Mathematical Concepts in Software Diagnostics and Software Data Analysis

Various mathematical analogies and metaphors inspired memory and log analysis patterns and some concepts of software diagnostics and software data analysis. We list them in alphabetical order:

Adjoints, see also
Braid groups
Braids, see also
Categories
Coalgebras, functors, 2-categories
Continuous and discontinuous functions
Curves
Derivatives, partial derivatives, see also
Direct sums and products of sets, see also
Divergence
Dual categories
Dynamical systems
Fiber bundles, see also
Fibrations
Fixed points
Fourier series
Galois connections
Graphs
Injections, surjections, bijections
Intervals
Lattices
Manifolds, gluing
Maps, see also
Motives, see also
Operads
Orbifolds
Piecewise linear functions
Poincaré map, Poincaré section
Posets
Presheaves
Projective spaces
Quotient groups
Riemann surfaces, multivalued functions
Rough sets
Sheaves
Step functions
Surfaces
Tensors
Topology
Ultrametric spaces, p-adic numbers
Variadic functions

The links to their definitions and examples can be found in the corresponding references. We give the original references to Memory Dump Analysis Anthology where possible, but most of them can also be found in Pattern-Oriented Software Diagnostics Reference books.