discrete · mathuser topics

discrete mathematics · topics

Propositional logic · induction · stable matching · graph theory · planar graphs · hypercubes · modular arithmetic. Each link opens a clean, structured note page.

01 · reasoning & proof

Propositional Logic

truth tables, connectives, implication, quantifiers, proof strategies — the language of mathematical reasoning.

↗ mathuser.com/propositional-logic/ ∧∨

02 · proof technique

Induction

simple & strong induction, sum formulas, inequalities, binary representation, strengthening the hypothesis.

↗ mathuser.com/induction/ ∑

03 · algorithms & design

Stable Matching

Gale–Shapley algorithm, perfect matching, stability, optimality, resident‑hospital / college admissions.

↗ mathuser.com/stable-matching/ GS

04 · fundamentals

Graph Theory

vertices, edges, degrees, handshaking lemma, paths, cycles, connectivity, trees — the language of networks.

↗ mathuser.com/graph-theory/ G

05 · drawing & coloring

Planar Graph & Coloring

Euler’s formula V−E+F=2, K₅ and K₃,₃ are non‑planar, 5‑color theorem, four‑color theorem.

↗ mathuser.com/planar-graph-and-coloring/ ⏢

06 · special families

Hypercubes & Complete

Kₙ : n(n−1)/2 edges, densest. Qₙ : bit‑string cubes, recursive construction, large‑cut theorem.

↗ mathuser.com/hypercubes-and-complete-graphs/ Qₙ

07 · number theory

Modular Arithmetic & GCD

congruences, inverses, gcd condition, Euclid’s algorithm, fast halving proof, last‑digit tricks.

↗ mathuser.com/modular-arithmetic-and-gcd/ mod