Should I take Real Analysis?

[Barny]

For an elementary analysis book I think the best one is Calculus by Michael Spivak.

Really? I'd say the opposite. It'd be like learning to play guitar by playing some Tommy Emmanuel songs. Pointless.

 

[Aaron Wong]

Really? I'd say the opposite. It'd be like learning to play guitar by playing some Tommy Emmanuel songs. Pointless.

To take an analysis course I would think you would have taken the calculus sequence already. With a good grasp of writing formal proofs I don't see why there would be a problem. This book was written for freshman university students. Honors students mind you but nonetheless freshman. I am taking that course as a sophomore and from what the math advisers are telling me, I will be among the very few that are not freshman in the class.

I'd go with Rudin's analysis if you want the more in depth stuff. Now that is serious stuff and is more along the lines of learning to play the guitar by playing Tommy Emmanuel songs.

 

[martingaletrader]

dedekind cuts and completeness or R are very important. usually when students take limits or appeal to convergence results they need to understand the foundations. but is it really useful in finance ?

Analysis on its own is useful and a rigorous study of it can set you free from an 'engineering math' mentality where you solve problems. on the other hand people get upset because proving existence results or delta-epsilon proofs can be a bit too much. it is kinda hard to learn on your own so a good professor teaching it can guide you.

for example I love the construction of real numbers by dedekind cuts - and the theory behind it is fascinating but I can't say it is useful to a finance guy.

 

[bigbadwolf]

dedekind cuts and completeness or R are very important. usually when students take limits or appeal to convergence results they need to understand the foundations. but is it really useful in finance ?

That's a good question. To what extent can the stochastic calculus used in finance be reconstituted in heuristic terms? I think -- like Wilmott -- that stochastic finance can and will be reconstituted on a heuristic basis (if it survives at all).