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Guided learning journeys that build knowledge step by step.
category · Learning · slug · learning · 7819 Paths
7819 Paths · page 716 / 782
This learning path provides a systematic introduction to discrete random variables and their distributions, focusing on expectation, variance, and the Bernoulli and binomial distributions. It begins with foundational probability concepts, builds the mathematical tools needed, and culminates in the study of these key discrete distributions.
A systematic path to understanding discrete probability spaces, covering sample spaces, events, probability, and conditional probability, with foundations in set theory and counting.
A systematic learning path for university students to master the pigeonhole principle, its generalizations, and combinatorial applications. Starting from basic counting and set theory, it progresses through the principle, its strong form, and advanced applications in number theory and Ramsey theory.
A systematic learning path for university students aiming to master advanced counting techniques. Starting from foundational combinatorics, it progresses through stars and bars, recurrence relations, generating functions, and advanced combinatorial formulas, culminating in the application of these methods to complex counting problems.
This learning path guides university students through the essential concepts of network flow theory, from graph fundamentals to the Max-Flow Min-Cut theorem and the Ford-Fulkerson algorithm, culminating in practical applications. It emphasizes the logical dependencies between topics to build a solid understanding.
A comprehensive learning path covering the theory of matchings in graphs, from fundamental definitions to Hall's theorem and its applications in combinatorial optimization and related fields.
This advanced university-level path systematically covers graph vertex coloring: from foundational graph theory and the chromatic number, through greedy and exact coloring algorithms, to structural theorems such as the four-color theorem and modern applications in scheduling, register allocation, and Sudoku. It emphasizes rigorous proofs and algorithmic thinking, with connections to related graph parameters.
A comprehensive learning path covering the fundamentals of graph theory, planar embeddings, Euler's formula, and Kuratowski's theorem, with rigorous proofs and applications.
This learning path introduces the concept of trees in discrete mathematics, covering their fundamental properties, rooted trees, spanning trees, and minimum spanning tree algorithms. It begins with necessary graph theory prerequisites and builds up to advanced topics.
This learning path introduces the foundational concepts of graph theory, focusing on paths, cycles, and various notions of connectivity. Starting with basic graph definitions, the path progresses through walks, trails, and paths, then explores cycles and trees, and finally covers cut vertices, bridges, and connected components. The path is designed for university students with a background in discrete mathematics.