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#math

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Two centuries ago (1825 and 1827), Gauss published two papers on intrinsic curvature of surfaces. In 2011, using page scans and OCR text generously provided by Brenda Lewis at Distributed Proofreaders, I digitized the English translation by Hiltebeitel and Morehead for Project Gutenberg.

This Very Short blog post introduces the geometric context (extrinsic and intrinsic curvature of surfaces) for non-mathematicians: diffgeom.com/blogs/free-online

The 1914 British second edition of Calculus Made Easy is by far the most popular ebook I helped produce for Project Gutenberg: diffgeom.com/blogs/free-online

Part of my 2010 post for the Distributed Proofreaders blog about the book (full text: blog.pgdp.net/2010/10/13/calcu)
---(snip)---
The mathematical study of rates of change and total change, also known as “the differential and integral calculus”, has frightened generations of students. Ironically, this scholastic trauma is often unnecessary: Many formal rules of calculus are nearly trivial to carry out. The mathematical difficulties lie in understanding and using the rigorous logical framework of the calculus—what mathematicians nowadays term “elementary real analysis”—and in establishing the correctness of the formal manipulations and their connections with mathematical interpretations.

Sylvanus Phillips Thompson’s “Calculus Made Easy” gives cogent yet entertaining and irreverent explanations of these easy calculational rules. Justifications are conceptual, but beneficially simplified and intuitive. Popularized and later updated by the recreational mathematics author Martin Gardner, “Calculus Made Easy” has remained a widely-read introductory text for the past century.

[...]

If you’ve had unpleasant experiences with calculus, if your knowledge has grown rusty, or if you’ve simply never encountered this powerful and intriguing branch of mathematics, Thompson’s gem of a textbook should prove a pleasant, thought-provoking, and ultimately rewarding read.
---(snip)---
#Math #Mathematics #ProjectGutenberg

Over the years I've helped create a variety of free online resources for teaching and learning math, including textbook manuscripts, public domain ebooks, and interactive software. I've posted haphazardly at mathstodon about a few of these items, but am starting a line of Very Short blog posts at my online shop Differential Geometry to showcase examples more systematically.
diffgeom.com/blogs/free-online
#Math #ProjectGutenberg #Mathematics

"La valeur durable des mathématiques, comme celle des autres sciences et arts, transcende de loin le flux quotidien d'un monde en mutation. En fait, l'apparente stabilité des mathématiques pourrait bien être l'une des raisons de leur attrait et du respect qui leur est accordé dans un monde où la sécurité est tellement hors d'atteinte" – Moses Richardson
#citation #mathématiques #maths #math

LOL if you ask ChatGPT for random numbers, more likely than not it will pick 42 (Thanks to Douglas Adams)

And funny enough, 73 is extremely popular, which I will blame on all of us ham radio folks out here. (73 is a traditional number code for saying goodbye on ham radio). #hamradio

Someone, somewhere, is going to win a lottery or drawing somewhere by picking the numbers most likely to be picked by an LLM, soon. Somebody is going to get the (dumb) idea to use one of the LLMs to pick winning numbers for their drawing, and it's going to be the most frequent choices due to the weighting towards specific numbers within the training material. (42 and 73 will be in there, LOL).

h/t @rrmutt

leniolabs.com/artificial-intel

#AI#LLM#randomness