Math Is Fun Forum

safp7

Member

Registered: 2011-07-24

Posts: 5

A new approach in Calculus

Hi all,

Have you heard of the new (and simple) approach to Calculus?

For details, search in YouTube "calculus of detachment" and go for the first video (can't post links here).

Thanks

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: A new approach in Calculus

hi safp7

welcome to the forum.Why can't you post links?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

safp7

Member

Registered: 2011-07-24

Posts: 5

Re: A new approach in Calculus

Hi,

I tried to post the link and I got this message:  "Sorry. In an effort to stop automated spam only established members can post links. Please describe where instead."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A new approach in Calculus

Hi safp7;

I have heard of that, but know little about it.

Links can not be posted any longer inside posts until you are a member.

Here is the link:

http://www.youtube.com/watch?v=cI53loTF9fQ

Welcome to the forum.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

safp7

Member

Registered: 2011-07-24

Posts: 5

Re: A new approach in Calculus

Dear bobbym,

Thank you for the link.
I recommend to watch that video.  It depicts a very beautiful and intutive idea in Calculus.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A new approach in Calculus

Hi safp7;

When I said I did not know much about it that was incorrect. I just did not recognize that video. I have even had that discussion on this forum. I think basically his approach of discretizing math is correct. If you read the work of Doron Zeilberger you will see that has been vigorously suggested already. Unfortunately it is has also been vigorously rejected. I do not want say how long I have been fighting with math types to get them to understand or even try computational math.

The ramifications of discretization are huge. Essentially most of continuous math and the ancient greek concept of proof is to be discarded, in favor of a mathematics that more easily lends itself to computation. They will not change in your lifetime.

I also recommend David Deutsch's book because it has stunning ideas. We call what we do, "Experimental Mathematics."

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

safp7

Member

Registered: 2011-07-24

Posts: 5

Re: A new approach in Calculus

Dear bobbym,

Could you please refer me to a work of Doron Zeilberger, David Deutsch, or even your own, on similar topics?

Thank you.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A new approach in Calculus

Hi safp7;

My memory for these things is not good.

This is Doron's opinions, they are good reading and inside them are some of his viewpoints. He also makes rather popular videos on youtube. His page is a good source of his heretical views.

http://www.math.rutgers.edu/~zeilberg/OPINIONS.html

His best mathematical work is A = B.

I think David's book is called the :The Fabric of Reality."

About the last, I can never find anything I blather about.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

safp7

Member

Registered: 2011-07-24

Posts: 5

Re: A new approach in Calculus

Dear bobbym,

Thank you.  Doron Zielberger seems like an interesting fellow.
I liked his YouTube video regarding the "continuous" mathematics being "contained" in discrete math 

Have you seen similar definitions to the one suggested at the video I posted, in the literature?  I'm talking about rigorous definitions, not just discussions regarding discretization of continuous mathematics.
Are you familiar with other discrete or semi-discrete versions of concepts in Calculus?

I would love to learn more about this field.

Thank you!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: A new approach in Calculus

Hi;

If you were able to understand him with his thick accent, then you are ahead of me.

I'm talking about rigorous definitions, not just discussions regarding discretization of continuous mathematics.
Are you familiar with other discrete or semi-discrete versions of concepts in Calculus?

The only part of it that I can understand is what I learned through numerical analysis. Discretizing happens all the time there! DE's are approximated by very small straight lines, curves are fit by using splines, areas are done by stuffing trapezoids inside them, sums replace integrals and differences replace derivatives.

I am afraid that there is no collected body of knowledge on this. You will have to search till your keyboard melts. Just make sure you write down where you find things else you will be in the same spot as me.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.