Engineering Mathematics
50 articles in this topic
Number of Simple Undirected Unlabeled Graphs: Counting Step by Step
Learn why labeled and unlabeled graph counts differ, enumerate every shape on three vertices, and use Burnside's lemma to obtain 11 shapes on four vertices.
Updated 31 Aug 20265 min readEngineering Mathematics
Introduction to Graphs: Loops, Parallel Edges and Adjacent Vertices with Worked Examples
Build every basic graph term from one five-vertex example. Track a loop and parallel edges correctly, audit the degree sum, then simplify the graph.
Updated 29 Aug 20265 min readEngineering Mathematics
Graph Matching: Maximal, Maximum and Perfect Matchings with Augmenting-Path Examples
Learn how maximal, maximum and perfect matchings differ. Follow one bipartite graph from a stuck greedy choice to a perfect matching using two augmenting paths.
Updated 27 Aug 20265 min readEngineering Mathematics
Logical Operators Explained: Negation, Conjunction and Disjunction with Worked Truth Tables
Learn how negation, conjunction and inclusive disjunction change truth values. Follow complete truth tables, scoped negations, De Morgan checks and a worked compound expression.
Updated 26 Aug 20265 min readEngineering Mathematics
Graph Traversal: Walk, Trail, Path, Circuit and Connectivity with Worked Examples
Use one six-vertex graph to distinguish walks, trails, paths, circuits and cycles. Then test reachability, components and a bridge with exact sequences.
Updated 24 Aug 20265 min readEngineering Mathematics
3D Object Representation, Geometric Transformations and Viewing: A Worked Pipeline
Track three vertices through a complete 3D graphics pipeline. The worked example makes matrix order, camera depth and viewport conversion explicit.
Updated 22 Aug 20266 min readEngineering Mathematics
Mathematical Representation of Points and Lines in Computer Graphics: From Equations to Pixels
Follow one segment from Cartesian coordinates to line equations, a point projection, a homogeneous intersection and seven selected pixels.
Updated 21 Aug 20266 min readEngineering Mathematics
Introduction to Viewing in Computer Graphics: Window-to-Viewport Mapping with a Worked Example
Follow a point and a triangle from a world window to a viewport. Derive the transform, audit the arithmetic, and separate clipping, distortion, and y-axis reversal.
Updated 19 Aug 20266 min readEngineering Mathematics
Order of Elements in Groups Explained: Formulas and Worked Examples
Learn how to find an element's order using direct powers, gcd formulas, cycle lengths and Lagrange's theorem. Each worked result is checked against its generated subgroup.
Updated 17 Aug 20266 min read66 viewsEngineering Mathematics
Set Theory in Discrete Mathematics: Operations, Laws and Worked Examples
Build set theory from elements and subsets to algebra, inclusion-exclusion and Cartesian products, with every important result worked out step by step.
Updated 15 Aug 20265 min read89 viewsEngineering Mathematics
Group Theory in Discrete Mathematics: Group Tests, Subgroups and Worked Examples
Learn a repeatable group test through addition and multiplication modulo 8, subgroups, cosets, a quotient map, and non-commuting permutations in S_3.
Updated 13 Aug 20266 min readEngineering Mathematics
Functions in Discrete Mathematics: Types, Counting and Worked Examples
Learn how to recognise function types, count constrained mappings, compose rules in the correct order and decide when an inverse exists. Each idea is checked on finite sets.
Updated 11 Aug 20266 min readEngineering Mathematics