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.
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.
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.
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.
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.
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.
Actually,combinatorial thinking is more useful for understanding Algebra and not the other way around.Key word is understanding.No need for a beautiful formula you cannot understand.