Way Cool Algebra: Fill & Download for Free

In maths??? It would depend on what capacity. Geometric constructions are cool, algebraic topology gets beyond my comprehension..but simply: it’s taking an expression, and breaking down the ways of getting to it… kinda like factoring(also an expanded form)..then matrices, and so forth…think: 1234=1000+200+30+4but I’m talking out of school, been a long time for me there…

No, and it’s extremely unlikely that it ever will.In the tree of ideas of mathematics there is a trunk (“math”), big branches, small branches, twigs, tiny twigs, and leaves. Branches are lemmas and theorems which are useful for a variety of applications, and are repeatedly used to prove other results.Leaves are “end results” which may be important, or cool, or historically significant, or applicable outside of math, but are not themselves useful ingredients for proving other things.The Classification of Finite Simple Groups is a huge, massive branch. So are the Fundamental Theorem of Arithmetic, the main theorems of Fourier analysis, Zorn’s Lemma, and many others.The modularity theorem[1][1][1][1], which was the main final ingredient in the proof of FLT, is a branch.The statement of FLT is a tiny, tiny leaf. It has great historical significance due to the way its legend motivated research in algebraic number theory, but never stood a chance of becoming a lemma.Footnotes[1] Modularity theorem - Wikipedia[1] Modularity theorem - Wikipedia[1] Modularity theorem - Wikipedia[1] Modularity theorem - Wikipedia

Long long time ago in High School…I had a Math teacher who did not like me. She wasn’t ‘hostile’, but she made it clear to me that I did not fit the profile of a ‘Snappy Student’ who would go places…“You don’t work Hard enough…” She would murmur deprecatingly as she walked away after leaving a test paper with lots of red marks on it.I didn’t like Math either. Geometry was Cool. Algebra was … Do-able. Calculus was Terror.One day, she put a Proof on the Board. And she turned to begin her usual terror campaign of turning her Fickle Finger of Humiliation on the class victim of the Day from her long list of ‘ne’erdowells’. After two or three stuttering chalkboard scratchings terminated by a wave to sit down and a molten look of disappointment over the rim of her glasses… she would then turn to her usual coterie of ‘Favorites’ to provide the correct answer.Her Favorite would get up, prance to the board and quickly snap out a series of equations and balance the whole thing in 7 steps.And then, for some reason, a Light-bulb went off in my head.I raised my hand and flapped and waggled it for attention. She raised an eyebrow (Just like Spock) in amazement. (I had interrupted her, BTW. The Temerity!)“Yes, Mr Veal?” (As in: what could YOU possibly have to say?)Me: “She took the Long way. I have a better answer…”Her: “Oh Really?” The Look in those eyes over the rim of her glasses still wasn’t HOSTILE…but it was COLD. “Show Us!”I got up and did the proof in 30 seconds flat with just 2 steps. (And no— I’ll be darned if I remember what the problem was nearly 40+ years on)The Favorite goggled at it. The Teacher just went still as statue as she visibly processed it.Then she turned to me again. Those eyes were still Ice Cold…but she actually smiled. I’ll never forget that smile— It wasn’t HOSTILE, but it wasn’t ‘Nice’, either.I never liked that woman….“Well, forgive me, Mr Veal…I take everything back.” She murmured. “You’re actually Industriously Lazy.”That was the one and ONLY frozen compliment I ever got from her.But she was right. I always look for the Simple Path. So I’m Industriously Lazy. I wear that with pride.