Caused by slipped strand mispairing.

TODO can anything interesting and deep be said about "why phase transition happens?" physics.stackexchange.com/questions/29128/what-causes-a-phase-transition on Physics Stack Exchange

It is exactly what you'd expect from the name, Waring was watching Netflix with Goldbach, when they suddenly came up with this.

A polynomial of degree 1, i.e. of form $ax+b$.

The by far dominating DNA sequencing company of the late 2000's and 2010's due to having the smallest cost per base pair.

Illumina actually bought their 2010's dominating technology from a Cambridge company called Solexa.

To understand how Illumina's technology works basically, watch this video: Video 1. "Illumina Sequencing by Synthesis by Illumina (2016)".

The key innovation of this method is the Bridge amplification step, which produces a large amount of identical DNA strands.

Marcel J. E. Golay was a prominent figure known for his contributions to the field of engineering, particularly in signal processing and the design of codes and systems for communication. He is perhaps best recognized for the "Golay codes," which are a pair of error-correcting codes that are optimal for certain types of applications. These codes have applications in various fields, including telecommunications and computer science.

TODO WTF is this? How is it built? What is special about it?

Mentioned a lot in the context of superconducting quantum computers, e.g. youtu.be/t5nxusm_Umk?t=268 from Video "Quantum Computing with Superconducting Qubits by Alexandre Blais (2012)",

A polynomial with multiple input arguments, e.g. with two inputs $x$ and $y$:as opposed to a polynomial with a single argument e.g. one with just $x$:

By default, we think of polynomials over the real numbers or complex numbers.

However, a polynomial can be defined over any other field just as well, the most notable example being that of a polynomial over a finite field.

For example, given the finite field of order 9, $GP(3)$ and with elements $\{0,1,2\}$, we can denote polynomials over that ring aswhere $x$ is the variable name.

For example, one such polynomial could be:and another one:Note how all the coefficients are members of the finite field we chose.

Given this, we could evaluate the polynomial for any element of the field, e.g.:and so on.

We can also add polynomials as usual over the field:and multiplication works analogously.

The usual definition of a polynomial is over a field as shown at polynomial over a field.

However, there is nothing in the immediate definition that prevents us from having a ring instead, i.e. a field but without the commutative property and inverse elements.

The only thing is that then we would need to differentiate between different orderings of the terms of multivariate polynomial, e.g. the following would all be potentially different terms:while for a field they would all go into a single term:so when considering a polynomial over a ring we end up with a lot more more possible terms.

If the ring is a commutative ring however, polynomials do look like proper polynomials: Section "Polynomial over a commutative ring".

The polynomials together with polynomial addition and multiplication form a commutative ring.

Mission: to live in a world where you can learn university-level mathematics, physics, chemistry, biology and engineering from perfect free books that anyone can write to get famous.

Live website: ourbigbook.com

Further information and rationale: Section "OurBigBook.com"

The project's mission is one of, or perhaps the most important, life objective of Ciro Santilli. Reproductive goals aside. These two types of goal are incommensurable. This is one of the great challenges of life.

This is ongoing project.

Ciro's goals in advertising this half done project are is partly to obtain some feedback, and partly to give the idea to someone else who might help push it further, be it in this stack or not.

Better editing support is a must, likely WYSIWYG.

But besides that, it is already in broad strokes the best approach Ciro Santilli can come up with to try and reach the mission statement only with technical advances, i.e. without large amounts of money or political influence which Ciro Santilli does not have.

Maybe that website isn't enough of a technical advance to reach its mission. Maybe there is some further not yet imagined technical insight that would push it into viability. Maybe not. But one must try. Only God can know the answer to these questions.

As of 2022, Ciro has spent about 2.5 years full time working on this project. First he spent about 1 year in 2014 on the first iteration: github.com/booktree/booktree, a GitLab fork, but then decided it was not the way to go.

Then around 2021 he put in some more 1.5 year of full time work, now with a possibly overly complicated (or perhaps just insane/immature) Next.js/Sequelize from scratch website stack.

It makes Ciro a bit ashamed to see that "so little user visible stuff was achieved in so much time". It is partly because he and many people underestimate the difficulty of web development. Perhaps there were some bad stack/useless feature choices issues. And a good dose of indulging in studying the natural sciences to bootstrap content and have fun. But really trying is the only way to learn.