions are straightforward (perhaps delibrately so) routine tests of convergence of sequences and series. However can you remember the proofs and reproduce them.
The real stuff will hit us in block II, When we get onto epsilon delta and for example the continuity but non differentiability of the blancmage function probably the hardest thing on the course. (OK you don't have to do this to get a good mark on the TMA or pass the exam). I do feel that M208 is in danger of lulling people into a false sense of security. There is always Cambridge to bring us back to a false sense of security.
Still if you find it genuinely easy I take my hat off to you
Best wishes Chris
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Sorry the phrase including Cambridge should read
"there is always Cambridge to bring us back to a sense of reality".
Good luck with the TMA this weekend.
Best wishes Chris
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Hi Chris
I don't think that either of us think that it's easy. It's [groping for words here] just that it all seems a bit obvious. [Not the right way to put it!]
What I was trying to get across is that this, superficially obvious thing, is, when you look at it properly, with the minds we are now building, a slippery customer.
Not having thought about analysis for a week did me good—when I came back there were a lot of, "wait a minute..." moments. That's a good sign, I think.
See you next tutorial?
arb
neil
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Yes fair enough, I guess the point of analysis is to make us realise just how unobvious the obvious is and just how difficult it is to make precise of just why what seems obvious at first sight isn't obvious. As you righthly point out on your blog Zeno's paradox being a prime example.
Ok those who haven't grasped the point will just dismiss analysis as mere pedantry and often it seems that way and even the answers in M208 aren't pedantic enough.
For example the proof's of something being a least upper bound of something usually involve sqrt(a/(b-m')) which is only real if b > m' So you can only appeal to the Archimedean principle if b > m'.
Or trigonometric functions are only bounded if the argument of the trigonometric function is an element of R.
Gosh becoming more pedantic than the answers in M208 must be learning something Once again good luck with the TMA. Only the last part of question 4 to go. Woo hoo I can have a break from maths tomorrow
Definitely must make the tutorial on Saturday
All the best mate
Chris