List of e-learning websites Updated 2025-07-16
Based God Updated 2025-07-16
Someone who is not a pussy.
Someone once called Ciro Santilli that: archive.is/W1ocv. It's an overstatement, considering that Ciro's parents have some money. Not infinite. But still. Changes everything. A real Based God is someone like Charles Bukowski, who had to work decades at the post office.
Being naughty and creative are correlated Updated 2025-07-16
Steve Jobs' 2005 Stanford Commencement Address Updated 2025-07-16
Ciro feels that this resonates a lot with his OurBigBook.com.
Supercut:
The minute I dropped out I could stop taking the required classes that didn't interest me, and begin dropping in on the ones that looked far more interesting.And much of what I stumbled into by following my curiosity and intuition turned out to be priceless later on.Because I had dropped out and didn't have to take the normal classes, I decided to take a calligraphy class to learn how to do this.If I had never dropped in on that single course in college, the Mac would have never had multiple typefaces or proportionally spaced fonts.Of course it was impossible to connect the dots looking forward when I was in college. But it was very, very clear looking backward 10 years later.Again, you can't connect the dots looking forward; you can only connect them looking backward. So you have to trust that the dots will somehow connect in your future. You have to trust in something — your gut, destiny, life, karma, whatever. This approach has never let me down, and it has made all the difference in my life.
Then:
You've got to find what you love.Your work is going to fill a large part of your life, and the only way to be truly satisfied is to do what you believe is great work.And the only way to do great work is to love what you do. If you haven't found it yet, keep looking.So keep looking until you find it.Don't settle.
And:Mirror and morning are not required though, a computer screen will do just fine: www.reddit.com/r/depression/comments/6jtamj/im_at_work_just_staring_at_my_computer_screen/
When I was 17, I read a quote that went something like: "If you live each day as if it was your last, someday you'll most certainly be right."
And then he quotes form the Whole Earth Catalog, a paper Atlas from the '70s he admired:
Stay Hungry. Stay Foolish
Survirvorship bias Updated 2025-07-16
Jack of all trades, master of none Updated 2025-07-16
Dirac delta function Updated 2025-07-16
There's not way to describe it as a classical function, making it the most important example of a distribution.
Applications:
- position operator in quantum mechanics. It's not a coincidence that the function is named after Paul Dirac.
Lie group Updated 2025-07-16
The key and central motivation for studying Lie groups and their Lie algebras appears to be to characterize symmetry in Lagrangian mechanics through Noether's theorem, just start from there.
Notably local symmetries appear to map to forces, and local means "around the identity", notably: local symmetries of the Lagrangian imply conserved currents.
More precisely: local symmetries of the Lagrangian imply conserved currents.
TODO Ciro Santilli really wants to understand what all the fuss is about:
Oh, there is a low dimensional classification! Ciro is a sucker for classification theorems! en.wikipedia.org/wiki/Classification_of_low-dimensional_real_Lie_algebras
The fact that there are elements arbitrarily close to the identity, which is only possible due to the group being continuous, is the key factor that simplifies the treatment of Lie groups, and follows the philosophy of continuous problems are simpler than discrete ones.
Bibliography:
- youtu.be/kpeP3ioiHcw?t=2655 "Particle Physics Topic 6: Lie Groups and Lie Algebras" by Alex Flournoy (2016). Good SO(3) explicit exponential expansion example. Then next lecture shows why SU(2) is the representation of SO(3). Next ones appear to eventually get to the physical usefulness of the thing, but I lost patience. Not too far out though.
- www.youtube.com/playlist?list=PLRlVmXqzHjURZO0fviJuyikvKlGS6rXrb "Lie Groups and Lie Algebras" playlist by XylyXylyX (2018). Tutorial with infinitely many hours
- www.staff.science.uu.nl/~hooft101/lectures/lieg07.pdf
- www.physics.drexel.edu/~bob/LieGroups.html
What is Lie theory? by Mathemaniac 2023
. Source. Euler number Updated 2025-07-16
Linear differential equation Updated 2025-07-16
The name is a bit obscure if you don't think in very generalized terms right out of the gate. It refers to a linear polynomial of multiple variables, which by definition must have the super simple form of:and then we just put the unknown and each derivative into that simple polynomial:except that now the are not just constants, but they can also depend on the argument (but not on or its derivatives).
Explicit solutions exist for the very specific cases of:
- constant coefficients, any degree. These were known for a long time, and are were studied when Ciro was at university in the University of São Paulo.
- degree 1 and any coefficient
Order of a differential equation Updated 2025-07-16
Order of the highest derivative that appears.
Ordinary differential equation Updated 2025-07-16
Partial differential equation Updated 2025-07-16
Phase space Updated 2025-07-16
This idea comes up particularly in the phase space coordinate of Hamiltonian mechanics.
Boundary condition Updated 2025-07-16
Control theory Updated 2025-07-16
This basically adds one more ingredient to partial differential equations: a function that we can select.
And then the question becomes: if this function has such and such limitation, can we make the solution of the differential equation have such and such property?
Control theory also takes into consideration possible discretization of the domain, which allows using numerical methods to solve partial differential equations, as well as digital, rather than analogue control methods.
Online dictionary Updated 2025-07-16
Chain rule Updated 2025-07-16
Differentiable function Updated 2025-07-16
Maxima and minima Updated 2025-07-16
Given a function :we want to find the points of the domain of where the value of is smaller (for minima, or larger for maxima) than all other points in some neighbourhood of .
- from some space. For beginners the real numbers but more generally topological spaces should work in general
- to the real numbers
In the case of Functionals, this problem is treated under the theory of the calculus of variations.
There are unlisted articles, also show them or only show them.