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/sci/ - Science & Math

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File: 10 KB, 314x475, 1487502601240.jpg [View same] [iqdb] [saucenao] [google]
9085994 No.9085994 [Reply] [Original]

Am I doomed to life as a brainlet if I was unable to solve 80% of the problems in Lang's Basic Mathematics that began in "prove" or "show"? I read through each chapter and every example problem, can do the plug and chug just fine, but more often than not I'd be having to copy the answers out of the back of the text for anything that involved me having to come up with something on my own.
It's sort of depressing, especially considering it took me half a year to work through it. I'm wondering if this experience is normal or am I just below average IQ?

>> No.9085996

Be grateful, ignorance is bliss.

>> No.9086009
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9086009

>>9085994
The right to math is one of the most fundamental human rights as it affects the vital elements of an individual’s intellectual freedom. Work hard for what you want because it won't come to you without a fight. take it easy on the exhale as well.

>> No.9086010
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9086010

>>9085994
To expand:
I made sure to re-read every chapter and spend hours searching the internet until I had a good understanding of the material, but when faced with something like pic related where I have to prove something on my own, I have no idea where to start.

>> No.9086055

>>9086010
Dude... really? If f is of degree 3, then g and h must be of degree 2 and 1 respectively (I ought to explain this more but I'm sure you can follow my logic). Therefore, one of g or h is linear (of the form x - a. a is a root of f. You gotta look at what you're given and think of their relationships.

>> No.9086056

>>9086010
1) f is of degree 3
2) f = g*h
3) this implies deg(g) + deg(h) = 3
4) this implies either deg(g) = 2 and deg(h) = 1 or the other way around, since both degrees are >= 1 and are integers
5) either way you've found a linear factor
6) hooray a root

>> No.9086084

>>9086010
>I have no idea where to start.
Did you solve exercise 1(h) before that? The formula you're supposed to use is written literally two lines above that exercise, are you trolling?

>> No.9086874

>>9086010
>I have no idea where to start.
That comes with experience.
Repeating solved exercises until you memorize them is not a bad idea.

Regarding the problem, you write down everything first and see what you can get out of it.

>> No.9086904

>>9086010
There is nothing to show?
It's just a special case of the fundamental theorem of algebra

>> No.9087024

>>9085994
>>9086010
No worries.
If you dont know where to start just start at some point that doesnt seem usefull,
if it works you are done.
if it does not it might reveal to you why it didnt work and provide a hint on the actual solution.

>> No.9089059

>>9086010
It doesn't specify if the root is rational or complex.

All polynomials have at least one complex root, therefore there is a root.

>> No.9089616

>>9085994
I'm working through the same book currently, was an absolute brainlet once, but getting better. Try to understand the bigger picture, read more advanced material even if you don't understand most of it, and try to shift your attention beyond the symbols an first-level thought processes, math is a lot about intuition and spatial/conceptual awareness. Don't try too hard when you're stuck somewhere, study something else, go for a walk or something, and come back to it with a refreshed mind. Good luck.

>> No.9090129

>>9085994
I had the same problems as you, I was never taught to prove anything before I came to Trig and Calc 1. These problems involve using the PROPERTIES of the function, and theorems to solve it, not the function itself.

Think to yourself when you see one:
"What does this function look like on a graph?"
"Can I simply this to make it easier to manage?"
"What properties does this function have?"
"Are there identities that I can exploit?"
"Are there theorems that I can exploit?"

Theorems are the big hitters here, because someone basically did all the work for you and put it in a book. The hard part is finding theorems to use, google is basically useless with regards to this.

>> No.9090153

Lang's book is basically trying to help you learn the language and techniques of mathematics.

He will ask you to prove obvious facts just so that you realize what it really means to prove something.