This is a book on Optimal Transport, it is a problem involving mathematics, engineering, probability and geometry everything that was said.

The answer?

Once you've done that, then there's the computation step.

Wow, wow!

8 and 13.

Are, the, the mathematical underpinnings of.

Burning lots of midnight oil.

So it's very physically easy for us to imagine.

Show it to you mathematically instead of this

Okay. So that's the cost function.

And on the right hand side is a proposed mathematical surrogate of a fast algorithm.

And we'll understand that a little bit more in the future.

I don't think anything is really B.

Here is a simple mathematical simulation of this from N. Wright.

These are just a few examples.

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How did we design the algorithms to do this?

And this isn't really going to be a finance video.

Music is a mathematical language.

With that we already solved the problem.

The figure will be astronomical.

Laplace Transform.

I want you to think about how you design computer programs to solve particular problems.

And that's where I work.

And the beginnings of the field were in artificial intelligence, imagine processing, and in pattern recognition.

And for the first time since high school,

We'll have linked concerts, parties, and cultural performances and collaboration world wide.

I'll give an example of what this means in just a second.

And these are all definitions.

Let's call that p.

And my colleague, James Fowler and I have been studying for quite sometime what are the mathematical, social, biological and psychological rules that govern how these networks are assembled and what are the similar rules that govern how they operate, how they affect our lives.

Any person with average quantitative intelligence who learns to read and write mathematics at an elementary level will, as in verbal language, have little difficulty picking up most of the fundamentals if they choose to master the mathspeak of most disciplines of science.

And, once again, this is very important.

2 4 is the same thing as 1 2.

Wrong!

like we have truths in math.

Well, the answer is explained by Newton's Second Law.

It should look that random.

So finally, let me give you a actual mathematical definition that you could use to do formal proofs.

What's the origin of this?

Another example a little bit more mathematical.

It doesn't make them good people, but it's at the heart of engineering, at the heart of a creative community, an innovative community, and the open source community, the basic ethos of it is, take what other people do, make it better, give it back so we all rise further.

Let's study and show them how it's done.

Well, we can do a little experiment.

Sometimes that is kind of obvious and straightforward.