When did math become hard for you? Share your experience

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In reading some stuff on this forum and about general math education in the US at least, I'm curious as to others' experience with math and when it "got hard" for them. People here I assume are mathphiles and love math. They've done well, math came easy, etc. I include myself in this category. But there came a point for me, and I think it comes for everyone, where math becomes more work and hard. For me it came when I took differential geometry. Everything before that - Calc I-III, Linear Algebra, Differential Equations, etc. came pretty easy. I took all honors courses and got all As. I had to work, but I never found it very difficult. When I took differential geometry, I felt I was a bit out of my element. I struggled, but ultimately did well. But it was an awakening. Looking back, I can't pinpoint exactly why. Maybe my smarts had reached their limit. Maybe the material I had studied before was not rigorous enough or sufficient enough to prepare me for that course. I feel more the latter. Looking back, even the honors courses were more computational-based than theoretical. Even the books used. And the transition hence was not a smooth one. But I could just as easily be rationalizing this and maybe I DID hit a mental block. Before that I could just read the books on my own, do the work, and get As. After that I had to work with others, ask more, book reading was not as easy and natural, etc. Was it a case of insufficient material leading up to it, my brainpower, or both? I still don't know, so am curious to hear other stories. Because I do think everyone hits a sort of wall at some point.
 

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  • #2
lisab
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The only math class that I loved was Geometry - it never felt like work. Linear Algebra was a lot like that, too.

Statistics (intro level) was the only math class I thought was not hard at all.

All the others I thought were hard. Not miserable, but hard enough that had I fallen behind, it would have been a disaster.
 
  • #3
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Prob & Stats was a bad class for me partly due to the teacher, but when I came back to it on my own it wasn't (hasn't been) so bad.

Topology. That's what hit me hard. I really like topology (general and a little algebraic), but taking the course nearly derailed me despite a good teacher. Every time I come back to it I learn a little more, but it is still a huge struggle and I really don't feel comfortable with it.
 
  • #4
Evo
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Geometry was my absolute favorite!
 
  • #5
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Do you guys think it was a mental "wall" one hits or more maybe lack of equally rigorous courses before that for a good preparation? This is the part I *still* can't figure out for myself, but as I was saying, I do think the courses I took before were a bit too easy and computational based, and in the end that hurt me. I perhaps was too confident, thought I understood all the material (and I did to the degree that it was being taught at), but perhaps I was wrong. It's like the rigor changed all of the sudden and I wasn't very prepared for it. But the question is, what could I have done? And looking back, the answer seems to be maybe supplemented on my own. Seems at least in the US, that colleges are watering down material, even honors courses, and maybe doing a disfavor to those that go on to more challenging courses that have different expectations.

BTW, I also loved geometry, but I felt and still feel it's increasingly becoming less important in the teaching methodology in the US system. It's more brief and being replaced by other things - more trig, stats, etc. And a really good foundation in geometry is SO important, is sort of sad.
 
  • #6
jim hardy
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I vote for mental wall. Vector calculus was my limit. Del was okay for i could visualize it.
Curl i never mastered and the coursework thereafter was reduced for me to alphabet juggling by memory.
I took great solace in an essay by one G H Hardy, a British mathematician who wrote : "There are students who simply cannot grasp higher math. But they can make meaningful contributions at a practical level. "

Diff eq and analytic geometry i loved, but had to work extremely hard at them.
 
  • #7
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Permutations and combinations.....one of the worst topics.

There is no particular Math topic I like but recently, I have been into too much integral calculus and series so maybe I can make this my favourite.
 
  • #8
collinsmark
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I can relate an anecdotal experience.

My first* go through the class of electromagnetic theory (for electrical engineering) we were introduced to the Laplacian operator.

*(that should tell you something right there)

In Cartesian coordinates, the Laplacian is pretty simple and friendly:

[tex] \nabla^2 f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2},[/tex]

which really isn't that bad. If you know f, you can find [itex] \nabla^2 f [/itex] just by taking a few derivatives and adding.

