A concise to describe a specific permutation.
A permutation group can then be described in terms of the generating set of a group of specific elements given in cycle notation.
E.g. en.wikipedia.org/w/index.php?title=Mathieu_group&oldid=1034060469#Permutation_groups mentions that the Mathieu group is generated by three elements:which feels quite compact for a simple group with 95040 elements, doesn't it!
- (0123456789a)
- (0b)(1a)(25)(37)(48)(69)
- (26a7)(3945)
Physics Videos by Eugene Khutoryansky by 
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01These videos can give some geometric insight and do have their value.
But they are sometimes too slow, there are never any mention of experiments, just "the truth".
And when things get "mathy", it sticks to a more qualitative view which may not be enough.
Very over the top with sexy demons and angels making appearances, and has some classic aesthetic artistic value :-)
Most important application: produce X-rays for X-ray crystallography.
Note however that the big experiments at CERN, like the Large Hadron Collider, are also synchrotrons.
List of facilities: en.wikipedia.org/wiki/List_of_synchrotron_radiation_facilities
Education has become an expensive bureaucratic exercise, completely dissociated from reality and usefulness.
It completely rejects what the individual wants to achieve, and instead attempts to mass homogenize and test people through endless hours of boredom.
And the only goals it achieves are testing student's resilience to stress, and facilitating the finding of sexual partners. True learning is completely absent.
Teachers only teach because they have to do it to get paid, not for passion. Their only true incentive is co-authoring papers.
We reject this bullshit.
Education is meant to help us, the students, achieve our goals through passionate learning.
And, we, the students, are individuals, with different goals and capabilities.
The way we protest is to publish the knowledge from University for free, on the Internet, so that anyone can access it.
And we do this is a law-abiding way, without copyright infringement, so that no one can legally take it down.
We come to our courses just for the useless roll calls. But we already know all the subject better than the "teacher" on the very first day.
And we are already more famous than the "teacher" online, and through the Internet have already taught more way way more people than they ever will.
The effect of this is to demoralize the entire school system at all levels, until only one conclusion is possible: implosion.
And from the ashes of the old system, we will build a new one, which does only what matters with absolute efficiency: help the individual students achieve their goals.
A system in which the only reason why university exist will be to allow the most knowledgeable students to access million dollar laboratory equipment, and to pay the most prolific content creators so they can continue content creating.
No more useless courses. No more useless tests. Only passion, usefulness and focus.
It would be really cool to have a PageRank-link algorithm that answers the key questions:However, Ciro has decided to leave this for phase two action plan, because it is impossible to tune such an algorithm if you have no users or test data.
- what is the best content for subject X.For example, if you are reading
cirosantilli/riemann-integraland it is crap, you would be able to click the buttonwhich leads you to the URL: ourbigbook.com/subject/mathematics. This URL then contains a list of all pages people have written about the subjectVersions by other authors
mathematics, sorted by some algorithm, containing for example:This URL would also contain a list of issues/comments that are related to the subject. - who knows the most about subject X. This can be found by visiting: ourbigbook.com/users/mathematics "Top Mathematics users", which would contain the list of users sorted by the algorithm:
Perhaps it is also worth looking into ExpertRank, they appear to do some kind of "expert in this area", but with clustering (unlike us, where the clustering would be more explicit).
Other dump of things worth looking into:
Basically everything that applies to the blogs section also applies here, but university lecture notes are so important to us that they deserve a bit more talk.
It is arguable that this is currently the best way to learn any university subject, and that it can already be used to learn any subject.
We basically just want to make the process more efficient and enjoyable, by making it easier:
- to find what you want based on an initial subject hit across the best version of any author
- and to publish your own stuff with one click, and get feedback if people like it or not, and improvement suggestions like you do you GitHub
One major problem with lecture notes is that, as the name suggests, they are merely a complement to the lecture, and don't contain enough detail for you to really learn solely from them without watching the lecture.
The only texts that generally teach in enough depth are actual books, which are almost always commercial.
