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Is this a group? math people
    #7391662 -

Before I dropped out of college, I was a math major. My last class was about groups. I didn't really understand it very well. But I think I have run into a group in my new career, I have chosen to start a specialty mushroom farm. I have three growing rooms for king oyster mushrooms. I have a 24 day turnover; ie begin spawn run on day 1 and harvest on day 24. Single flush. Since 24/3=8, I start a new spawnrun every 8 days and I have a perpetual cycle. Can you tell if this really is a group or just a cycle of numbers?

The right coordinate is the day from the beginning of the first spawnrun. The left coordinate is the day in each individual growrooms cycle(3 growrooms).
1-1
2-2
3-3
4-4
5-5
6-6
7-7
8-8,1
9-9,2
10-10,3
11-11,4
12-12,5
13-13,6
14-14,7
15-15,8
16-16,9,1
17-17,10,2
18-18,11,3
19-19,12,4
20-20,13,5
21-21,14,6
22-22,15,7
23-23,16,8
24-24,17,9
25-1,18,10
26-2,19,11
And so on...

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Re: Is this a group? math people [Re: YidakiMan]
    #7392006 -

Fuck numbers. And time too.

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Re: Is this a group? math people [Re: Rustifer]
    #7393933 -

Hey I took an intro course on abstract algebra so I only have superfacil understanding of the subject. Abstract Algebra was a pretty tough class for me (I'm a slow math person to begin with), a lot of mind warping proofs, and I took 3 other 4th year math class along with it (excuses,excuses). I like differential equations a lot more than abstract algebra tell you the truth. I felt a lot of joy once I begin to understand the Navier-Stokes equations (and numerical solutions to these types of problems, as I'm reading up on this subject right now)! You see I use to work at a lab doing Computational Fluid Dynamics so to be able to finally understanding what it's all about has been joyful. Much more fun than abstract algebra for me personally. But I only have an undergrad education in Math so I'm pretty clueless.

What is a Group?

A nonempty set G is said to be a group if in G there is an operation * such that:

(a) a,b in G then a * b in G, the closure property.
(b) a,b,c in G, then a*(b*c)=(a*b)*c. Associativity.
(c) There exists an element e in G such that a*e = e*a = a for ALL a in G. Existence of a unit element e.
(d) For every a in G, there exists an element b in G such that a*b = b*a = e. Existence of inverses.

So what is your * here?

Examples of Groups: The set of all integers under the operation +.
Nth roots of unity etc...

What do you mean by is these numbers a Group?


----------------

Also, why so much hate against Math??? Math is simply a way to describe things rigorously. Why so much hate against it?


--------------------
Be like water my friend!

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Re: Is this a group? math people [Re: SymmetryGroup8]
    #7394160 -

what are you trying to do here? Are you saying you want to have fruiting every 8 days?


--------------------
Be like water my friend!

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Re: Is this a group? math people [Re: SymmetryGroup8]
    #7398596 -

I'm not sure what I was trying to prove.
I also took an Intro to Abstract Algebra, but I didnt understand much. I thought it looked like something from the class.

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Re: Is this a group? math people [Re: YidakiMan]
    #7398629 -

We learned something that looked like this

1 2 3 4 5 6 7 8 9
1 8 3 4 5 6 7 2 9

It was said verbally as "One goes to one, two goes to eight, three goes to three,...,eight goes to two, etc"

What is that called?

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Re: Is this a group? math people [Re: YidakiMan]
    #7398988 -

http://en.wikipedia.org/wiki/Permutation_group
http://en.wikipedia.org/wiki/Symmetric_group
http://en.wikipedia.org/wiki/Cayley_table

My memories are hazy on this subject but we started with learning about A(S), i.e the set of 1-1 mappings of S onto itself. If S is finite then there is n! elements in A(S)

For example, suppose S=[1,2,3] (note here you can call 1,2,3 as x,y,z or whatever the fuck you want to call it). Let's write out explicitly all the mappings.

1. i:1->1, 2->2, 3->3 (i.e 1 maps to 1)
2. f:1->2, 2->3, 3->1
3. g:1->2, 2->1, 3->3
4. g o f (i.e g compose f): 1->1,2->3,3->2
5. f o g: 1->3, 2->2, 3->1
6. f o f: 1->3, 2->1, 3->2

From the study of Sn one can learn a lot about finite groups.

Yeah this sure explains a lot doesn't it... LOL.

Bye bye.

Why is abstract algebra relevant? I don't know but supposedly advanced mathematical physics uses this stuff extensively. Some physics dude want to enlighten us on applications?

Seriously man, all this is hardcore shit for me. All I remember is racking my brains doing proofs for homeworks. And in the end I skipped out a few homework and was basically fucked after that. I made a C in the class. Although my teacher sent me an email after the final telling me how my proofs on the final was pretty clear,how my proof skills improved etc. On second thought he probably did that so I won't go postal on they asses LOL. I kid kid.


--------------------
Be like water my friend!

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Re: Is this a group? math people [Re: SymmetryGroup8]
    #7399005 -

BTW, I think the purpose of this intro class was to teach students about doing proofs. It's a proof heavy class. I don't know how it compares with say an advanced calculus class (i.e proof heavy class) because I never took advanced calculus.


--------------------
Be like water my friend!

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Re: Is this a group? math people [Re: SymmetryGroup8]
    #7399333 -

Dude you piked my interest in this shit again (been reading wikipedia lol). I think I'm going to do some reviewing and continue studying from where we stopped...But I'm trying to code some fluid simulation right now so this will have to wait...


--------------------
Be like water my friend!

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