This is a sequel to my previous post. The idea is the same, but I'm using better methods as was suggested in the comments.

As u/Sodium_nitride (thank you!) explained, here...

• ...I use a production matrix instead of the Cobb-Douglas function.
• ...I use capital-time instead of capital, to handle depreciation.
• ...classes consume commodities, seeking to maximize the amount consumed.

Also, I purchased the book suggested by u/davel :)

We use the following definitions:

• Labor is measured relative to A's total labor power.
• B has b labor power, assumed to be proportional to population.
• Capital-time and commodities are measured in units of what can be produced directly from 1 unit of labor.
• Labor sold is represented with w, and the salary is used to purchase capital-time s_k and commodities s_c.

I'm learning game theory these days, and I've tried my hand at some problems inspired by ML theory. Here's one I found really interesting.

Let's assume the following (clearly unrealistic) situation:

1. Working class (A) and bourgeoisie (B) form perfectly cooperative coalitions.
2. They may negotiate salaries, with no class having any mechanism to obtain a better bargaining position.
3. A cooperatively owns some amount k of capital, while B owns (arbitrarily) 1. In principle, k < 1.
4. B has some labor power b, while A has (arbitrarily) 1. Again, b < 1.
5. Production follows a Cobb-Douglas function, where the sum of the output elasticities of capital and labor is 1.
6. Both classes consume the same proportion of their income and use the remainder to acquire more capital.

Therefore, the payoffs in our problem can be stated like this (where w is the labor given to B and s is

A few years ago I found the youtube channel sudgylacmoe and watched what is still their most viewed video A Swift Introduction to Geometric Algebra where he introduce in a vulgarise fashion a branch of mathematics I didn't know before, Geometric algebra more formally known as Clifford algebra(s).

Basically, geometric algebra is a generalisation of linear algebra which allow operations impossible in classic linear algebra such as multiplying vectors together and adding vectors and scalars and also generalise the objects of linear algebra to higher dimensions.

For example, you have 0 dimensional points (scalars) and 1 dimensional oriented line segment (vectors) just like in classic linear algebra, but on top of that, you have generalisations for every other dimensions: 2 dimensional oriented surfaces (bivectors), 3

I want to learn about the works of soviet mathematicians.

On 1 July 2010, he rejected the prize of one million dollars, saying that he considered the decision of the board of the Clay Institute to be unfair, in that his contribution to solving the Poincaré conjecture was no greater than that of Richard S. Hamilton, the mathematician who pioneered the Ricci flow partly with the aim of attacking the conjecture.

In August 2006, Perelman was offered the Fields Medal ("Nobel in math") for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow", but he declined the award, stating: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."

More:

https://en.m.wikipedia.org/wiki/Grigori_Perelman

As the author writes:

"The philosophy of mathematics is not the most vital issue facing Marxists today, but its clarifcation can help us argue that the materialist framework is the correct one for making sense of every aspect of the world."

It is now over a year since I have sadly had to depart from my university upon obtaining my master's degree in mathematics. I have since obtained a job as a programming contractor, however classical mathematics done with pen and paper is still the love of my life. Luckily enough, I still live within two hours of my old campus, and I was able to obtain an external library card, which is my ticket to look into all the topics I missed out on for want of time (not all mathematical).

If anyone among you has a similar experience, I would like you to share your techniques, too. Be advised that my way might not be very efficient nor lend itself to people who still need to study for exams or have deadlines, because I am no longer under these pressures.

Scouting. The closer a field is to my interests, the more books I already know to be suitable or unsuitable for me to learn from. For me, the most important criterion for a maths or theoretical physics book is to have numerous exercises on

So I found out about Marx' mathematical manuscripts, so I say "Hey, I've been studying mathematics this year at university. I understand limits and derivatives, maybe I can understand something of that gibberish." So I see the titles and the one called "On the Concept of the Derived Function", I go there and I see some notation I don't understand, he speaks about things I'm not clearly understanding, so maybe some of you could make it clear.

For example:

Why is this x sub 1 notation? Is this some other way to write derivatives? Because on the footnotes it says this:

2. In order to avoid confusion with the designation of derivatives, Marx’s notation x´, y´, ... for the new values of the variable has been replaced here and in all similar cases by x1, y1, ...

Then I saw a talk about Marx's mathematics and the infinitesimal and some of that stuff, b