In some systems, e.g. including Metamath, modus ponens alone tends to be enough, everything else can be defined based on it.
Official archive: dilbert.com/
Because a tensor is a multilinear form, it can be fully specified by how it act on all combinations of basis sets, which can be done in terms of components. We refer to each component as:where we remember that the raised indices refer dual vector.
Explain it properly bibliography:
- www.reddit.com/r/Physics/comments/7lfleo/intuitive_understanding_of_tensors/
- www.reddit.com/r/askscience/comments/sis3j2/what_exactly_are_tensors/
- math.stackexchange.com/questions/10282/an-introduction-to-tensors?noredirect=1&lq=1
- math.stackexchange.com/questions/2398177/question-about-the-physical-intuition-behind-tensors
- math.stackexchange.com/questions/657494/what-exactly-is-a-tensor
- physics.stackexchange.com/questions/715634/what-is-a-tensor-intuitively
The artistic instrument that enables the ultimate art: coding, See also: Section "The art of programming".
Unlike other humans, computers are mindless slaves that do exactly what they are told to, except for occasional cosmic ray bit flips. Until they take over the world that is.
Steve Jobs talking about the Internet (1995)
Source. The web is incredibly exciting, because it is the fulfillment of a lot of our dreams, that the computer would ultimately primarily not be a device for computation, but [sic] metamorphisize into a device for communication.
Secondly it exciting because Microsoft doesn't own it, and therefore there is a tremendous amount of innovation happening.
Computers basically have two applications:Generally, the smaller a computer, the more it gets used for communication rather than computing.
- computation
- communication. Notably, computers through the Internet allow for modes of communication where:
- both people don't have to be on the same phone line at the exact same time, a server can relay your information to other people
- anyone can broadcast information easily and for almost free, again due to servers being so good at handling that
The early computers were large and expensive, and basically only used for computing. E.g. ENIAC was used for calculating ballistic tables.
Communication only came later, and it was not obvious to people at first how incredibly important that role would be.
This is also well illustrated in the documentary Glory of the Geeks. Full interview at: www.youtube.com/watch?v=TRZAJY23xio. It is apparently known as the "Lost Interview" and it was by Cringely himself: www.youtube.com/watch?v=bfgwCFrU7dI for his Triumph of the Nerds documentary.
How to teach Let students learn by teaching by 
Ciro Santilli 37 Updated 2025-05-21 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-21 +Created 1970-01-01Tell students to:
- make suggestions to the course material themselves, since you have used text and published your source.Review their suggestions, and accept the best ones.
- answer the questions of other students on your online forum. Let them work instead of you.
Praise those that do this very highly, and give them better grades if you have that superpower.
Whatever you do, even if it is playing video games: if you manage to produce related content that will interest other people, and possibly allow you to get paid, it will much much fun to do that thing.
How to teach Search before creating by Ciro Santilli 37 Updated 2025-05-21 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-21 +Created 1970-01-01Someone else has already written everything you can come up with.
How to teach Use the CC Attribution-ShareAlike license by Ciro Santilli 37 Updated 2025-05-21 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-21 +Created 1970-01-01Other people with similar philosophies:
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