Substitute Algebra with Combinatorics and you will be fine.I do not understand this Algebra worship.Speaking as someone who graduated magna cum laude in in College Math.
I'm struggling to see how this makes sense. What's the evidence that someone can study advanced maths without understanding middle school algebra? It underlies calculus, analytic geometry, even a lot of combinatorics.
Analytical geometry underlies calculus,not Algebra.And combinatorics is a completely different arm of the two cultures of mathematics.Also Geometry was fine before Rene Descartes messed it up with Algebra and then we christened it Analytical Geometry.The method of exhaustion,amply developed by Archimedes with zero Algebra is the basis of intergration.It is because we start out with differentiation that we think Algebra is super important.Tom Apostol comes close in his calculus textbook when he actually starts with intergration.
A compromise would be to have two streams:The left-brained folks should follow the Algebra ->Geometry->Calculus track;the right-brained folks should have a Combinatorics ->Geometry ->Calculus track.
Hell, I think you need basic algebra for basic abstract algebra! And you're not convincing me you know anything about upper-level math if you don't know basic like... group theory.
Are you saying that because they end with "Algebra"?You can get an A+ in basic Algebra and have no clue about Abstract Algebra.It is the chain of reasoning rather than the mindless manipulation present in baby Algebra.
Still E=mc2, the Schrödinger equation, the Dirac equation, Maxwell's equations... It's hard to understand the equations if you don't understand equations.
It is easy to understand the equations if you have physical intuition of what is going on.Then derive from first principles.Memorizing formulas is the key to failing advance math.
Some believed we lacked the programming language to describe your perfect world. But I believe that, as a species, human beings define their reality through misery and suffering. The perfect world was a dream that your primitive cerebrum kept trying to wake up from. Which is why the Matrix was redesigned to this, the peak of your civilization. I say your civilization because as soon as we started thinking for you, it really became our civilization, which is, of course, what this is all about: Evolution, Morpheus, evolution. Like the dinosaur. Look out that window. You had your time. The future is our world, Morpheus. The future is our time.
First, it relates to the Matrix transcript, which is referenced across the song.
"it was just like a movie, it was just like a song", establishes that the song and movie are related.
"made us RESTless" references the "lacking the programming language to describe your perfect world" part of the transcript, REST being the architectural foundation of the web, "programming language" being a simplification that exemplifies the lack of understanding from Agent Smith, and also a common misconception regarding what REST is (an architectural style, not a language, not a protocol). The web still works upon REST pillars, despite what many people say.
The coincidences can be used to assert a point in time in which the web "is getting old", and abandoning those old foundations.
It is declared by many that AI will be the technology that brings us to that point. A "simulation" (movie reference to the training on web content) built to resemble the web as a "photograph" (song reference to the training on the web content), both alluding to the idea that this could be the very last moments we will see the web "in this light" (song reference to end of the web), the clouds will go dark (movie reference to the end of the web).
There is a very slick proof for the irrationality of the number 2 that is found in Baby Rudin.I thought it was his invention.Turns out it appears verbatim in Hardy's A course of Pure Mathematics.
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