## APPLIED COMBINATORICS (Widely-Applicable Mathematics Series. Volume 0)

**Back cover description**

**Material covered: Combinatorics** essentially means systematic counting. We present some Combinatorics topics that are both simple and widely applicable, by which they are very much worth knowing,

understanding and applying. These include *permutations*,* combinations*, other *selections*, *partitions*, *generating series*, and * pigeonhole* and* inclusion-exclusion principles*.* Group-theory-based enumerations*, and especially *graphs*, *posets*, and *lattices*. Applications covered include to Computer Science, Chemistry, Geometry and to the Feynman diagrams of Quantum Physics. And toward starting to gain a basic understanding of some topics in Topology: notions of connectivity, of traversability, of cover, and of separation,

topological spaces, and a brief introduction to knots.

This is a Mathematics book, and yet we start from

scratch as regards Readers interested in applications

who are not (primarily) Mathematicians. A total of almost 1000 exercises, worked proofs and worked examples

are included.

**Some of our innovations:** Useful relative difference variables and ratio variables are systematically introduced, and applied toward understanding not only the graphs but also the spaces of graphs. And not only the partitions but also the spaces of partitions, and so on.

These developments are applying successful ‘Shape Theory’ or ‘relational’ ideas – usually found in Geometry

and in high-end approaches to Physics – now to basic Combinatorics as well. In particular,

the theory of each type of mathematical object

involves not only the structures of those objects

but also the structure of the *arena*: the space formed by

those objects. *This is one of the ways in whichTopology enters the theory of every other STEM subject*,

often accompanied by one of Order Theory – posets

and lattices – or Geometry. These parts of the current Volume are not only presented accessibly for beginners,

but are also innovative enough to source new research in Mathematics and in many other areas of STEM.

Throughout, Conceptual Thinking, including finding Truer Names for all the main objects and results encountered, is included and encouraged.

**Our format:** This Volume has been made freely available

in electronic form in support of the new Generation Z’s

considerable desire to become self-sufficient. Two affordably-priced series of Books are growing from

the current Volume. Since these will on many occasions

refer to the current Volume, its free availability can effectively be viewed as part of this affordable pricing.