[newton_method] Update lecture code and fix typos

[kp992]

This PR:

• updates the code to latest style guide like using typing.NamedTuple
• pep8 fixes
• typos and math errors
• converts code to use jax

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[HumphreyYang]

Many thanks, @kp992! Great changes!

In this lecture, we used autograd because we were trying to avoid using JAX in the intermediate series. Since we are now migrating to JAX, I think we can use jax.jacobian here by adapting some functions from this lecture:

https://jax.quantecon.org/newtons_method.html

Let me know if that sounds good to you!

(CC @mmcky)

[kp992]

Thanks @HumphreyYang for the review. I was wondering if we want to keep just a single lecture on Newton's method using JAX or if we are planning to keep two versions -- one here and the other in JAX series?

[HumphreyYang]

Hi @kp992,

Thanks @HumphreyYang for the review. I was wondering if we want to keep just a single lecture on Newton's method using JAX or if we are planning to keep two versions -- one here and the other in JAX series?

Yes! Our plan is to replace them with JAX implementation and keep the old JAX series and rename it to 'GPU computing for computational economics'.

[kp992]

Thanks @HumphreyYang for the clarification. I will update the lecture to use JAX then.

[kp992]

Our plan is to replace them with JAX implementation and keep the old JAX series

So basically, we should host the same lecture in this series too, right? I mean we can copy over the JAX lecture here and update the code with styling fixes and typos?

[HumphreyYang]

Our plan is to replace them with JAX implementation and keep the old JAX series

So basically, we should host the same lecture in this series too, right? I mean we can copy over the JAX lecture here and update the code with styling fixes and typos?

Hi @kp992, yes, but I recall that for some lectures, the JAX version we wrote is a simplified version without discussions. For code that has overlaps, I think we can copy things over (like the newton)

[kp992]

The lecture is now updated to optimized version of JAX and removed numpy/autograd support.

[Copilot]

Pull Request Overview

This PR modernizes the Newton's method lecture by updating the code to follow current best practices, fixing typos, and correcting mathematical notation errors. The changes improve code quality and educational clarity while maintaining the lecture's pedagogical structure.

Key changes:

• Migrates from deprecated autograd to jax for automatic differentiation
• Updates from collections.namedtuple to typing.NamedTuple for better type support
• Corrects mathematical notation and fixes various typos throughout

[mmcky]

nice work @kp992 -- I have left some minor comments for you. Mainly just minor adjustments for pep8 etc.

[kp992]

Thanks for the review @mmcky.

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[HumphreyYang]

Many thanks @kp992!

I just pushed some minor changes, setting seed to 0 and removing the link to the JAX series since we are using JAX here.

Other than those it looks great to me!!

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[mmcky]

@HumphreyYang are you happy for this to be merged?