Navigating the Overwhelming World of College Mathematics

[DavidSmith]

I have determined that there is too much mathematics for a college student to learn. Almost any textbook you try to grasp will likely contain century old math andwith the repaid pace of ever more complicated math begin introduced it is impossible to learn it all.

We have exceedingly complicated topological and abstract problems that are taught in the major universities. Folding surfaces on other surfaves.

Then there is tripple integration of complex air flows and vector spaces and otehr stuff

 

[ekrim]

being a math major would have been sweet a couple hundred years ago

 

[ice109]

yes learning all of a field is nearly impossible, this is why specialization is necessary

 

[Hurkyl]

I have determined that there is too much mathematics for a college student to learn.

That's a good thing. If you learned it all, then there's be nothing left to learn, and nothing new to develop.

 

[robphy]

Because of advances, curriculum changes as well.

I remember looking at an old course catalogue from my college [which has a master's program].
There were three advanced courses of note:
"Maxwell Equations in rectangular coordinates"
"Maxwell Equations in cylindrical coordinates"
"Maxwell Equations in spherical coordinates"

Needless to say, the emphasis has shifted away from those aspects...
[and those particular courses are no longer offered]
making room for new topics.. or old topics presented in new ways.

 

[ice109]

Because of advances, curriculum changes as well.

I remember looking at an old course catalogue from my college [which has a master's program].
There were three advanced courses of note:
"Maxwell Equations in rectangular coordinates"
"Maxwell Equations in cylindrical coordinates"
"Maxwell Equations in spherical coordinates"

Needless to say, the emphasis has shifted away from those aspects...
[and those particular courses are no longer offered]
making room for new topics.. or old topics presented in new ways.

ha now all three of those are in one good E&M course

 

[TheRyan]

This post makes me think a little. You say there is too much math to learn, but just how much math is there? Does anyone know what the "most difficult" math is to learn? To many, calculus is "the end." They don't think about how much further you could go with it. How far does math go?

I understand that eventually it just becomes mind-numbingly complex with equations (as in those that could be used in statistical projections and large civilization simulators). What is the most complex concept/topic to learn in math? Is there some kind of math that, if understood, one is said to be a mathematical genius or something?

 

[MathematicalPhysicist]

to your questions starting from last:
1. Is there some kind of math that, if understood, one is said to be a mathematical genius or something? No.
2.What is the most complex concept/topic to learn in math? Well although it's subjective, but for me I had last week an exam on calculus2 and a week before i had an exam in logic, i found the proofs in logic longer than calculus 2 and more interesting.
3.for what you understand it does become more complex, but still if you take the time to learn it and absorb it then it will come to you as natural as the sunshine (although the sun is not there to last forever, or so they tell us (-: ).

 

[genneth]

Difficult maths... is what's at the frontier. The most difficult maths I've yet come across is Alain Conne's Noncommutative Geometry. That really is difficult. But even there, I wouldn't say that understanding requires "genius". As it happens, as maths becomes more difficult, the equations usually get simpler, though probably with more symbols, and typographically interesting stuff. The way it works is that the abstraction level gets continuously raised, so that very soon, it's no longer possible to describe what's necessary with equations.

 

[MathematicalPhysicist]

well, ofocurse you don't need the equation itself, but the equation itself is some kind of abstraction by its own.