Math Is Fun Forum

luzbyrd

Novice

Registered: 2024-03-10

Posts: 1

Practical applications of abstract algebra

Hello everyone, I'm curious about the practical applications of abstract algebra in real-world scenarios. Can anyone share examples of how concepts from abstract algebra are used in various fields?

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 47,696

Re: Practical applications of abstract algebra

Hi,

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: Practical applications of abstract algebra

hi luzbyrd

Welcome to the forum.

The one area I already knew about is the application of group theory in solving the Rubik's cube.  If you're interested search for the name Singmaster.

Then I asked my pal google and came up with:

fields __ telecoms, medical imaging, navigation, power generation

complex geometry __ computer graphics, architecture, design

rings __ industrial control systems

linear algebra __ algorithms, graphics, data mining, machine learning.

At this point I decided to stop.  You can complete your search by trying google yourself.

I should emphasize: I don't know the underlying theory for most of the above.

The other point that is worth making is this.  Many areas of 'pure' mathematics seemed to be just there because mathematicians like to play around with ideas but who can predict when these theories might become useful in the real world?  Who would have thought that a study of number bases and, in particular, base 2,  would have become the basis for all computing or that prime numbers would be useful in encryption. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 224

Re: Practical applications of abstract algebra

I am 75. I was fortunate that, since I was teen, I have enjoyed the most every time I had difficult math problems to be solved (numerical and logical). For example, while the boys and girls played together around the swimming pool, I enjoyed solving new math problems instead

Naturally, this helped me be an independent professional designer in electronics (hardware and software), right after finishing my high studies. Since then, I design and produce various electronic controllers which are needed by the local consumers in every period of time.
This is how I was able to gain my daily bread (and of my few assistants) while working independently.
(Please note that working independently may not be possible for engineers living in some other countries).

Kerim

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.