Additional Topics Summary

GRE Math Subject · Axiom Academy

Complete unit review: Combinatorics, probability, graph theory, complex analysis, and numerical methods The "Additional Topics" section of the GRE Math Subject Test is a grab bag covering roughly 10-15% of the exam. These topics range from discrete math (combinatorics, graph theory) to complex analysis and numerical methods. The questions tend to be more computational and formula-driven, making them high-value if you know the key results. Multiplication principle: If task A has outcomes and task B has outcomes, there are ways to do both. Addition principle: If tasks A and B are mutually exclusive, there are ways to do one or the other. Inclusion-Exclusion: . Extends to three or more sets. Combinations (order doesn't matter): Stars and bars: ways to place identical objects into bins If items go into containers and m"> , at least one container holds more than one item. The generalized version: some container holds at least items. GRE use: Existence proofs. "Show that among any 5 integers, two have the same remainder mod 4." Definitions: for uniform sample spaces. . Independence: iff A and B are independent. Expected value: (discrete) or (continuous). Poisson: , mean and variance both A graph consists of vertices and edges. Key concepts: Degree: Number of edges incident to a vertex. Handshaking lemma: Connected graph: Path exists between any two vertices Tree: Connected graph with no cycles. A tree on vertices has exactly edges.

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