Mathematics & Scientific Computing
A working notebook on the mathematical foundations of numerical computation. Published notes cover measure-theoretic convergence and floating-point arithmetic. The study plans continue through optimization and iterative solvers toward numerical PDEs, preconditioning, and parallel implementation.
Mathematical foundations → Numerical methods → Solvers → Parallel implementation → Research experiments
Reading starting points
- Measure theory — foundations, convergence theorems, and seminar notes.
- IEEE 754, Errors, and Algorithms — numerical representation and stable computation.
- From steepest descent to conjugate gradients — derivations and MATLAB implementations, with preconditioning planned.
Study series
Published notes are organized by prerequisites and reading order.
Recent notes
Study areas
Mathematics
Linear algebra, analysis, functional analysis, and PDE foundations.
Numerical Methods
Discretization, approximation, numerical stability, and algorithms.
Solvers
Iterative linear solvers, preconditioning, multigrid, and domain decomposition.
Scientific Computing
Parallel implementation, reproducible experiments, and performance analysis.
Implementation and evidence
Existing notes contain MATLAB and Python code and C++-style pseudocode. Project pages distinguish published derivations and code from planned FEM, domain decomposition, and MPI experiments. Reproducible timings and scaling results will be linked when available.