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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:

• 2-categories
• Adjoints, see also
• Bethe ansatz
• 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
• Dimension
• Direct sums and products of sets, see also
• Divergence, see also
• Dual categories
• Duality
• Dynamical systems
• Edge contraction
• Equivalence relation
• Fiber bundles, see also
• Fibrations
• Fixed points
• Flag, filtration
• Foliation
• Fourier series
• Functor
• Fuzzy sets
• Galois connections
• Graphs, see also
• Hasse diagrams
• Homotopy, see also
• Injections, surjections, bijections
• Intervals
• Isomorphism
• Jaccard index
• Karnaugh map
• Lattices
• Manifolds, gluing
• Maps, see also
• Minimal surface
• Model Theory
• Moduli space
• Monoids
• Motives, see also
• Motivic integration
• Nerve complex
• Open and closed sets
• Operads
• Orbifolds
• Order duality
• Ordinals
• Feynman path integral
• Phase
• Piecewise linear functions
• Poincaré map, Poincaré section
• Polynomials
• Posets
• Powerset
• Presheaves
• Projective spaces
• Quotient groups
• Quotient space
• Retraction
• Riemann surfaces, multivalued functions
• Residue
• Rough sets
• Scalar field
• Semigroups, see also
• Sheaves
• Significant digits
• Simplicial complex
• Step functions
• Structure Sheaf
• Surfaces
• Tensors
• Topology
• Ultrametric spaces, p-adic numbers
• Variadic functions
• Whiskering, also

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.