I'm going to make math majors out of you(longish)

I was sitting in advanced calculus yesterday and my teacher must have watched Patch Adams the day before because instead of "I'm going to make doctors out of you" we got the "I'm going to make math majors out of you" speech and I had to bite my lip to stop from laughing.

We were trying to prove that the sequence: an = (√n+1)/(n+7) converges to 0, which it does(take the limit as n ->∞ and you will get 0).

The proof goes as shown below:
Let ε > 0
Choose a positive integer N such that N > 4/ε^2
Then if n≥N we have

|an - A| = |(√n+1)/(n+7) -0|
= |(√n+1)/(n+7) |
= (√n+1)/(n+7)
≤ (√n+1)/n
≤ (√n+√n)/n
= (2√n)/n
= 2/√n
≤ = 2/√N
< 2/(2/ε)
= ε
therefore the sequence converges to 0.

After we got done with this proof one of the kids in the class raises his hand and asks if every step in the math portion of the proof had to be shown(as you can see thats a lot of work to show). The teacher didn't really get what he was asking so she said "Yes" and the student fought with her for about 5 minutes about not wanting to show all his work. After about 5 minutes of them arguing the teacher and about 5 students in the class(me included) just look at him and in unison say "Just do the work." And then the teacher goes on this rant on how any idiot can take derivatives and integrals but it takes a special person to be able to write down why they work the way they do. And what she was trying to do was teach us how to write like mathematicians to separate us from the evil engineers(sorry all those engineers out there). She ranted for about 10 minutes on this and it really felt like I was watching Patch Adams...lol. "I going to make math majors out of you". I left the class and busted out laughing in the hall.

*smiles and nods*

You would have to start ALOT SIMPLER for me!! Math was not a good subject for me.

Thats another thing I forgot. She said that we were to write up these proofs so every Joe somebody walking down the street could understand them. I totally disagree with this because unless you have a background in mathematics none of this even makes sense. Gail you just proved my point, thanks .

If I could understand them what would I do with them anyway?

You would have appreciated me explaining to my client this morning the correct way to plant grass seed. I think it went in one ear and out the other! He didn't want to to know the methodology he just wanted it done.

For someone who failed Algebra 4 times, that looks like a foreign language to me...

Oh and Gail please don't think I called you a joe somebody because that's not what I meant. And I understand them and I'm not even sure what I'm going to do with them...lol. Other than spit it back on a test I don't think I will ever use this stuff in real life. I'm going to be teaching algebra and geometry and will never need to show why a sequence converges, I just need to teach them how to find what it converges to.

You do know that calculus was developed by a bunch of mathemeticians after spending a week in a sensory deprevation chamber? (Well, this is my theory develooped after a semester of calculus. )

Originally Posted by gemlady

You do know that calculus was developed by a bunch of mathematicians after spending a week in a sensory deprivation chamber? (Well, this is my theory developed after a semester of calculus.

)

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Actually your partially right. One of the co founders(there is a BIG debate on who founded calculus) was Sir Issac Newton(of physics fame). And he spent months locked up in his room just developing calculus. He cut himself off completely from the rest of the world and went almost mad.

Originally Posted by AlleyGirl

*smiles and nods*

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Thats kind of how I felt with that proof because the simplification didn't make sense to me so I just smiled and nodded. I mean its all true but how she knew to use those numbers I didn't understand.

That's not even a particularly long proof! The proof for some things is the length of a Harry Potter novel! How would the student cope then?

My bf is really bad at showing every step, he works out too much in his head and has huge leaps of calculation between every written line. His teachers get really annoyed when he does that. And he makes really stupid mistakes then too (like putting a plus instead of a minus)

Originally Posted by cata_mint

My bf is really bad at showing every step, he works out too much in his head and has huge leaps of calculation between every written line. His teachers get really annoyed when he does that. And he makes really stupid mistakes then too (like putting a plus instead of a minus)

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I do the same thing. Work everything (math and otherwise) in my head, usually the mistakes happen when I have to write it down because I'll write stuff down wrong. It's not laziness, though, just that usually everything is whirring around in my head.

Originally Posted by Whisky'sDad

For someone who failed Algebra 4 times, that looks like a foreign language to me...

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I've read somewhere that the part of the brain used in learning and working mathematics is the same used when learning a foreign language. That would explain why I have problem learning languages (yet useless stuff in other languages stick in my head...).

Originally Posted by strange_wings

I do the same thing. Work everything (math and otherwise) in my head, usually the mistakes happen when I have to write it down because I'll write stuff down wrong. It's not laziness, though, just that usually everything is whirring around in my head.

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Its the same for him, he just can't seem to slow down, and even though he's really good at maths he loses marks for silly little mistakes. He tries to hold too much in his head at once, so things fall out the sides

Originally Posted by cata_mint

IHe tries to hold too much in his head at once, so things fall out the sides

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I love the way you phrased that!

Originally Posted by algebrapro18

And what she was trying to do was teach us how to write like mathematicians to separate us from the evil engineers(sorry all those engineers out there).

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You would hate what physicists do with the chain rule when you have dx/dy on one side and want to separate the variables: "you move dy over to the other side and now you can integrate!"

No need to get bogged down in the details, math is just a tool!

Originally Posted by cata_mint

He tries to hold too much in his head at once, so things fall out the sides

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You have described my husband to a T. He can do complex equations and proofs in his head, but the he cannot describe how he got there properly, and always misses his negative signs.

Also, he can never find his keys, but he can tell you the scores of the last several football games and the statistics of all of his video game characters.

It's so cute.

Originally Posted by algebrapro18

And what she was trying to do was teach us how to write like mathematicians to separate us from the evil engineers(sorry all those engineers out there).

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Yes, we engineers are quite evil. We brought the dark art of technology to humanity and now we have iPods, Ferraris, intercontinental ballistic missiles, androids, koosh balls, shoes that go boing, and those evil cell phone things that turn people into yammering nonsense machines and kids use to cheat on tests with. We couldn't leave math well enough alone and had to go muck with it and see if we could actually apply it to the real world. Evil evil engineers.

Originally Posted by Lemur 6

Yes, we engineers are quite evil. We brought the dark art of technology to humanity and now we have iPods, Ferraris, intercontinental ballistic missiles, androids, koosh balls, shoes that go boing, and those evil cell phone things that turn people into yammering nonsense machines and kids use to cheat on tests with. We couldn't leave math well enough alone and had to go muck with it and see if we could actually apply it to the real world. Evil evil engineers.

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I think it's good that she wanted every step documented. Our society as a whole depends too much on calculators and computers to do our thinking for us. By showing each step on paper, that shows the student understands exactly what the process is and how to reach the conclusion. I think it's pointless (although easier) to show students how to get a quick answer...it's better in the long run to show students how to get the answer on their own using their own mind.

I applaud your teacher. To this day, I have no idea what sine and cosine, tangent and co-tangent mean, and maybe if my teacher would have explained it instead of just telling us what button to hit on our calculator (or the reason behind them) I would have a better understanding.