thread to discuss the textbook, its exercises, rant about probability theory, and journal as you go through the chapters one by one

Spent some time reading chapter 1.
I notice that boolean algebra is intensely intertwined with probability theory.
The chapter seems quite easy, as far as I've read. I have heard that the difficulty climbs up steeply as we progress, so I'll aim to at least get through two chapters before deciding whether to abandon this textbook or not

P21933
No, I haven't read that book. Is there a reason I should? Why did you mention it?

I started reading the preface. It seems pretty interesting so far.

From what I understand, most university classes and textbooks about probability theory start with measure theory and the Kolmogorov axioms. This book takes a different approach in which probability is seen as an extension of logic:
>However, neither the Bayesian nor the frequentist approach is universally applicable, so in the present, more general, work we take a broader view of things. Our theme is simply: probability theory as extended logic. The ‘new’ perception amounts to the recognition that the mathematical rules of probability theory are not merely rules for calculating frequencies of ‘random variables’; they are also the unique consistent rules for conducting inference (i.e. plausible reasoning) of any kind, and we shall apply them in full generality to that end.

But the book isn't entirely divorced from the standard view, because:
>As noted in Appendix A, each of his axioms turns out to be, for all practical purposes, derivable from the Pólya–Cox desiderata of rationality and consistency. In short, we regard our system of probability as not contradicting Kolmogorov’s; but rather seeking a deeper logical foundation that permits its extension in the directions that are needed for modern applications.

elaborating on P21953
I find the usual approach with measure theory and the Kolmogorov axioms very dreary and formalistic. It's good to have a different approach.

Got to the point where he writes
>Degrees of plausibility are represented by real numbers.

This is something I've wondered about. Real numbers are something we invented to cope with real-world geometry. Natural numbers, integers, and rational numbers suffice for a lot of things, but they can't express the length of the hypotenuse of an isosceles right triangle in units equal to the length of its legs. So we had to invent the much more complicated system of real numbers to model those things. Most of the things we traditionally model as real numbers are related to geometry in some way. The big exception seems to be probability.

The Little Red School Book is a great book to read for pleasure. Although, it was written in <redacted, sha256=fd21cc3cb5062bc4ac714c489e1ca0e37a577c19ba23b0d00e9767f598d37636>, It is still relevant today.

Read through chapter 1. Chapter 2, where he starts explaining how this stuff works, should be interesting.

P22557
***** off *****

P22748
no u

>Exercise 2.1: Is it possible to find a general formula for p(C|A + B), analogous to (2.66), from the product and sum rules? If so, derive it; if not, explain why this cannot be done.
For context, here's (2.66), the generalized sum rule:
>p(A + B|C) = p(A|C) + p(B|C) − p(AB|C)

I believe that we cannot derive a general formula because the product and sum rules both do not touch the prior. Is this correct?

P24226
Seems like it, yes. The sum rule and the product rule both leave the priors untouched.

P24226
Not sure if the intention is to get it from only p(C|A), p(C|B), and p(C|AB) or if we're allowed to use other things. If we can use other stuff, then we can derive

P(C|A+B) = p(A|A+B) p(C|A) + p(B|A+B) p(C|B) - p(AB|A+B) p(C|AB).

If it's supposed to be just from p(C|A), p(C|B), and p(C|AB), it can't be done because it depends on the relative plausibilities of A, B, and AB.

never read it
whats the chance of two people on an obscure ib having read the same book

I am more or less a high school dropout (or the equivalent where I come from) and I never got any real math education beside the basics you learn in high school. Back then I struggled with simple algebra and linear functions, which where a topic I couldn't understand no matter what. But I program a lot and every once in a while I need to use some math. It's fine as is, but for certain puzzles I would like to learn some more complex math. I learn the best from books and when I read this thread is about I textbook I wanted to ask for recommendations. What are some easy-to-get-into math text books that could be teach math relevant for programming puzzles?

P26459
Ray's New Higher / Practical Arithmetic (Algebra, Conic Sections etc..)
You could start with the primary arithmetic book..

You can either buy the reprint or find the original + Answer books on archive dot org