Competencies: Mathematics > Applied Mathematics
Applied Mathematics
Body of Knowledge
| Topic | Description | Relevance | Career Tracks |
|---|---|---|---|
Coverage Analysis |
Measure theory concepts applied to completeness metrics including ratio calculations, gap analysis, and sigma-algebra conceptual frameworks for defining measurable spaces. |
Medium |
Quality Assurance, Data Science, Documentation Engineering |
Networking Mathematics |
Binary arithmetic, subnet calculation (CIDR notation, wildcard masks, supernetting), VLSM design, and IP address planning. Daily application in network engineering. |
High |
Network Engineer, Infrastructure Engineer, Security Engineer |
Numerical Methods |
Root finding, interpolation, numerical integration, floating-point issues |
Medium |
Data Scientist, Engineer, Quantitative Analyst |
Optimization Theory |
Linear programming, convex optimization, constraint optimization |
High |
ML Engineer, Operations Research, Data Scientist |
Signal Processing |
Fourier transforms, filtering, sampling theorem, digital signal processing |
Medium |
Data Engineer, ML Engineer, Audio/Video Developer |
Queueing Theory |
Arrival/service rates, Little’s law, M/M/1 queues, capacity planning |
Medium |
SRE, Performance Engineer, Network Engineer |
Personal Status
| Topic | Level | Evidence | Active Projects | Gaps |
|---|---|---|---|---|
Coverage Analysis |
Intermediate |
Measure theory concepts applied to documentation coverage — defined coverage as ratio of documented to total items; gap analysis methodology; sigma-algebra conceptual framework |
PRJ-domus-math: Mathematics for Infrastructure Professionals, Association Engine |
No formal measure theory, no probability spaces, no integration theory |
Networking Mathematics |
Advanced |
Binary arithmetic, subnet calculation (CIDR notation, wildcard masks, supernetting), VLSM design; daily use in network engineering at CHLA and home lab |
No IPv6 addressing math (128-bit), no algorithmic approach to IP planning |