I needed to write a math song.
I wish this song had existed back in the 2nd year of uni.
The Vector Space Axioms
If you want to have a vector space over a field
If you want to get it tight
Then all the axioms must be in place
For it all to work out right
The axioms are simple, true
And they seem quite obvious
But if not strictly followed you
Might be confused and mussed!
Axiom 1:
The commutativity of addition - that's x + y is the same as y + x
Axiom 2:
The associativity of addition - that's x + y, plus z is the same as x, plus y +z
Axiom 3:
The existence of zero- an element in the space where x + 0 = x for all x in the field
Axiom 4:
The existence of the additive inverse - for every x, there is a y, so x+y = 0
Axiom 5:
For every x in the space, 1x = x
Axiom 6:
For every a and b in the field, a (b x) equals (ab) x
Axiom 7:
For every a in the field, a (x + y) equals ax + ay
Axiom 8:
For each pair a and b in the field (a+b)x = ax + bx
The axioms are simple, but it's true
Without these you just can't do
Linear algebra at all.
@wacha Mar 20
I hated math when I was younger but grew to appreciate it in my brief stint in college. Nice job on this one, the melody is really catchy.
@robinh Mar 3
Good, more math songs ðŸ˜€ You could put together an album by now, I'm sure? Thanks for the refresher.
@elliottlawrence Mar 3
Haha! I was a math major so this is giving me life. Thanks for the refresher on these axioms, I forgot there were 8 of them! Also I love the tags, not too common to see a "math" and "celtic" combo I'm sure ðŸ˜€
@cnidaria Feb 27
Oh my god. ðŸ˜€ This made my morning. I don't know why I've never written an advanced mathematics song before! I might have to squeeze one today or tomorrow. Love the chipper mandolin.
@andygetch Feb 23
Learning by memorizing through song for the win!