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
Cartesian Product
Categories
Causal sets, see also, and also
Coalgebras, functors, 2-categories
Cones
Continuous and discontinuous functions
Cover
Critical points, Morse theory
Curves
Defect group of a block
Derivatives, partial derivatives, see also
Dessin d’enfant
Direct sums and products of sets, see also
Divergence
Dual categories
Dynamical systems
Equivalence relation
Fiber bundles, see also
Fibrations
Fixed points
Flag, filtration
Foliation
Fourier series
Galois connections
Graphs
Hasse diagrams
Homotopy, see also
Injections, surjections, bijections
Intervals
Jaccard index
Lattices
Manifolds, gluing
Maps, see also
Minimal surface
Moduli space
Motives, see also
Motivic integration
Open and closed sets
Operads
Orbifolds
Order duality
Ordinals
Phase
Piecewise linear functions
Poincaré map, Poincaré section
Posets
Powerset
Presheaves
Projective spaces
Quotient groups
Quotient space
Riemann surfaces, multivalued functions
Residue
Rough sets
Scalar field
Sheaves
Significant digits
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.