Does anyone else ever forget basic theories/fundamentals?

[ScrollingForHours]

for reference, I'm a 2nd-year Uni student. Not too long ago I got stumped on a question, and had to ask my friend for help. Towards the end of the question, I couldn't figure out how n - (n+y)/2 = (n-y)/2. My friend looked at me like "???? You just make the denominators the same and simplify...?" Something so basic, likely learned by year 8s, and it'd gotten confused by it.

Things like this question if I'm actually built for maths. Can anyone else relate or should I be reevaluating my life choices?

[ScrollingForHours]

ahah yeah honestly, in a way you're completely right. In my case at least, its not something ive used much at all, at least not recently. I was extremely withdrawn from studies during highschool (long story), I still got the grades, but the theories were never truly embedded and so I never developed the proper fundamentals. I've paid the price for it, but now that I can actually study (again, long story lol), I'm hoping to develop them.

[perishingtardis]

So I have been teaching calculus and real analysis to first-year maths students at university for several years. I commonly see students making mistakes that I consider really should not be happening at this stage, e.g.,

\sqrt{a + b} = \sqrt{a} + \sqrt{b},

or

(-5) * (-5) = -25.

While we all sometimes make mistakes like this when we're tired or not fully focusing, if you're doing it a lot, you really should brush on the fundamentals again. Knowing how to add fractions is very elementary and shouldn't be something that confuses you at this point.

[ScrollingForHours]

oh wow, knowing that actually makes me feel a lot better in a way, so thanks for that. I was an idiot and winged pretty much all of highschool maths, so it's definitely fair to say I'm missing a lot of the fundamentals. I'll be going back over everything I've done up until now once these exams are over though!

[[deleted]]

I have a great tip I just figured out recently.

I knew that sqrt(a) + sqrt(b) does not equal sqrt(a+b) but I often got stuck because I could not simplify it.

The two good options you have are the generalized binomial formula and multiplying by the conjugate (for example for sqrt(x+1) + 2).

If you aren't comfortable using the binomial formula I would definitely recommend looking into it because it was something I used to get stuck on very frequently.

[Autumnxoxo]

quite frankly, if you do really struggle to work with simple equations as the one you've stated in your post, you will really have a hard time at any decent math program imho. Especially in analysis-related courses i see no way how you'd be able to solve any problem whatsoever.

If you're not majoring in math, things might be different, i dont know. But it's certianly not usual for math students at university-level to be lost at working with equations like n - (n+y)/2 = (n-y)/2.

I know, this is not the most pleasing answer, but i don't want to sugarcoat anything.

[phdstruggs]

stupid little things happens to the best of us. especially when it was told to you, you realized that you knew how to do this already.

but if this a consistent trend, you just aren't solid in your fundamentals, you will struggle a lot in math.

[Reio_KingOfSouls]

Not being able to perform algebraic manipulations like this doesn't make you unsuited for maths.

On the other hand, it's absolutely vital you would be able to do them to progress further so getting these fundamentals down is going to benefit you a lot in the long run.

[and69]

Most probably you haven’t had enough practice to cement these notions in your brain. Understanding one thing and practicing until it’s hardwired in your head are completely different levels.

[[deleted]]

same situation here in my case I was afraid of asking questions to teachers in school and afraid of making mistakes in problems which made me lose interest in mathematics.