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> then in Grade 12, there's Advanced (!) Functions." Then in university, there’s Elementary Functional Analysis!

• dagw 2y ago
  The first math course as math major in university involved proving that a+b=b+a and that a+(b+c)=(a+b)+c. It's quite fun to go from 'advanced' calculus during the final classes of high school, to "OK, let's consider the expression 1+1=2. What does it actually mean and why is it true?"
  • thaumasiotes 2y ago
    > The first math course as math major in university involved proving that a+b=b+a and that a+(b+c)=(a+b)+c. Really? What were the axioms?
    • dagw 2y ago
      Basically the Peano axioms
      • thaumasiotes 2y ago
        How did that proof work for rational numbers?
        • dagw 2y ago
          It's been 20+ years, and I don't remember the exact steps the course went thought. But basically we started with defining N using the Peano axioms (although I don't recall the name 'Peano' being mentioned) and proving some basic rules of addition and equality. Then we defined subtraction, multiplication and inverse elements, and constructed Z and Q. From there you get to algebraic groups, and from there you can hand wave a lot of details. As I said it was literally one of the first math courses we did, so it wasn't super rigorous with all the technical and logical details.