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Welcome to the DiscreteMathematics wiki!

Discrete mathematics can be daunting and hard to wrap your head around. With this extremely summarized study guide, I hope you make better understanding of the subject. Try solving the examples on your own and you will get better by doing so. Good luck!

Contents

0. Introduction

• Types of Numbers
• Common Operations

1. Logic

• Proposition
  • Truth Value and Proposition
  • Logical Operation and Compound Proposition
  • How To Solve A Compound Proposition
  • Conditional Proposition
  • Converse, Inverse, Contraposition
• Logical Equivalence
  • Definition
  • Useful Laws
• Proposition with variables
  • Propositional Function
  • Quantifiers
• Inference
  • Types of Inference
  • Logical Inference Laws

2. Proofs

• Types of Proofs
  • Direct Proof
  • Proof by Contraposition
  • Proof by Contradiction
  • Existence Proof
  • Proof by Counter-Example
• Mathematical Induction

3. Functions

• Classes of Function
• Function Composition
• Useful Tips

4. Graphs

• Definitions
• Types

5. Trees

• Definitions
• Binary Tree
• Tree Traversals
• Binary Search Tree
• Tree Implementation

6. Intro to Algorithms

• Complexity
• Basic Algorithms
  • Euclidean Algorithm
  • Recursive Algorithm
  • Linear Search Algorithm
  • Binary Search Algorithm
  • Bubble Sort
  • Insertion Sort
  • Quick Sort
  • Merge Sort

Feel free to email me at jongwoo2@illinois.edu if you want me to add more contents!

Acknowledgement

• Mathematics for Computer Science MIT
• Wolfram Alpha
• GeeksForGeeks