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-   -   Resources for learning mathematics (https://www.mersenneforum.org/showthread.php?t=21331)

Blackadder 2019-12-23 08:15

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

jwaltos 2020-01-07 01:45

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 1949-55) 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.

Nick 2020-01-07 10:40

[QUOTE=jwaltos;534453]Here is a link to Huang's paper on the Sensitivity Conjecture[/QUOTE]
Nice!

Nick 2020-11-12 20:05

Paul Pollack's Number Theory books.
The first one can be downloaded free!
[URL]http://pollack.uga.edu/index.html#books[/URL]

Dr Sardonicus 2020-11-13 00:46

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.

xilman 2020-11-13 10:06

[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].

Nick 2020-11-13 10:43

[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.

Dr Sardonicus 2020-11-13 14:07

[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 Jean-Pierre Serre...

jwaltos 2020-11-26 20:17

[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.

Nick 2021-05-18 18:10

A professor who was (and maybe still is) a forum member has written
a leisurely introduction to some foundational concepts of university-level mathematics,
and made it freely available [URL="https://math.byu.edu/~pace/Transition-ereader.pdf"]here.[/URL]

chalsall 2021-05-18 19:23

[QUOTE=Nick;578658]A professor who was (and maybe still is) a forum member has written a leisurely introduction to some foundational concepts of university-level mathematics, and made it freely available [URL="https://math.byu.edu/~pace/Transition-ereader.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 non-zero percentage will find it valuable! :tu:


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