Bill_Wang_01的博客

Absolute Value InequalityBase FormVariant 1ProofVariant 2ProofVariant 3x,y∈Rx,y\in\Rx,y∈RBase Form∣x+y∣≤∣x∣+∣y∣|x+y|≤|x|+|y|∣x+y∣≤∣x∣+∣y∣Variant 1∣∣x∣−∣y∣∣≤∣x−y∣||x|-|y|| ≤ |x- y|∣∣x∣−∣y∣∣≤∣x−y∣ProofWe use the technique of “adding 000 wisely”x

We go over the contents and the application of the CLT along with some preliminary introduction to Random Variables and Unbiased Estimators of population parameters. We offer a computational example of CLT in estimating the Sample Mean's distribution.

This note goes over the Fisher-Yates Shuffling, its proof, and implementation in Java.

Counting TechniquesMultiplication PrincipleCoin TossPermutation nPnnPnnPnPermutation nPrnPrnPrCombination nCrnCrnCrnCr=nCn−rnCr=nCn-rnCr=nCn−rMore Coin Toss ProblemPermutation With RepetationMultiplication PrincipleIf procedure AAA has aaa (distinct) ou

Is the Minimum Spanning Tree Unique?The following problem with two parts explores a condition that always implies a unique minimum spanning tree.

This note proves Prim's Algorithm for finding MST, and it shows why an edge with the minimum weight is always in every MST.

This note goes over a theorem about spanning trees: A Connected Graph has a Spanning Tree

In a connected graph, removing any single edge from a cycle retains connectivity.

This note briefly goes over a theorem that introduces some key properties of trees. This applies to any kind of trees.

This is a short note about the Hand Shaking Lemma and a formula for the sum of degrees of all vertices in a graph. It also provides an example of its application.

This note briefly goes over some (i.e. not all) topics about graphs and trees. It also contains links to additional posts about relevant topics written by myself.

This note briefly goes over the Adjacency Matrix and relevant theorems about how the Adjacency Matrix is related to Graph Isomorphism.