Resources for learning mathematics

[Blackadder]

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

[jwaltos]

Here is a link to Huang's paper on the Sensitivity Conjecture as noted within the recent issue of Discover magazine: https://arxiv.org/pdf/1907.00847.pdf

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]

Originally Posted by jwaltos

Here is a link to Huang's paper on the Sensitivity Conjecture

Nice!

[Nick]

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

[Dr Sardonicus]

In the Number Theory Discussion Group 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 Basic Number Theory, these consist of introductory material.

[xilman]

Originally Posted by Dr Sardonicus

In the Number Theory Discussion Group 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 Basic Number Theory, these consist of introductory material.

As in texts which cover Elementary Particle Physics.

[Nick]

Originally Posted by xilman

As in texts which cover Elementary Particle Physics.

Algebraic Number Theory can legitimately be thought of as both the algebraic branch of number theory and the theory of algebraic numbers.

[Dr Sardonicus]

Originally Posted by Nick

Algebraic Number Theory can legitimately be thought of as both the algebraic branch of number theory and the theory of algebraic numbers.

One time a grad school classmate referred to Analytic Number Theory as "the theory of analytic numbers." Oops.

Of course, the title Basic Number Theory was somewhat in jest -- it is "basic" in the sense that it covers the basics of Class Field Theory. But it is definitely not 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 Number Theory for Beginners.

Reminds me, my third grade math class was really hard! The textbook was A Course in Arithmetic by Jean-Pierre Serre...

[jwaltos]

Originally Posted by xilman

As in texts which cover Elementary Particle Physics.

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.