Computational Mathematics

Arithmetic

• Integer Division
• Comparison
• Floating-point Arithmetic
• Arbitrary-precision Arithmetic

Algorithms

• Recursion

  • Memoization

• Branchless

• Data Types

  • Abstract Data Types

• Sequences

  • Sorting
    • Comparison Sorts
      • Selection Sort (Python)
      • Insertion Sort (Python)
      • Merge Sort (Python)
      • Heapsort (Python)
      • Quicksort (Python)
    • Integer Sorting
      • Bucket Sort (Python)
      • Counting Sort (Python)
      • Radix Sort (Python)
  • Merging
  • Search
    • Minimum
    • Binary Search
  • Substrings
    • Search
      • String-set-searching Algorithms
    • Longest Common Substrings
    • Longest Repeated Substring Problem
  • Subsequences
    • Longest Common Subsequences

• Ranges

  • Range Sets
  • Range Maps

• Sparse Matrices

  • Sparse Arrays

• Hash Tables

  • Seperate Chaining
  • Open Addressing
  • Perfect Hashing

• Trees

  • Binary Trees
    • Threaded Binary Trees
  • Tries
    • Hash Tries
    • Suffix Trees
      • Suffix Arrays
  • Traversal

• Graphs

  • Graph Search

    • Uninformed Search
      • Breadth-first Search
      • Depth-first Search
      • Uniform-cost Search
      • Bidirectional search
    • Informed Search
      • Greedy Best-first Search
      • A* Search

  • Sorting: Topological Sort

    • Dynamic Topological Sort
    • Constrained Topological Sort

  • Routing

    • Travelling Salesman Problem

• Succinct Data Structures

Numerical Analysis

• Error Analysis
• Order of Convergence
• Root Finding
  • Bracketing Methods
  • Fixed-Point Iteration
  • Newton's Methods
• Numerical Linear Algebra
  • Matrix Transposition
  • Matrix Decompositions
    • Lower-Upper Decomposition
  • Solutions of Linear Systems
    • Gaussian Elimination
    • Jacobi Methods
• Interpolation
  • Polynomial Interpolation
• Curve Fitting
  • Least Squares
• Numerical Integration
  • Quadrature Rules Based on Interpolating Functions
  • Adaptive Quadrature
• Numerical Optimization
  • Bracketing Search Methods
• Differential Equations
  • Euler Method
  • Runge-Kutta Methods

Libraries

SageMath

• Installation
• Python
• Symbolic Computation
  • Symbolic Expressions
  • Symbolic Functions

Tools

• WolframAlpha: Computational Intelligence
• Jupyter

MATLAB

• Built-ins
• Matrices
• Functions