Tested as of Ubuntu 20.04, there is no Mongo package available by default due to their change to Server Side Public License, which Debian opposed. Therefore, you have to add their custom PPA as mentioned at: docs.mongodb.com/manual/tutorial/install-mongodb-on-ubuntu/

Complexity: NP-intermediate as of 2020:

The basis of RSA: RSA. But not proved NP-complete, which leads to:

One of the most simply classification algorithm one can think of: just see whatever kind of point your new point seems to be closer to, and say it is also of that type! Then it is just a question of defining "close".

Scikit-learn implementation scikit-learn.org/stable/auto_examples/neighbors/plot_classification.html at python/sklearn/knn.py

www.nytimes.com/2023/07/09/world/asia/north-korea-china-defectors.htmlK-drama, the ultimate symbol of resistance. Epic.

TODO why do we care about this?

Note that if a group is k-transitive, then it is also k-1-transitive.

They died so completely, Googling "ICL" now has higher hits such as Imperial College London.

cyclotrons produce the better images, but they are expensive/you have to move to them and order a timeslot.

Lab-based just use some X-ray source from the lab, so it is much move convenient e.g. for a pharmaceutical company doing a bunch of images. The Wikipedia image shows such a self-contained lab system: en.wikipedia.org/wiki/File:Freezed_XRD.jpg

www.physics.udel.edu/~jim/PHYS424_17F/Class%20Notes/Class_5.pdf by James MacDonald shows it well.

The operators are a natural guess on the lines of "if p and x were integers".

And then we can prove the ladder properties easily.

The commutator appear in the middle of this analysis.

Originally it was likely created to study constrained mechanical systems where you want to use some "custom convenient" variables to parametrize things instead of global x, y, z. Classical examples that you must have in mind include:lagrangian mechanics lectures by Michel van Biezen (2017) is a good starting point.

When doing lagrangian mechanics, we just lump together all generalized coordinates into a single vector $\overrightarrow{q}(t):\mathbb{R}\to {\mathbb{R}}^n$ that maps time to the full state:where each component can be anything, either the x/y/z coordinates relative to the ground of different particles, or angles, or nay other crazy thing we want.

The Lagrangian is a function ${\mathbb{R}}^n\times {\mathbb{R}}^n\times \mathbb{R}\to \mathbb{R}$ that maps:to a real number.

Then, the stationary action principle says that the actual path taken obeys the Euler-Lagrange equation:This produces a system of partial differential equations with:

The mixture of so many derivatives is a bit mind mending, so we can clarify them a bit further. At:the $q_i$ is just identifying which argument of the Lagrangian we are differentiating by: the i-th according to the order of our definition of the Lagrangian. It is not the actual function, just a mnemonic.

Then at:

However, people later noticed that the Lagrangian had some nice properties related to Lie group continuous symmetries.

Basically it seems that the easiest way to come up with new quantum field theory models is to first find the Lagrangian, and then derive the equations of motion from them.

For every continuous symmetry in the system (modelled by a Lie group), there is a corresponding conservation law: local symmetries of the Lagrangian imply conserved currents.
Genius: Richard Feynman and Modern Physics by James Gleick (1994) chapter "The Best Path" mentions that Richard Feynman didn't like the Lagrangian mechanics approach when he started university at MIT, because he felt it was too magical. The reason is that the Lagrangian approach basically starts from the principle that "nature minimizes the action across time globally". This implies that things that will happen in the future are also taken into consideration when deciding what has to happen before them! Much like the lifeguard in the lifegard problem making global decisions about the future. However, chapter "Least Action in Quantum Mechanics" comments that Feynman later notice that this was indeed necessary while developping Wheeler-Feynman absorber theory into quantum electrodynamics, because they felt that it would make more sense to consider things that way while playing with ideas such as positrons are electrons travelling back in time. This is in contrast with Hamiltonian mechanics, where the idea of time moving foward is more directly present, e.g. as in the Schrödinger equation.

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

And partly due to the above observations, it was noticed that the easiest way to describe the fundamental laws of particle physics and make calculations with them is to first formulate their Lagrangian somehow: S.

TODO advantages:

Bibliography:

Interestingly, the very first programming language with an actual implementation was interpreted: Short Code in 1950.

This is not surprising, as interpreters are easier to write than compilers.

And just like modern scripting languages, it reduced execution speed by about 50x.

Original playlist name: "PHYSICS 68 ADVANCED MECHANICS: LAGRANGIAN MECHANICS"

Author: Michel van Biezen.

High school classical mechanics material, no mention of the key continuous symmetry part.

But does have a few classic pendulum/pulley/spring worked out examples that would be really wise to get under your belt first.