infinite products

wildrabbitt · 2020-01-30, 09:31

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) ?

R. Gerbicz · 2020-01-30, 09:55

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.

Nick · 2020-01-30, 10:37

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.

pinhodecarlos · 2020-01-30, 10:38

Quote:

Originally Posted by R. Gerbicz

With proper education you can learn that first at high school.

Here at nursery level.

CRGreathouse · 2020-01-30, 14:24

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.

M344587487 · 2020-01-30, 14:54

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.

Dr Sardonicus · 2020-01-30, 16:35

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

wildrabbitt · 2020-02-03, 16:04

Merci beaucoup docteur. Quelque choses a faire maintenant.

ricardos · 2020-02-11, 13:00

Thank you. It's very useful and smart definition.

2020-01-30, 09:31	#1
wildrabbitt Jul 2014 110111111₂ 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) ?

2020-02-03, 16:04	#8
wildrabbitt Jul 2014 1BF₁₆ Posts	Merci. Merci beaucoup docteur. Quelque choses a faire maintenant.

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2020-01-30, 14:54	#6
M344587487 "Composite as Heck" Oct 2017 761 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 10E0₁₆ 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

2020-02-11, 13:00	#9
ricardos "ricardos" Feb 2020 USA 5 Posts	Thank you. It's very useful and smart definition.