Matrix Computing
Solving massive systems of equations and changing coordinate spaces – Gaussian Elimination, Singular Value Decomposition, Krylov Subspace Iteration.
Numerical Analysis
Finding mathematical roots, computing derivatives/integrals, and max/min complex functions – Newton-Raphson, Runge-Kutta, Simplex Method.
Sorting & Searching
Organizing arbitrary data arrays to drop search and lookup complexities down to (O(\log n)) or O(1) – Quicksort & Merge Sort, Binary Search, Hashing, B-Trees & Skip List.
Graph & Routing
Finding the shortest path, analyzing cluster connections, or optimizing throughput – Dijkstra’s & A* Search, Page Rank, Kruskal’s & Prim’s, Ford-Fulkerson.
Stochastic Method
Approximating impossible integrals, assessing financial risk, and simulating quantum mechanics – Monte Carlo, Kalman Filter, Bloom Filters, RSA & Diffie-Hellman Key Exchange.
Signal & Learning
Translating raw spatial or temporal arrays into semantic meaning or extreme compression – Fast Fourier Transform, Gradient Descent, Discrete Cosine Transform, Markov Model.