V_2_17 — Homological Algebra: Chain Complexes, Exact Sequences, and Derived Functors

Homological algebra provides a powerful, abstract framework for studying algebraic structures — groups, rings, modules, sheaves — by analyzing chain complexes (sequences of abelian groups or modules connected by homomorp

V_2_19 — Category Theory: Abstract Structure, Functors & Topos Theory

Category theory — often called the "mathematics of mathematics" — provides a universal language for describing mathematical structures and the relationships between them, emphasizing morphisms (arrows, maps, transformati

ZD_1_08 — Lambda Calculus and Functional Programming

Lambda calculus, invented by Alonzo Church in the 1930s as a formal system for expressing computation via function abstraction and application, stands alongside Turing machines as a foundational model of computation. Chu

ZD_1_14 — Type Theory: Lambda Calculus, Dependent Types, and the Curry-Howard Correspondence

Type theory is a foundational framework in mathematics, logic, and computer science that classifies values and expressions into types — categories that determine what operations are valid: a natural number can be added t

ZA_5_13 — Anyons and Fractional Quantum Hall Effect

Anyons are quasiparticles that exist exclusively in two-dimensional systems and obey quantum statistics intermediate between bosons and fermions — when two identical anyons are exchanged, the wave function acquires a pha

V_2_11 — Abstract Algebra: Groups, Rings, and Fields

Abstract algebra is the study of algebraic structures — sets equipped with operations satisfying specific axioms — that generalize familiar arithmetic operations to reveal deep structural patterns across mathematics and

V_2_12 — Algebraic Geometry

Algebraic geometry — the study of geometric objects defined by polynomial equations — is one of the most central and technically demanding branches of modern mathematics, connecting algebra, geometry, topology, and numbe

V_2_00 — Pure Mathematics: Subfolder Summary