Burning lots of midnight oil.

This doesn't really make sense what we would do with this.

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

The answer?

Scientific software package for numerical computations

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

Generally speaking is measurement, but I'll break this lecture up into two segments.

It's not just the tools, it's not just the sciences, you know, the mathematics and the numerical stuff and the statistics, because we heard, very much on this stage, people talked about music being mathematical.

So parameter is just a numerical measure that describes some characteristic of the population.

Wow, wow!

8 and 13.

And this data set happens to be fittable by a linear regression model without any residual error.

Are, the, the mathematical underpinnings of.

There are a large number of possibilities 51, 51, all the way up to 89 2 and just writing this out took much less room.

Okay, I know where I sit. I know where I'm situated.

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.

Prev

And this is really just the sum of all the numbers divided by this is a human constructed definition that we've found useful the sum of all these numbers divided by the number of numbers we have.

So my provocative statement is that we desperately need a serious scientific theory of cities.

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.

Let me tell you about a truly magical algorithm called value iteration.

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.

This given the numerical solution to what is the inverse of A. So let me just write, inverse of A equals P inverse of

If we want to maximize the product, we can play a number of interesting tricks.

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

It's not as pure of a computation as, say, finding the circumference of the circle, which there really is that was kind of we studied the universe. And that just fell out of our study of the universe.

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.

It first shows up as the ratio of the circumference to the diameter, but you're going to learn as you go through your mathematical journey, that it shows up everywhere.