Competencies: Mathematics > Discrete Mathematics

Discrete Mathematics

Body of Knowledge

Topic	Description	Relevance	Career Tracks
Graph Theory	Mathematical study of graphs including nodes, edges, adjacency, paths, cycles, connectivity, and degree. Foundation for network analysis, algorithm design, and knowledge representation.	High	Software Engineer, Data Scientist, Algorithm Engineer
Set Theory (Applied)	Practical application of set operations (union, intersection, complement) to access control, group membership, and classification problems. Foundation for Boolean logic and database theory.	Medium	Software Engineer, Security Engineer, Data Engineer
Boolean Algebra	Logical operations (AND, OR, NOT) applied to access control lists, firewall rules, and policy evaluation. Includes truth tables and expression simplification.	High	Security Engineer, Network Engineer, Software Engineer
Combinatorics	Counting principles including permutations, combinations, and their applications to password complexity, brute-force estimation, and probability calculations.	Medium	Security Engineer, Cryptographer, Data Scientist
Relations & Functions	Binary relations, equivalence relations, partial orders, function properties	Medium	Software Engineer, Data Scientist
Recurrence Relations	Solving recurrences, algorithm complexity analysis, dynamic programming	Medium	Software Engineer, Algorithm Designer
Number Theory	Primes, modular arithmetic, GCD, Euler’s theorem, applications to cryptography	High	Security Engineer, Cryptographer

Topic

Description

Relevance

Career Tracks

Graph Theory

Mathematical study of graphs including nodes, edges, adjacency, paths, cycles, connectivity, and degree. Foundation for network analysis, algorithm design, and knowledge representation.

High

Software Engineer, Data Scientist, Algorithm Engineer

Set Theory (Applied)

Practical application of set operations (union, intersection, complement) to access control, group membership, and classification problems. Foundation for Boolean logic and database theory.

Medium

Software Engineer, Security Engineer, Data Engineer

Boolean Algebra

Logical operations (AND, OR, NOT) applied to access control lists, firewall rules, and policy evaluation. Includes truth tables and expression simplification.

High

Security Engineer, Network Engineer, Software Engineer

Combinatorics

Counting principles including permutations, combinations, and their applications to password complexity, brute-force estimation, and probability calculations.

Medium

Security Engineer, Cryptographer, Data Scientist

Relations & Functions

Binary relations, equivalence relations, partial orders, function properties

Medium

Software Engineer, Data Scientist

Recurrence Relations

Solving recurrences, algorithm complexity analysis, dynamic programming

Medium

Software Engineer, Algorithm Designer

Number Theory

Primes, modular arithmetic, GCD, Euler’s theorem, applications to cryptography

High

Security Engineer, Cryptographer

Personal Status

Topic	Level	Evidence	Active Projects	Gaps
Graph Theory	Intermediate	Built association-engine on graph theory foundations — nodes, edges, adjacency, paths, cycles, connectivity, degree; applied to knowledge management domain	Association Engine, PRJ-domus-math: Mathematics for Infrastructure Professionals	No formal proofs (induction on graphs), no advanced algorithms (Dijkstra, A*, minimum spanning tree)
Set Theory (Applied)	Intermediate	Set operations applied to ISE policy groups, VLAN membership, ACL logic; union/intersection/complement in access control contexts; association-engine node classification	Association Engine	No formal set theory (ZFC axioms), no proofs involving cardinality
Boolean Algebra	Intermediate	ACL logic (AND/OR/NOT), ISE policy conditions, firewall rule evaluation; truth tables for debugging complex access policies	ISE Policy	No formal Boolean algebra study, no Karnaugh maps, no logic gate optimization
Combinatorics	Beginner	Password complexity calculations, permutations for brute-force estimation; basic counting principles from Security+ and CISSP	CISSP Study Guide	No generating functions, no advanced counting, no pigeonhole principle applications

Topic

Level

Evidence

Active Projects

Gaps

Graph Theory

Intermediate

Built association-engine on graph theory foundations — nodes, edges, adjacency, paths, cycles, connectivity, degree; applied to knowledge management domain

Association Engine, PRJ-domus-math: Mathematics for Infrastructure Professionals

No formal proofs (induction on graphs), no advanced algorithms (Dijkstra, A*, minimum spanning tree)

Set Theory (Applied)

Intermediate

Set operations applied to ISE policy groups, VLAN membership, ACL logic; union/intersection/complement in access control contexts; association-engine node classification

Association Engine

No formal set theory (ZFC axioms), no proofs involving cardinality

Boolean Algebra

Intermediate

ACL logic (AND/OR/NOT), ISE policy conditions, firewall rule evaluation; truth tables for debugging complex access policies

ISE Policy

No formal Boolean algebra study, no Karnaugh maps, no logic gate optimization

Combinatorics

Beginner

Password complexity calculations, permutations for brute-force estimation; basic counting principles from Security+ and CISSP

CISSP Study Guide

No generating functions, no advanced counting, no pigeonhole principle applications