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Comment by vorgol | Hacker News Reader

Can you meaningfully study advanced math without understanding algebra?

Depends on your definition of both of those terms. Being able to solve a simple equation is generally useful. You probably don't need much more than that to understand Set Theory or much of Logic. You can learn to write proofs without knowing calculus, etc.

Maths is such a wide field that terms like "advanced" have little meaning imo. Or rather, advanced doesn't have to mean complex, and even complex doesn't have to mean inscrutable. But then even simple problems can turn out to be fiendishly hard.

Advanced means you got through the basic quick enough to need more stuff to do. Or move up a year early.

Advanced math builds on algebra, without it, most concepts won’t fully connect.

Yes.

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.

No, I am obviously not saying math ends with algebra.

Say hello to rings.

Algebra seems kind of fundamental to things like physics and chemistry.

Geometry is fundamental to physics and chemistry,not Algebra.Look at the thinking style,not the content.

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.

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