# Weird Question about Majoring in Math

1. Nov 8, 2008

### PhysicsHelp12

Im in 2nd year now...and Ive been worrying about really trivial things

but its been driving me crazy ...

and Ive been getting really good marks with no trouble

but Ive been thinking about How do I know what to do

Like When I substitute into an equation ...

SOmetimes I use brackets...sometimes I dont use brackets at all

and just see the answer...

Like when im shifting the index of a powe series ---I dont bracket

(k+1)-1
if im subbing in k+1 for n-1 ...I just do it ...

or if this were like

1-x replace x with (t-1)^3 ...I wouldnt use brackets...

Id just go 1-(t-1)^3 ...

but the people on Yahoo Answers said to always use brackets

but now I'm worried that if I continue to just not think....

that one day itll get too complicated and I wont know what to do

DO you all use brackets in your head...

or do you skip steps when youre doing trivial things

I just find it really discomforting that I can do the questions --but its

become subconscious so I really dont know how I do it ...it just

happens in a flash..

throwing brackets on things happens ....and I dont know why ....

and then when I reason it out ---It slows me down considerably

so either I go back to not thinking about it --and just doing it

but I dont know if this is normal ...

Im worried that Ill forget it and fail ...

2. Nov 9, 2008

### CompuChip

Well, it all depends (ok, that's not the helpful answer, I know, but I think it's the truth). You don't write brackets to sooth your conscience. You write brackets to make it clear what you mean. This can either be to avoid ambiguity; for example, if you mean: 3 - 4 + 1 is not the same as 3 - (4 + 1). Or you can use them in a derivation, for example (as you said) in an expression like
$$\sum_{k = a}^b k - 1 = \sum_{p = a - 1}^{b - 1} (p + 1) - 1$$
it makes it more obvious what it is you did (in this case, replacing k by p + 1). However, if the derivation went on like
$$\cdots = \sum_{p = a - 1}^{b - 1} p + (1 - 1) = \sum_{p = a - 1}^{b - 1} p = F(x)$$
I would skip the former steps and just write down: $\cdots = F(x)$ immediately.

Finally, it also depends on your audience. When writing for high school students, you will want to include more steps as not to leave them puzzled; when writing for mathematicians who have graduated 10 years ago you will want to be more brief so that they will not get utterly bored. (Of course, as long as you are a student, your teacher will be an exception - especially they don't usually appreciate stuff like "the calculation is lengthy, the reader can easily check that it gives ...").

3. Nov 9, 2008

### Pere Callahan

Well, this is extremely ambigious...

4. Nov 9, 2008

### CompuChip

I would usually take that to mean
$$\sum (k - 1)$$
however clearly, "usually" is not very good either (in practice, I wonder how much confusion arises because of such notational sloppiness).

To be completely clear, I agree with you one would have to write either that or
$$\left( \sum k \right) - 1$$
though.

Putting brackets is also not always ideal though
I once read an expression like
$$H(t_f - t_i)$$
and it took me some conscious thought to realise that H was just a constant multiplied by some difference, rather than a function of it (especially since the text went on to explain that we could introduce some function $f(t_i, t_f)$ which actually only depended on that difference as well, and hence could be written as $f(t_f - t_i)$).

5. Nov 9, 2008

### HallsofIvy

Then what do you mean by "brackets"? You have used parentheses and that's all the "brackets" you need.