Ciro Santilli @cirosantilli 35

The cause of variable number tandem repeat.

Topology is the plumbing of calculus.

The key concept of topology is a neighbourhood.

Just by havin the notion of neighbourhood, concepts such as limit and continuity can be defined without the need to specify a precise numerical value to the distance between two points with a metric.

As an example. consider the orthogonal group, which is also naturally a topological space. That group does not usually have a notion of distance defined for it by default. However, we can still talk about certain properties of it, e.g. that the orthogonal group is compact, and that the orthogonal group has two connected components.

Others:

Generally, if something is labelled as "e-learning", it's not a good sign, as it implies that it adheres to the "teacher"/"student" separation which Ciro Santilli much despises: E-learning websites must allow students to create learning content.

For every continuous symmetry in the system (Lie group), there is a corresponding conservation law.

Furthermore, given the symmetry, we can calculate the derived conservation law, and vice versa.

As mentioned at buzzard.ups.edu/courses/2017spring/projects/schumann-lie-group-ups-434-2017.pdf, what the symmetry (Lie group) acts on (obviously?!) are the Lagrangian generalized coordinates. And from that, we immediately guess that manifolds are going to be important, because the generalized variables of the Lagrangian can trivially be Non-Euclidean geometry, e.g. the pendulum lives on an infinite cylinder.

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.

Ciro Santilli wants to make sure that you get clear highlights of what your donation money is going into!Sponsors also receive the "Ciro's Edit" email newsletter if desired, which contains similar updates to the above, but delivered directly to their inbox.

The remedy to cowardice, inattention, censorship and amorality.

Due to Ciro Santilli's campaign for freedom of speech in China, Ciro Santilli maintains information on this at mostly at:

Dan Dascalescu's "Web page archiving" comparison table: web.archive.org/web/20130922192354/http://wiki.dandascalescu.com/reviews/online_services/web_page_archiving

Vs metric:

One major difference between the elliptic curve over a finite field or the elliptic curve over the rational numbers the elliptic curve over the real numbers is that not every possible $x$ generates a member of the curve.

This is because on the Equation "Definition of the elliptic curves" we see that given an $x$, we calculate $x^3+ax+b$, which always produces an element $y^2$.

But then we are not necessarily able to find an $y$ for the $y^2$, because not all fields are not quadratically closed fields.

For example: with $a=1$ and $b=1$, taking $x=1$ gives:and therefore there is no $y\in \mathbb{Q}$ that satisfies the equation. So $x=1$ is not on the curve if we consider this elliptic curve over the rational numbers.

That $x$ would also not belong to Elliptic curve over the finite field ${\mathbb{F}}_4$, because doing everything $\mathrm{mod}4$ we have:Therefore, there is no element $y\in {\mathbb{F}}_4$ such that $y\times y=2$ or $y\times y=3$, i.e. $2$ and $3$ don't have a multiplicative inverse.

For the real numbers, it would work however, because the real numbers are a quadratically closed field, and $\sqrt{3}\in \mathbb{R}$.

For this reason, it is not necessarily trivial to determine the number of elements of an elliptic curve.