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 2020-01-30, 09:31 #1 wildrabbitt   Jul 2014 3·149 Posts infinite products I've got a maths degree but I was never taught about infinite products. I'd like to ask something : when do people usually learn about infinite products? I suppose it must be at masters level but then there are different masters degrees, so perhaps it's in a particular branch of maths (maybe analytic number theory) ?
2020-01-30, 09:55   #2
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

2×7×103 Posts

Quote:
 Originally Posted by wildrabbitt I've got a maths degree but I was never taught about infinite products. I'd like to ask something : when do people usually learn about infinite products?
With proper education you can learn that first at high school.

2020-01-30, 10:37   #3
Nick

Dec 2012
The Netherlands

31218 Posts

Quote:
 Originally Posted by wildrabbitt when do people usually learn about infinite products?
Here in the Netherlands, we teach infinite products and direct sums (of various mathematical structures) in the 2nd year of the 3 year university bachelor in mathematics.

2020-01-30, 10:38   #4
pinhodecarlos

"Carlos Pinho"
Oct 2011
Milton Keynes, UK

5×7×139 Posts

Quote:
 Originally Posted by R. Gerbicz With proper education you can learn that first at high school.
Here at nursery level.

2020-01-30, 14:24   #5
CRGreathouse

Aug 2006

22×1,493 Posts

Quote:
 Originally Posted by R. Gerbicz With proper education you can learn that first at high school.
It's a part of calculus, so in high school or early in college I think.

 2020-01-30, 14:54 #6 M344587487     "Composite as Heck" Oct 2017 2FA16 Posts In the UK it's at A levels but different exam boards might not have it on the curriculum, there's at least 3 popular exam boards. The majority of my first year at uni was recapping A levels in a bit more depth to get everyone up to same level, it's a very wasteful system that could do with an overhaul.
 2020-01-30, 16:35 #7 Dr Sardonicus     Feb 2017 Nowhere 10000111010002 Posts You need to know about convergence, and most likely natural logarithms also. (Convergence of an infinite product is often equated to convergence of the series of natural logs of (all but finitely many of) the factors, assuming a branch of the log for which ln(1) is 0. So probably first semester calculus at earliest -- late HS or early college. You might not run into infinite products until you take complex analysis. That would be a bit later. An amusing example is $\prod_{n=0}^{\infty}(1\;+\;z^{2^{n}})$ which converges for |z| < 1. Premultiply by 1 - z and watch what happens
 2020-02-03, 16:04 #8 wildrabbitt   Jul 2014 3·149 Posts Merci. Merci beaucoup docteur. Quelque choses a faire maintenant.
 2020-02-11, 13:00 #9 ricardos   "ricardos" Feb 2020 USA 5 Posts Thank you. It's very useful and smart definition.

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