Ciro Santilli @cirosantilli 37

It is a shame that they refocused to more applied courses. This also highlights their highly "managed" approach to content creation. Their 2022 pitch on front page says it all:

for as few as 10 hours a week, you can get the in-demand skills you need to help land a high-paying tech job

they are focused on the highly paid character of many software engineering jobs.

But one cool point of this website is how they hire tutors to help on the courses. This is a very good thing. It is a fair way of monetizing: e-learning websites must keep content free, only charge for certification.

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Linear operator by

Ciro Santilli 37 Updated 2025-07-16

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We define it as a linear map where the domain is the same as the image, i.e. an endofunction.

Examples:

a 2x2 matrix can represent a linear map from $R^{2}$ to $R^{2}$ , so which is a linear operator
the derivative is a linear map from $C^{\infty}$ to $C^{\infty}$ , so which is also a linear operator

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Applications of Lie groups to differential equations by

Ciro Santilli 37 Updated 2025-07-16

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Solving differential equations was apparently Lie's original motivation for developing Lie groups. It is therefore likely one of the most understandable ways to approach it.

It appears that Lie's goal was to understand when can a differential equation have an explicitly written solution, much like Galois theory had done for algebraic equations. Both approaches use symmetry as the key tool.

www.researchgate.net/profile/Michael_Frewer/publication/269465435_Lie-Groups_as_a_Tool_for_Solving_Differential_Equations/links/548cbf250cf214269f20e267/Lie-Groups-as-a-Tool-for-Solving-Differential-Equations.pdf Lie-Groups as a Tool for Solving Differential Equations by Michael Frewer. Slides with good examples.

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Simple Lie group by

Ciro Santilli 37 Updated 2025-07-16

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Molecular biology by

Ciro Santilli 37 Updated 2025-07-16

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Ciro Santilli believes that molecular biology technologies will be a large part of the next big things as shown at: Section "Molecular biology technologies".

Bibliography:

www.youtube.com/watch?v=mS563_Teges&list=PLQbPquAyEw4dQ3zOLrdS1eF_KJJbUUyBx Biophysical Techniques Course 2022 by the MRC Laboratory of Molecular Biology. Holy crap that playlist is a tour de force of molecular biology techniques in 2022!

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