Books that use probabilistic/combinatorial/graph theoretical/physical/geometrical methods to solve problems from other branches of mathematics I am searching for some books that describe useful, interesting, not-so-common, (possibly) intuitive and non-standard methods (see note *) for approaching problems and interpreting theorems and results in number theory, analysis, algebra, linear algebra, and other branches of mathematics. 
(*) Such methods can be (but not limited to) from the areas of 


*

*probability;

*combinatorics;

*graph theory;

*physics;

*geometry.


Examples of such books can be Uspenskii's Some Applications of Mechanics to Mathematics or Apostol's and Mnatsakanian's New Horizons in geometry.

We're using   A Combinatorial Introduction to Topology by Henle as a supplemental resource in my general topology class right now.   Some of the alternate proofs are interesting,  like using Sperner's lemma to give a combinatorial proof of the Brouwer Fixed point theorem in $\mathbb R ^2$