But in spherical coordinates, the Laplacian becomes

[tex] \nabla^2 f = \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial f}{\partial r} \right) + \frac{1}{r^2 \sin \theta} \frac{\partial}{\partial \theta} \left( \sin \theta \frac{\partial f}{\partial \theta} \right) + \frac{1}{r^2 \sin^2 \theta} \frac{\partial^2 f}{\partial^2 \phi}[/tex]

Rather than just memorize the spherical coordinate version, I figured that all I really had to do was just re-derive it on the fly, even during an exam, knowing that

[itex] x = r \cos \theta \sin \phi [/itex]
[itex] y = r \sin \theta \sin \phi [/itex]
[itex] z = r \cos \phi [/itex]

Boy, that was a big mistake. Big mistake. While going from Cartesian to spherical coordinates by substitution is possible, it takes about ten pages to math to do it. :frown:
 
  • #9
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I honestly felt like it only got easier.
 
  • #10
Borek
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It got hard when I went to school, I had no problems with math earlier.
 
  • #11
PhysicoRaj
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Math was a nightmare for me at primary and high school. I hated geometry! I somewhat liked (liked means hated the least!) Algebra. I bunked statistics classes :tongue:.

But when I got to 11th and 12th, things changed radically. I simply loved combinatorics :!!)
I became an addict to calculus! I was mad at differentiation:cry: and a crazy integrals fanatic!
So as an undergrad I was a full fledged math fan. Let's see what I become of later..
 
  • #12
CAF123
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@collinsmark: We were always told in advance that we would be given the expression for the laplacian in spherical coordinates in an exam if we needed it. The derivation I think was in a tutorial and I have been told by many professors it was one of those things that a physicist should do at least once :smile:

My situation is similar to PhysicoRaj. When at primary school, Maths was the subject I least looked forward to every day. I remember struggling with the idea of a composite shape. At the beginning of high school I was also nervous in Maths. I think it wasn't until half way through high school that I started to appreciate it more and develop an interest.
 
  • #13
AlephZero
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  • #14
dlgoff
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I honestly felt like it only got easier.

Sometime during my differential equations course things clicked and math seemed to get easier. But that was then. Now things have unclicked.
 
  • #15
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Sometime during my differential equations course things clicked and math seemed to get easier. But that was then. Now things have unclicked.

I didn't feel like there was anything to click. After trudging through those types of classes with the "here's the problem. Here's the way some old dead guy figured out how to solve it. Remember it. Use that" experience, it became something else entirely. Math became the study of making sense. I'd rather show some property about a topological space than solve a differential equation (as a DE student would) any day. The former is about an idea that makes sense. The latter is the manipulation of some abstract symbols according to rules that your teacher told you (from the perspective of a DE student) that requires that you know nothing but how to manipulate those symbols - that's not fun, and it's confusing. Of course, some DE students know the mechanisms behind what they are studying, but that's the minority IMHO.
 
  • #16
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It became hard when i saw the JEE question paper.
 
  • #17
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It got hard for me at manifold theory.
 
  • #18
WannabeNewton
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Arithmetic was hardcore. I gave up on math after that.
 
  • #19
dlgoff
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Arithmetic was hardcore. I gave up on math after that.
:rofl:
So you know Arithmetic, right?
 
  • #20
WannabeNewton
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:rofl:
So you know Arithmetic, right?

Given by my frequent inability to correctly add and subtract even single digit numbers, I would have to say no.
 
  • #21
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Third semester of calculus. Pesky 3D graphs.
[itex] x = r \cos \theta \sin \phi [/itex]
[itex] y = r \sin \theta \sin \phi [/itex]
[itex] z = r \cos \phi [/itex]
It's here too! Spherical coordinates! Noooooooooooooooooo!
 
  • #22
ZombieFeynman
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For me it was combinatorics. Perhaps I was just out of my element as a student of physics, but I never quite got as adept as I'd like at counting.
 

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