I am currently reading Euler's “Introductio in analysin infinitorum” (https://en.wikipedia.org/wiki/Introductio_in_analysin_infinitorum). The Wikipedia article calls it “the first precalculus book” — which is true in a strict sense, since there are no integrals or derivatives in it, but the book contains so much material about infinite series and products that it cannot be called precalculus in the modern sense.
The text looks quite modern (since all later authors followed Euler's style) but a lot of notations that today we take for granted are still missing, especially sum and product sign and even indices. How does he then manage to write about infinite series?
A generic power series takes for Euler the form

𝐴 + 𝐵𝑥 + 𝐶𝑥𝑥 + 𝐷𝑥³ + 𝐸𝑥⁴ &ct.,

and he also speaks of the series of coefficients, 𝐴, 𝐵, 𝐶, 𝐷, 𝐸 &ct., even if he apparently has no concept of a series as a mathematical object in its own right.
For more complex manipulations of series, Euler use the concept of the general term of a series (so that the general term of the geometric series is 𝑥ⁿ), and with this concept one can do almost the same calculations as with a sum operator.
And what is if there is more than one infinite series? A second series is for Euler often

𝑎 + 𝑏𝑥 + 𝑐𝑥𝑥 + 𝑑𝑥³ + 𝑒𝑥⁴ &ct.

and a third and fourth series may have the coefficients 𝑎', 𝑏', 𝑐', 𝑑', 𝑒' &ct. and 𝑎'', 𝑏'', 𝑐'', 𝑑'', 𝑒'' &ct. This way he produces a lot of mathematics.

And in one place (§214), when he has used up all other methods to create new types of coefficients, he even distinguishes between a series with coefficients in italics and one with coefficients in straight letters:

A + B𝑥 + C𝑥𝑥 + D𝑥³ + E𝑥⁴ &ct.,

#Mathematics #HistoryOfScience #Notations #LeonardEuler #Analysis

Exploring Simplified Lambda Calculus Notations

https://jevko.github.io/writing/2023-07-20-lambda.html

[N.G. de Bruijn 1972] introduced a way to eliminate names from the syntax of lambda calculus, making it much simpler and “easy to handle in metalingual discussion”.

[J. Tromp 2023] incorporated and expanded upon this idea in his Binary Lambda Calculus (BLC) syntax.

#Exploring #Simplified #Lambda #Calculus #LambdaCalculus #Notations #Summary #deBruijn #syntax #Tromp #Binary #BLC

Named Tensor Notation

David Chiang, Alexander M Rush, Boaz Barak

https://openreview.net/forum?id=hVT7SHlilx

#tensors #tensor #notations

Des commentaires par les pairs à la co-création | Thot Cursus
https://cursus.edu/articles/42800/des-commentaires-par-les-pairs-a-la-co-creation#.XKhtureTLfo

#Commentaires #encadrants #étudiants #Évaluations #notations #Co-Évaluation