Are You Struggling to Remember Basic Math Concepts?

[DrSuage]

As I continue to study higher and higher level mathematics, I start to worry that I'm losing touch/fluency with some of the fundamentals. Anybody else had this kind of problem?

 

[e.bar.goum]

As I continue to study higher and higher level mathematics, I start to worry that I'm losing touch/fluency with some of the fundamentals. Anybody else had this kind of problem?

I think a lot of people go through this, and not only in mathematics! It's just a matter of using the tool, so forgetting it over time. If you're worried about it, go back to some fundamentals, and spend an evening or two going through some practice problems. You've learned it all once, so it's not like learning concepts from scratch.

 

[Greg Bernhardt]

I start to worry that I'm losing touch/fluency with some of the fundamentals.

Keep mentally fit by helping students here at PF

 

[dipole]

I'm halfway through my PhD work (in Physics) and I can barely remember how to solve most integrals... probably because most of the time the ones you actually care about solving you need to do numerically anyways.

 

[e.bar.goum]

I'm halfway through my PhD work (in Physics) and I can barely remember how to solve most integrals... probably because most of the time the ones you actually care about solving you need to do numerically anyways.

Same here (except I'm near the end), if you asked me to solve an integral by hand, I'd be going to my computer and telling you that "this is why we have computers".

Ok, let's not kid myself, if you asked me to do complicated long division by hand, I'd be pulling out my calculator.

 

[alw34]

Anybody else had this kind of problem?

yes.
And it does not get any better with age.

 

[jedishrfu]

Become a teacher of the things you're forgetting.

I've noticed in my own experience that you lose what you learned last first.

Now as I study Vector Analysis again, I realize that I never really understood it like I understand it now (kind-of). I question more what I'm learning now even to the point of finding proofs of things and am trying to understand things at a deeper level. I'm also trying to visualize how things work so I can use it more effectively.

 

[russ_watters]

Keep mentally fit by helping students here at PF

Seriously, I credit PF with helping me stay sharp to pass a couple of recent professional exams. Unused tools definitely go dull.

 

[Borek]

Helping at PF is like using flashcards - you never know what will show and it keeps you on your toes all the time.

 

[DiracPool]

you lose what you learned last first.

Hmm.. So that would be LIFO, right? Last in, first out?

 

[Borek]

Or LUFO - least used first out.

 

[gleem]

I have a lot of data on forgetting stuff. It is enlightening to go through texts or notes of courses that you have taken but have not use in your subsequent endeavors. I was surprised recently when I picked up my text on Quantum Field Theory which I took about 50 years ago. If I didn't see the book annotated in the margin I wouldn't have thought that I ever took the course. The most I remembered about the course was the professor's name. BTW it was one of the last formal courses I took.

 

[alw34]

I've noticed in my own experience that you lose what you learned last first.

good point.

I have always wondered if that's because I did not understand it as well or whether I just never used it as much as some of the older.
Whatever the reason, it's especially annoying because what you learned last was the most expensive.

 

[alw34]

If I didn't see the book annotated in the margin I wouldn't have thought that I ever took the course.

Been there, done worse, I think.

I recently happened to go through some [elective math] papers I saved from graduate school EE almost 50 years ago and I could not even figure out my own solutions to problems.

 

[micromass]

As I continue to study higher and higher level mathematics, I start to worry that I'm losing touch/fluency with some of the fundamentals. Anybody else had this kind of problem?

They often say that any academic subject has a half-life time. The time required to forget half of the material. This is personal of course, but many people I talked to have had the same experience.
For example, analysis and group theory with me have a very long half-life. I think I still remember a lot more than 50%. I think it's also very universal that something like Galois theory has an extremely short half-life time, a period of months I'd say.

 

[Greg Bernhardt]

Most importantly, do you have the skills and organization of references to find the information you have lost from memory.

 

[DrSuage]

^ I really like that analogy. Just hoping my group theory holds strong enough to last me out the year!

 

[alw34]

Most importantly, do you have the skills and organization of references to find the information you have lost from memory.

oh, how I wish.

now what was I doing...

 

[gleem]

They often say that any academic subject has a half-life time. The time required to forget half of the material. This is personal of course, but many people I talked to have had the same experience.

If so the half life may be shorter for newer subjects if we do not use those subjects.

I seem to be able to remember much of my undergraduate subjects at least insofar as I can fairly quickly track down or reconstruct most aspects of my previous understanding of those subjects. However wrt QFT which I commented on before I would have begin from scratch to build that knowledge base and that was one of the last subjects I learned and never used professionally.

 

[DrSuage]

I took a year out and am now "half a year" back into a theory MSc. I thought I had QFT pretty good at 4th year undergrad level. Boy oh boy was I wrong!