For me, the leap to multivariate calculus gave me a lot of trouble.
Differential equations was doable but no longer fun for me, either.
It was a combination of multivariate calculus, linear algebra, and differential equations where I just wasn’t having fun with math anymore. Those subjects represented the end of pure math education for me, and later engineering classes requiring knowledge in those were also not a ton of fun. Went from a self-described math and science guy to just…not describing myself in that way anymore.
Honestly the standard curriculum was fine. It was when you got into trying to apply those skills to deciphering academic literature in a meaningful way as part of a broader career that things got tricky.
At a certain point my pattern recognition skills reached their limit to where learning each new concept was still the same, but I had a lot more trouble organically seeing and identifying when a particular technique was useful for a particular type of problem. Which is something that happens to a lot of different people at different stages of their math education, just happens to different people at different points.
And maybe I could’ve stuck with it, or used it enough to where I eventually got it easily the way I had done with all math topics before that, but I ended up steering the rest of my engineering education into topics that weren’t as heavy on that type of math. More programming and logic and microcontrollers, less electromagnetics and radio signals.
In my experience, it really wasn’t an “advanced subject” for me. Sure, the majority of majors who are trying to become doctors, CS, or computer engineers only have to take up to calc 2 (and diff eq) for their bachelors, but I still wouldn’t say MVC or diff eq is an advanced math subject. Real analysis or algebra – where you have to take a math course on mathematical proofs before taking these classes – is where I’ll say math becomes more abstract on its applications and advanced.
Diff eq was not challenging at all, I spent probably 6 hours a week on average (which includes the 4 hours of lecture). Its as simple as solving a linear equations, with it being slightly more tedious. If you understand derivatives, integrals, and partial fraction decomp (for Laplace transforms) its a breeze of a class.
MVC on the other hand was slightly more challenging, but having finished calculus 2, that too was also very enjoyable.
Point is, MVC and diff eq aren’t hard classes I wouldn’t even call them advanced classes as that title goes to analysis.
The start of calculus is relatively easy and intuitive, ive heard there are some schools that teach the basics of it to children at the same time they normally learn algebra.
Then theres the real bastard calculus that can and will make grown adults cry.
When there is more letters than numbers. When the letters change to weird shapes (integral). When there are multiple successive brackets. I dunno, I am not a mathematician.
From my experience, books titled “advanced calculus” cover the fundamentals in a lot more detail, with focus on δ-ε proofs. Usually, “advanced calculus” comes between elementary calculus (Calc 1-3 in a US institution) and real analysis.
If there’s advanced calculus, there’s presumably also regular calculus, so at what point does calculus start to be advanced?
For me, the leap to multivariate calculus gave me a lot of trouble.
Differential equations was doable but no longer fun for me, either.
It was a combination of multivariate calculus, linear algebra, and differential equations where I just wasn’t having fun with math anymore. Those subjects represented the end of pure math education for me, and later engineering classes requiring knowledge in those were also not a ton of fun. Went from a self-described math and science guy to just…not describing myself in that way anymore.
Honestly the standard curriculum was fine. It was when you got into trying to apply those skills to deciphering academic literature in a meaningful way as part of a broader career that things got tricky.
Is it just that it becomes so difficult/technical at that point?
At a certain point my pattern recognition skills reached their limit to where learning each new concept was still the same, but I had a lot more trouble organically seeing and identifying when a particular technique was useful for a particular type of problem. Which is something that happens to a lot of different people at different stages of their math education, just happens to different people at different points.
And maybe I could’ve stuck with it, or used it enough to where I eventually got it easily the way I had done with all math topics before that, but I ended up steering the rest of my engineering education into topics that weren’t as heavy on that type of math. More programming and logic and microcontrollers, less electromagnetics and radio signals.
In my experience, it really wasn’t an “advanced subject” for me. Sure, the majority of majors who are trying to become doctors, CS, or computer engineers only have to take up to calc 2 (and diff eq) for their bachelors, but I still wouldn’t say MVC or diff eq is an advanced math subject. Real analysis or algebra – where you have to take a math course on mathematical proofs before taking these classes – is where I’ll say math becomes more abstract on its applications and advanced.
Diff eq was not challenging at all, I spent probably 6 hours a week on average (which includes the 4 hours of lecture). Its as simple as solving a linear equations, with it being slightly more tedious. If you understand derivatives, integrals, and partial fraction decomp (for Laplace transforms) its a breeze of a class.
MVC on the other hand was slightly more challenging, but having finished calculus 2, that too was also very enjoyable.
Point is, MVC and diff eq aren’t hard classes I wouldn’t even call them advanced classes as that title goes to analysis.
The start of calculus is relatively easy and intuitive, ive heard there are some schools that teach the basics of it to children at the same time they normally learn algebra.
Then theres the real bastard calculus that can and will make grown adults cry.
Regular algebra makes me cry…
I had a full blown melt down over something called linear algebra. Good times, good times.
When I calc the ulus
I can think of a few potential cut offs, taking differential calculus to be basic.
Integral calculus. Multivariate calculus. Differential equations. Epsilon-Lamba calculus.
But that’s just my opinion.
After three semesters
Probably around analysis and abstract algebra which come after multi variate calculus and differential equations.
When there is more letters than numbers. When the letters change to weird shapes (integral). When there are multiple successive brackets. I dunno, I am not a mathematician.
From my experience, books titled “advanced calculus” cover the fundamentals in a lot more detail, with focus on δ-ε proofs. Usually, “advanced calculus” comes between elementary calculus (Calc 1-3 in a US institution) and real analysis.
Loved complex analysis. Poles for days. Such weird maths
More than one variable.