So in a sense, this project can be seen as a path to upgrade free lecture notes into full blown free books, from which you can learn from scratch without any external material.
And a major way in which we believe this can be done is through the reuse of sections of lecture notes by from other universities, which greatly reduces the useless effort of writing things from scratch.
The intended mental picture is clear: the topics feature docs.ourbigbook.com/#ourbigbook-web-topics will is intended to act as the missing horizontal topic integration across lecture notes of specific universities, e.g:
MIT calculus course UCLA calculus course
* Calculus <---> * Calculus
* Limit <---> * Limit
* Limit of a function
* Limit of a series <---> * Limit of a series
* Derivative <---> * Derivative
* L'Hôpital's rule
* Integral <---> * Integral
Example topics page of OurBigBook.com
. One important advantage of lecture notes is that since they are written by the teacher, they should match exactly what "students are supposed to learn to get good grades", which unfortunately is a major motivation for student's learning weather we want it or not.
One big open question for this project is to what extent notes written for lectures at one university will be relevant to the lectures at another university?
Is it possible to write notes in a way that they are naturally reusable?
It is our gut feeling that this is possible. But it almost certainly requires an small intentional effort on the part of authors.
The question then becomes whether the "become famous by getting your content viewed in other universities" factor is strong enough to attract users.
And we believe that it might, it just might be.
- HyperCard: we are kind of a "multiuser" version of HyperCard, trying to tie up cards made by different users. It is worth noting that HyperCard was one of the inspirations for WikiWikiWeb, which then inspired Wikipedia
- Semantic Web
- NLab
- physicstravelguide.com/ Nice manifesto: physicstravelguide.com/about by Jakob Schwichtenberg.
- OpenStax
- www.ft.com/content/5515ec3e-0040-4d90-85a9-df19d6e3ebd2 (archive) Twilio’s Jeff Lawson: an evangelist for software developersYou can never be first. But you can have the correct business model. That company's website must have gone into IP Purgatory, and could never be released as an open source website.As a student at the University of Michigan, he started a company that made lecture notes available free online, drawing a large audience of Midwestern college students and, soon enough, advertisers. At the height of the dotcom bubble, he dropped out of college, raised $10m from the venture firm Venrock and moved the company to Silicon Valley.His start-up drew interest from an acquirer that was planning to go public early in 2000. They closed the acquisition but missed their IPO window as the market plunged, and by August the company had filed for bankruptcy. Stock that Lawson and investors in his start-up received from the sale became worthless.The website was called stubhub.com/, as of 2021 the domain had been sold to an unrelated website.He might actually be interested in donating to OurBigBook.com if it move forward now that he's a billionaire.
- Knol: basically the exact same thing by Google but 14 years earlier and declared a failure. Quite ominous:
Any contributor could create and own new Knol articles, and there could be multiple articles on the same topic with each written by a different author.
- leanpub: similar goals, markdown-based, but the usual "you own your book copyright and you are trying to sell your book" approach
- nature Scitable
OK, just going random now:
Group of rotations of a rigid body.
Like orthogonal group but without reflections. So it is a "special case" of the orthogonal group.
This is a subgroup of both the orthogonal group and the special linear group.
Active compound in pepper.
A more precise term for those in the know: open source software that also has a liberal license, for some definition of liberal.
Ciro Santilli defines liberal as: "can be commercialized without paying anything back" (but possibly subject to other restrictions).
He therefore does not consider Creative Commons licenses with NC to be FOSS.
For the newbs, the term open source software is good enough, since most open source software is also FOSS.
But when it's not, it's crucial to know.
Closed source is less bad on online services by Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-28 +Created 1970-01-01Ciro Santilli can accept closed source on server products more easily than offline, because the servers have to be paid for somehow (by stealing your private data).
Nutrient that a given species cannot produce and must ingest in its diet.
Does not have any non-trivial normal subgroup.
And therefore, going back to our intuition that due to the fundamental theorem on homomorphisms there is one normal group per homomorphism, a simple group is one that has no non-trivial homomorphisms.
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