Counting, arrangement and the structure of finite systems.
11 topics · 15 curated works
No prior grounding assumed.
Solutio problematis ad geometriam situs pertinentis
Leonhard Euler · 1736
Solves the Konigsberg bridges puzzle by discarding distance and shape entirely and reasoning only about which crossings connect which landmasses, the…
+1 more at this level
Assumes you know the vocabulary.
On a Problem in Combinations
Thomas P. Kirkman · 1847
Poses and partly solves the fifteen schoolgirls problem, asking for a schedule of triples covering every pair exactly once, a question whose answer…
+3 more at this level
Primary sources and full treatments.
On a Problem of Formal Logic
Frank P. Ramsey · 1930
Proves that any sufficiently large structure must contain a highly ordered substructure, showing total disorder is itself impossible past a certain…
+8 more at this level
12 of 15 works
Leonhard Euler
Solves the Konigsberg bridges puzzle by discarding distance and shape entirely and reasoning only about which crossings connect which landmasses, the founding argument of graph theory.
link checked 17 Sept 2026Ron Graham (Numberphile)
Explains the Happy Ending problem — that enough points in general position always contain a convex quadrilateral — as Ramsey theory in miniature, and traces the bound's link to Graham's number.
link checked 17 Sept 2026Thomas P. Kirkman
Poses and partly solves the fifteen schoolgirls problem, asking for a schedule of triples covering every pair exactly once, a question whose answer became the founding example of a combinatorial design.
link checked 17 Sept 2026Herbert S. Wilf
Shows that almost any counting problem becomes tractable once phrased as a generating function, and builds the algebraic machinery needed to extract answers from the resulting power series.
link checked 17 Sept 2026James Oxley
Surveys matroids as the abstract structure common to linear independence in vector spaces and cycle-freeness in graphs, and explains why the greedy algorithm works exactly on structures of this kind.
link checked 17 Sept 2026Tom Leighton (MIT OpenCourseWare)
Covers the discrete mathematics computer science actually uses — proof technique, induction, number theory, counting and probability — with algorithmic correctness as the motivating example throughout.
link checked 17 Sept 2026Frank P. Ramsey
Proves that any sufficiently large structure must contain a highly ordered substructure, showing total disorder is itself impossible past a certain size.
link checked 17 Sept 2026Paul Erdos & George Szekeres
Gives a new proof of Ramsey's theorem via the pigeonhole principle and uses it to show that enough points in general position always contain a convex polygon of any given size.
link checked 17 Sept 2026Hassler Whitney
Axiomatises the notion of linear dependence shared by vector spaces and graphs into a single abstract structure, founding matroid theory.
29 pageslink checked 17 Sept 2026Garrett Birkhoff
Treats the partial order underlying lattices as the primary object of study, unifying Boolean algebras, topologies and subgroup structures under one algebraic theory of order.
link checked 17 Sept 2026Paul Erdos
Shows a graph with the Ramsey property must exist by counting random graphs rather than constructing one directly, the founding argument of the probabilistic method.
link checked 17 Sept 2026Reinhard Diestel
Organises graph theory around a small set of core theorems on connectivity, colouring, planarity and minors, chosen because each one generalises rather than merely illustrates a technique.
link checked 17 Sept 2026