computational-mathematics

The notion of spectral sequence is an algorithm or computational tool in homological algebra and more generally in homotopy theory which allows to compute chain homology groups/homotopy groups of bi-graded objects from the homology/homotopy of the two graded components. Notably there is a spectral sequence for computing the homology of the total complex of a double complex from the homology of it…

analysis (differential/integral calculus, functional analysis, topology) metric space, normed vector space open ball, open subset, neighbourhood convergence, limit of a sequence compactness, sequential compactness … … constructive mathematics, realizability, computability propositions as types, proofs as programs, computational trinitarianism basic constructions: strong axioms further In real ana…

Across disciplines, advances in computational mathematics are transforming how large-scale scientific data is analyzed, interpreted, and translated into deployable workflows. In the Earth and space monitoring domains, extreme weather risk, disaster response, precision agriculture, and solar activity forecasting rely on turning petabytes of satellite and sensor data into actionable insights. Found…

We are excited to share that Dr. Abba Ramadan and Dr. Leah Mungai have been selected as mentors for the 2026 SIAM–Simons Undergraduate Research Program, a nationally recognized initiative supported by the Simons Foundation. The project will be a collaboration with Dr. Leah Mungai (Geography), and together they will mentor undergraduate students in mathematics, computational science, and data scie…

Congratulations to Dr. Shan Zhao who has been awarded an NSF grant from DMS Computational Mathematics program: “Collaborative Research: Implicit solvent modeling and fast algorithm development for simulating solutes with atomic polarizable multipoles”. This is a collaborative project with Dr. Weihua Geng at Southern Methodist University, with a total award of $448K. Dr. Zhao is the lead-PI of thi…

Mojdeh Rasoulzadeh Associate Professor - mrasoulzadeh@ua.edu - (205) 348-5072 - 213A Gordon Palmer Hall - Curriculum Vitae - Website Office Hours See syllabus Research Areas - Applied & Computational Math

basic constructions: strong axioms further constructive mathematics, realizability, computability propositions as types, proofs as programs, computational trinitarianism The limited principle of omniscience () states that the existential quantification of any decidable proposition is again decidable. That is, or equivalently We have not stated the domain of quantification of the variable . If you…