I collect such sources here: [url]http://philomath.boards.net/board/93/mathematics[/url]

Here is a link to Huang's paper on the Sensitivity Conjecture as noted within the recent issue of Discover magazine: [url]https://arxiv.org/pdf/1907.00847.pdf[/url]
A related (possibly dated around 194955) paper from the University of Illinois Urbana which I photocopied years ago used 3D cubes of unit resistances to develop some interesting results..Fibonacci, etc.. Some original papers by G. Kron are also worth a look. These kinds of papers showed me at that time how circuit theory and certain kinds of mathematics are essentially interchangeable. Computer Science extends this methodology. 
[QUOTE=jwaltos;534453]Here is a link to Huang's paper on the Sensitivity Conjecture[/QUOTE]
Nice! 
Paul Pollack's Number Theory books.
The first one can be downloaded free! [URL]http://pollack.uga.edu/index.html#books[/URL] 
In the [url=https://www.mersenneforum.org/forumdisplay.php?f=132]Number Theory Discussion Group[/url] subforum of the Math forum, there is a series of threads whose titles begin "Basic Number Theory" followed by numbers  1&2, 3, 4, 5, ..., 22.
Unlike Andre Weil's book infamously titled [u]Basic Number Theory[/u], these consist of introductory material. 
[QUOTE=Dr Sardonicus;563050]In the [url=https://www.mersenneforum.org/forumdisplay.php?f=132]Number Theory Discussion Group[/url] subforum of the Math forum, there is a series of threads whose titles begin "Basic Number Theory" followed by numbers  1&2, 3, 4, 5, ..., 22.
Unlike Andre Weil's book infamously titled [u]Basic Number Theory[/u], these consist of introductory material.[/QUOTE]As in texts which cover [u]Elementary Particle Physics[/u]. 
[QUOTE=xilman;563086]As in texts which cover [U]Elementary Particle Physics[/U].[/QUOTE]
Algebraic Number Theory can legitimately be thought of as both the algebraic branch of number theory and the theory of algebraic numbers. 
[QUOTE=Nick;563088]Algebraic Number Theory can legitimately be thought of as both the algebraic branch of number theory and the theory of algebraic numbers.[/QUOTE]One time a grad school classmate referred to Analytic Number Theory as "the theory of analytic numbers." Oops.
Of course, the title [u]Basic Number Theory[/u] was somewhat in jest  it [i]is[/i] "basic" in the sense that it covers the basics of Class Field Theory. But it is definitely [i]not[/i] an introductory text. I don't know whether Weil ever became exasperated with the jokes about the book title, but it is a fact that 12 years later, he came out with another book called [u]Number Theory for Beginners[/u]. Reminds me, my third grade math class was really [i]hard![/i] The textbook was [u]A Course in Arithmetic[/u] by JeanPierre Serre... 
[QUOTE=xilman;563086]As in texts which cover [u]Elementary Particle Physics[/u].[/QUOTE]
The ideas of particle physics: An Introduction for Scientists. Coughlan and Dodd. Cambridge University Press The above book is a decent introduction for "beginners" and is a great starting point for further inquiry. This is one of those books where even if you skim through it superficially you will retain something..which is always a good thing. 
A professor who was (and maybe still is) a forum member has written
a leisurely introduction to some foundational concepts of universitylevel mathematics, and made it freely available [URL="https://math.byu.edu/~pace/Transitionereader.pdf"]here.[/URL] 
[QUOTE=Nick;578658]A professor who was (and maybe still is) a forum member has written a leisurely introduction to some foundational concepts of universitylevel mathematics, and made it freely available [URL="https://math.byu.edu/~pace/Transitionereader.pdf"]here.[/URL][/QUOTE]
This is absolutely amazingly awesome!!! Personally, I will never get to the level of many of you when it comes to deep maths. But even just understanding the nomenclature and notation a little bit can go a long way. I will be sharing this around. A nonzero percentage will find it valuable! :tu: 
All times are UTC. The time now is 02:37. 
Powered by vBulletin® Version 3.8.11
Copyright ©2000  2022, Jelsoft Enterprises Ltd.