+1 for this comment. Calculus, i.e., Calculating with mostly finite numbers and (usually) a known set of well defined rules is only a part of mathematics.

As a student that currently learns Analysis and linear algebra, it is far more complex and abstract than calculus. It is not neccessarily harder to learn but different. And adapting to this paradigma takes time (and effort).

It is similiar to learning Assembley as a Python developer. Knowing Python will help with Assembley. But the levels of abstraction are obviously different and will require a lot of learning.

Not them but I def would. I built a fintech/econometric-lite system in python years back and it was mostly just taking in a ton of “obvious” knowledge and realizing the cool stuff you could do in practice

I don't understand this comment. Calculus as taught to mathematics undergrads is analysis, right?

Where is calculus "often taught" without "theorems/proofs that are used to build up calculus"?

Not US, but for GCSE A's further math equivalent, calculus primarily involved applying intermediate rules (chain rules, trig identities, etc.) to evaluate differentiation/integrals on elementary functions, and a bit on geometric and arithmetic series.

Analysis discusses less well behaved functions and spaces than these.

You can do the first part without even relying on analysis in a mathematical sense. You simply define a differential algebra, by introducing a derivation function that just happens to respect the correct rules. Then "calculus" is the topic of how to perform computations in such an algebra. Note however that you do need analysis to rigorously address other parts of a typical "calculus course", especially those dealing with infinities, sequences and etc.

In most US universities, the courses called "calculus" are mostly about computing integrals and derivatives. Yes, they'll have some theorems (Fundamental Theorem, Mean Value Theorem, etc), but most of the problems are related to computation than proving.

Unfortunately, since engineering students outnumber math majors by a large margin, the departments cater to them and not the math majors. The latter study analysis in later years - usually third or fourth.[1] Universities with strong math programs may offer it in the first or second year.

[1] I just checked my undergrad's program. They begin taking analysis in their 4th year, and it's offered only one semester a year!

That's just sad.

I was taught Calculus in high school, years 11 and 12 (two optional senior years for those that want more education prior to university, etc rather than transfer to a trade apprenticeship or leave school altogether).

That was a mixture of basic theory and proof and some computation (eg: derive an expression for the volume of intersection of two pipes at right angles, etc).

University went straight in to heavy analysis and foundations (for Math 100 - math for the serious (math, physics, hard chemistry)), with seperate streams for "casual math" - engineering, business, law, etc.

Engineering math prepped people for calculating dynamics and kinetics with vary loads, masses, thrusts, harmonic forces, network propagation, mesh computations, etc.

This was Australia in 1980.

> They begin taking analysis in their 4th year, and it's offered only one semester a year!

This is insane to me. In the UK about ten years ago, on literally the first day of my degree, my first class was real analysis. Yes, it was the easy stuff like proving sequences and series converge, various things about continuous functions, but we learnt how to prove it all and the exam was all about proving various things. And we built up to harder stuff as the year went on.

What is even happening if math majors aren't studying analysis until their fourth year?

Sorry I'm so incredulous, it's just that I literally don't know what I would've been studying if analysis had been delayed so much.