Hello and good morning physicists.

Usin Google Groups:

"
Results for "Einstein notation" in sci.physics.research
Results: about 0 for "Einstein notation"
No results found
"

How odd.

I would think the Einstein notation, for the identity matrix at
least, would be in the 10th grade American algebra and functions
curriculum if not a lower grade's.

Douglas "Doofus Einstein" Goncz
Replikon Research FCN 783774974

[[Mod. note -- I fear the author is quite over-optimistic about the
level of mathematical sophistication in American (or Canadian, for
that matter) 10th grade algebra curricula.

Einstein notation (https://en.wikipedia.org/wiki/Einstein_notation),
a.k.a., the Einstein summation convention, is not generally introduced
in math or physics curricula until it's introduced as part of tensor
calculus, which is often only an optional course taken late in a 3-
or 4-year university degree.

There has been a recent movement introducing general relativity in
such courses/degrees -- see, e.g.,
Christensen & Moore, /Physics Today/ 65(6), 41 (2012),
http://dx.doi.org/10.1063/PT.3.1605

Such courses typically include an elementary treatment of tensor
calculus, including the use of the Einstein summation convention.
The book
James B Hartle
"Gravity: AN Introduction to Einstein's General Relativity"
Addison-Wesley, 2003, ISBN-10 0-8053-8662-9
is a class & widely-priased textbook for such courses.
-- jt]]

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On Tuesday, March 31, 2020 at 1:39:24 AM UTC-4, Douglas Dana Edward^2 Parker-Goncz (fully) wrote:

Hello and good morning physicists.

Usin Google Groups:

"
Results for "Einstein notation" in sci.physics.research
Results: about 0 for "Einstein notation"
No results found
"

How odd.

I would think the Einstein notation, for the identity matrix at
least, would be in the 10th grade American algebra and functions
curriculum if not a lower grade's.

Douglas "Doofus Einstein" Goncz
Replikon Research FCN 783774974

[[Mod. note -- I fear the author is quite over-optimistic about the
level of mathematical sophistication in American (or Canadian, for
that matter) 10th grade algebra curricula.

Einstein notation (https://en.wikipedia.org/wiki/Einstein_notation),
a.k.a., the Einstein summation convention, is not generally introduced
in math or physics curricula until it's introduced as part of tensor calculus, which is often only an optional course taken late in a 3-
or 4-year university degree.

There has been a recent movement introducing general relativity in
such courses/degrees -- see, e.g.,
Christensen & Moore, /Physics Today/ 65(6), 41 (2012),
http://dx.doi.org/10.1063/PT.3.1605

Such courses typically include an elementary treatment of tensor
calculus, including the use of the Einstein summation convention.
The book
James B Hartle
"Gravity: AN Introduction to Einstein's General Relativity"
Addison-Wesley, 2003, ISBN-10 0-8053-8662-9
is a class & widely-priased textbook for such courses.
-- jt]]

[Moderator's note: I guess that Jonathan means "classic and widely
praised textbook". -P.H.]

I've never understood why we don't teach Einstein notation to
undergraduate math majors taking Linear Algebra. Many basic facts about matrices are easy to prove using the notation. For example, basic facts
about determinants (e.g. multiplicativity and the equivalence between nonvanishing of the determinant and invertibility of the matrix) are
effortless to prove if one introduces the antisymmetric epsilon symbol
and writes the definition of the determinant that way.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 20/04/23 1:07 PM, Michael Cole wrote:

On Tuesday, March 31, 2020 at 1:39:24 AM UTC-4, Douglas Dana Edward^2 Parker-Goncz (fully) wrote:

...
...

Einstein notation (https://en.wikipedia.org/wiki/Einstein_notation),
a.k.a., the Einstein summation convention, is not generally introduced
in math or physics curricula until it's introduced as part of tensor
calculus, which is often only an optional course taken late in a 3-
or 4-year university degree.

There has been a recent movement introducing general relativity in
such courses/degrees -- see, e.g.,
Christensen & Moore, /Physics Today/ 65(6), 41 (2012),
http://dx.doi.org/10.1063/PT.3.1605

Such courses typically include an elementary treatment of tensor
calculus, including the use of the Einstein summation convention.
The book
James B Hartle
"Gravity: AN Introduction to Einstein's General Relativity"
Addison-Wesley, 2003, ISBN-10 0-8053-8662-9
is a class & widely-priased textbook for such courses.
-- jt]]

[Moderator's note: I guess that Jonathan means "classic and widely
praised textbook". -P.H.]

I've never understood why we don't teach Einstein notation to
undergraduate math majors taking Linear Algebra.

But maybe to do it right at once, we should then teach them using the differential forms notation. Then Einstein's theories are expressed even
easier (and Maxwell's as well). Although perhaps not everyone agrees..

<https://www.quora.com/Is-general-relativity-ever-done-in-terms-of-differential-forms-and-exterior-calculus-or-is-it-exclusively-done-using-tensors-and-index-notation>

<https://physics.stackexchange.com/questions/91867/general-relativity-in-terms-of-differential-forms>

<https://physics.stackexchange.com/questions/487976/is-there-differential-form-notation-for-maxwells-equation-in-curved-spacetime>

... Many basic facts about
matrices are easy to prove using the notation. For example, basic facts about determinants (e.g. multiplicativity and the equivalence between nonvanishing of the determinant and invertibility of the matrix) are effortless to prove if one introduces the antisymmetric epsilon symbol
and writes the definition of the determinant that way.

Well, those things that follow from coordinate independence would
certainly be obvious (but even more so when using differential forms
and exterior derivatives). For proofs where more is needed, we may
still need to really understand what it all means! :-)

--
Jos

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