Engineering Mathematics
29 articles in this topic
Trees in Graph Theory: Properties, Eccentricity, Diameter, Radius and Center
Build every important tree metric from one eight-vertex example, then use structural tests, a distance table and the two-sweep method to check each answer.
Spanning Tree and Spanning Forest: Definitions, Construction and Worked Examples
Learn how to construct and verify spanning trees and forests, why their edge counts are n - 1 and n - c, and when edge weights change the question.
Planar Graphs and Kuratowski's Theorem: Homeomorphism, K5 and K3,3 Worked Examples
Learn why crossings and edge bounds can mislead, then expose a hidden K3,3 by suppressing degree-two vertices in a complete worked example.
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.
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.
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.
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.
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.
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.
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.
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.
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.