Is math suppose to be rigorous?

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Is math suppose to be rigorous? I love it and I hate it. Is this right? So far I'm in trig, I'm struggling a bit. Is math suppose to be tough, do you have to work at it everyday and study for 4 to 5 hrs or does it come easy to you? Please share. Thanks..
 

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  • #2
tiny-tim
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Hi CrossFit415! :smile:
Is math suppose to be rigorous?
'fraid so! :redface:

The tastiness of maths is in the proving. :wink:
I love it and I hate it. Is this right? So far I'm in trig, I'm struggling a bit. Is math suppose to be tough, do you have to work at it everyday and study for 4 to 5 hrs or does it come easy to you? Please share. Thanks..
I remember that the guys who were going to get a first did hardly any work, they just attended the lectures, breezed through the set questions, and took the rest of the week off.

The guys who were going to get a second worked two or three days a week.

And the guys who were going to get a third had to work full-time.
 
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Is math suppose to be rigorous? I love it and I hate it. Is this right? So far I'm in trig, I'm struggling a bit. Is math suppose to be tough, do you have to work at it everyday and study for 4 to 5 hrs or does it come easy to you? Please share. Thanks..
4 or 5 hours a week outside of class sounds about right. 4 or 5 hours a night, 5 nights a week is excessive and probably indicates that math isn't for you.
 
  • #4
Nothing easy is worth learning -- except conservation of energy :)
 
  • #5
Hurkyl
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If it's taking you a lot of work, one possibility is that you just aren't thinking about things in the right way.

What kind of problem do you find hard? Describe the hardness.

(e.g. do you have problem solving equations? And is it hard because you sit there and stare at the problem but still can't figure out what the next step is?)
 
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Is the scientific method supposed to be used in Physics, or any branch of human knowledge that calls itself a "science"? Is experiment the ultimate truth?

These are the same questions you're asking, applied to Physics. :)
 
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I can do the problems but at times my mind drifts off somewhere else.

I'm thinking that I could be doing something else useful with my time and that doing one single problem is time consuming and tedious at times... I view it as "These numbers don't talk back to me so why should I care if I find x or solve for an equation?" "Even if I solved the equation or graph yet I'm not rewarded for solving it, no pats on the back.." Sounds childish I know..

In other words I approach math as "alright.. read, absorb info, learn and get out" But then I have to do the problem and understand the formulas to really get a grasp of it. Now I see that math is not something that I can just sprint through.
I guess being patient about learning the subject would help me...

Thank you my friends.
 
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  • #8
You're in the early stage. Imagine a graph of your grasp of mathematics. You're at x=1 of the e^x graph. Calculus is x=2, and so on and so forth. It plateaus after a while, but generally, the higher the math you take, the more comfortable you are with it.
 
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Ahhh I see now..
 
  • #10
chiro
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Is math suppose to be rigorous? I love it and I hate it. Is this right? So far I'm in trig, I'm struggling a bit. Is math suppose to be tough, do you have to work at it everyday and study for 4 to 5 hrs or does it come easy to you? Please share. Thanks..
Good teachers will have the ability to tell you in the simplest terms what is behind the symbols.

One thing you should realize is that it has been created by humans, and that there is some kind of intuition behind what you are learning.

With regard to it being rigorous, it has to be because if there is an ambiguity, then everyone won't have the right idea and one reason why math is so powerful is that it (for the most part) is unambiguous.

Its like the difference between saying something is a "red porsche model XRAFAD year 2002" (made up) vs saying that something is a "car". There's no room for second guessing what something means when its formulated rigorously and because of that it is in some ways easier and predictable.
 
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obviously it's going to be a lot of work
 
  • #12
A. Neumaier
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I'm thinking that I could be doing something else useful with my time and that doing one single problem is time consuming and tedious at times... I view it as "These numbers don't talk back to me so why should I care if I find x or solve for an equation?" "Even if I solved the equation or graph yet I'm not rewarded for solving it, no pats on the back.." Sounds childish I know..
If you want to understand mathematics, doing problems is worth its time since you get badly needed practice.

As long as you meet obstacles while solving problems, your reward should be recognizing the obstacle and finding a way around it. If the same thing in the next problem is no longer an obstacle, you may pat yourself on the back - you learnt something from the previous problem. That's how it works.

You can stop doing problems on a particular topic only when you have enough practice so that you can see fairly directly how things would go if you solved them and you don't learn anything new from trying another one.
 
  • #13
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From what I understand (still in sophomore year),
being rigorous may guarantee (verify) the math to be true in certain framework..
similar think with physics, we need the experiments to verify the physical model we have..

Rigorous treatment may also give some new results..

Still, some of my professors from the math department mentioned that at later stage intuitive approach is also important..found something first, prove it later
 
  • #14
A. Neumaier
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Still, some of my professors from the math department mentioned that at later stage intuitive approach is also important..found something first, prove it later
Sure - one needs both: intuition to guide one to interesting things, and rigor to save one from blunders and fallacies.

Rigor without intuition leads to correct but irrelevant ''productivity''.

Intuition without rigor leads you somewhere, but you are never sure whether you deceive yourself - and it is very common to deceive oneself in areas where one doesn't have enough practice.

So one plans the way with one's intuition and then walks it with one's rigor.
 

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