6120a Discrete Mathematics And Proof For Computer Science Fix Jun 2026

Recurrences, Asymptotic Notation (Big-O), Algorithm Analysis. Probability: Discrete Probability and Counting. Part 1: How to "Fix" Your Approach to Proofs

A set $A$ is a subset of a set $B$, denoted by $A \subseteq B$, if every element of $A$ is also an element of $B$. Recurrences, Asymptotic Notation (Big-O), Algorithm Analysis

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Base case (n = 1): A tree with 1 vertex has no edges. Then |E| = 0 = 1 − 1. ✓ : Base case (n = 1): A tree with 1 vertex has no edges

This specific course focuses heavily on logic and proofs, which are the bedrock of theoretical computer science. You won't just be plugging numbers into formulas; you'll be learning to think like a mathematician and a computer scientist, constructing airtight logical arguments to validate computational ideas. You won't just be plugging numbers into formulas;

Understand that a single counterexample breaks a universal statement. Practice Induction: Do not just read proofs; write them. Understand Invariants: Think like a state machine. Visualize Graphs: Use Euler's formula ( ) for planar graphs. Define Big-O: Use the formal ≤is less than or equal to ≥is greater than or equal to definitions.

Logic is the programming language of mathematics. If your logic foundations are shaky, your proofs will fail.