ADUM Project

📖 Intuitive Set Theory: From Finite Sets to the Transfinite (PDF) This book is an introduction to set theory that begins from the intuitive viewpoint most readers naturally bring to the subject and leads, by careful stages, to two of its deepest themes: Cantor’s theory of infinite size and the …

📖 Abstract Algebra: From Symmetry to Galois Theory (PDF) This book develops abstract algebra from its most concrete beginnings to two of the subject’s most beautiful structural results. It is organized around a single, unifying conviction: the seemingly separate worlds of symmetry, arithmetic, linear structure, and polynomial equations are not …

This book presents a guided first pass through the core of linear and nonlinear functional analysis. It is organized around a single, concrete guiding question: How much of linear algebra survives in infinite dimensions, what fails, and which new geometric and compactness principles replace the missing finite-dimensional miracles? The exposition …

📖 Discrete Calculus (PDF) This book presents a unified treatment of discrete calculus, beginning with the classical calculus of finite differences and culminating in the discrete Hodge decomposition theorem on simplicial complexes. The Hodge decomposition asserts that every discrete differential form on a finite simplicial complex decomposes uniquely and orthogonally …