Discrete Mathematics

  1. Trees
    1. Tree Fundamentals
      1. Definition and Properties
        1. Acyclic Connected Graphs
          1. Equivalent Definitions
            1. Basic Properties
            2. Tree Terminology
              1. Roots and Leaves
                1. Parents and Children
                  1. Siblings and Ancestors
                    1. Descendants and Subtrees
                      1. Height and Depth
                      2. Types of Trees
                        1. Rooted Trees
                          1. Binary Trees
                            1. m-ary Trees
                              1. Ordered Trees
                                1. Full and Complete Trees
                              2. Tree Traversals
                                1. Depth-First Traversals
                                  1. Preorder Traversal
                                    1. Inorder Traversal
                                      1. Postorder Traversal
                                      2. Breadth-First Traversal
                                        1. Level Order Traversal
                                        2. Tree Reconstruction
                                          1. From Traversal Sequences
                                            1. Unique Reconstruction Conditions
                                          2. Spanning Trees
                                            1. Definition and Existence
                                              1. Spanning Tree Properties
                                                1. Number of Spanning Trees
                                                2. Minimum Spanning Trees
                                                  1. Weight and Cost
                                                    1. Optimality Conditions
                                                      1. Uniqueness Conditions
                                                      2. Algorithms for MST
                                                        1. Kruskal's Algorithm
                                                          1. Prim's Algorithm
                                                            1. Comparison of Algorithms
                                                          2. Tree Applications
                                                            1. Binary Search Trees
                                                              1. Structure and Properties
                                                                1. Search Operations
                                                                  1. Insertion and Deletion
                                                                  2. Expression Trees
                                                                    1. Arithmetic Expressions
                                                                      1. Evaluation Methods
                                                                        1. Construction from Expressions
                                                                        2. Decision Trees
                                                                          1. Structure and Applications
                                                                            1. Optimization Problems
                                                                            2. Huffman Coding
                                                                              1. Optimal Prefix Codes
                                                                                1. Huffman Algorithm
                                                                                  1. Applications in Compression

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                                                                              7. Discrete Probability