TECHNIQUES FOR GENERATING RANDOM NUMBERS

Test for Random numbers

Tests for Autocorrelation

Linear Congruential Method in R & Chi-square Test in R |

Monte Carlo simulation

Fundamental of Data Science

Graph Theory (Part-I)

Subgraphs, Spanning Subgraphs, Operation on Graphs

Walk, Trails, Path and connected Graphs

At most number of edges with n vertices and k component

Cycle in Graph

Euler Graph and Hamiltonian Graph

Tree

Theorem on Tree, Spanning Tree and Fundamental circuits

Dijkstra's algorithm (Example)

Floyd-Warshall's Algorithm

Dijkstra's Algorithm (examples-2)

Floyd-Warshall's Algorithm (Example-2)

Kruskal's Algorithm and Prim's Algorithm

Breadth First Search Algorithm

Matrix Representation on Graph

Adjacency Matrix

The Law of Large Numbers

High Dimensional object is that Most of their volume is near the surface

Volume of the Unit Ball in d-dimensional space

Most of the volume is near equator

Near Orthogonality, Generating points Uniformly & Gaussians in High Dim. |

Random Projection & Johnson-Lindenstrauss Lemma

Separating Gaussian

Degree Distribution in G(n,p) model

Existence of triangle in G(n,d/n) model

First & Second Moment Methods , Phase transition

Threshold for graph diameter Two

Disappearance of Isolated Vertices

Hamilton Circuits and The Giant component

Emergence of cycle

Giant Component in Random Graphs with Given Degree Distribution

Power Method

Small world Graph

Singular value Decomposition

Image compression using SVD

Images and Matrices

Minimum length solution

Random Walk (Part-I)