Discrete mathematics: logic, proof and algorithms
Define finite structures, count outcomes, construct proofs and counterexamples, and analyze graph and algorithm behavior.
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Recommended preparation and ways to catch up
- Work with whole numbers, powers and simple expressions.
- No prior proof-writing or programming is required; proof practice is authored and reviewed separately from numeric checks.
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Your units and lessons
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Statements, sets and counting
Define the domain and distinguish logical and counting rules.
Turn statements into sets and truth values
Is “A implies B” the same as “A and B”?
Count only after naming the outcomes
How do order and reuse change the number of possibilities?
Counterexamples and general arguments
Refute false universal claims and write a valid induction argument.
Refute a claim—or justify every case
What can a finite search establish about a universal statement?
Prove a recurrence pattern
What makes a step from k to k+1 work for every k?
Graphs and growth
Trace a cycle-safe graph search and justify named work counts.
Explore a graph without getting trapped
How does a queue find shortest unweighted paths despite cycles?
Count how work grows
Does doubling input double the work of every algorithm?
Find an item without checking everything
When does dividing the search space save work?
Prove and test a small discrete method
Specify a finite problem, count its outcomes, provide one counterexample and one complete proof, and trace an algorithm on a graph or recurrence. A matching number does not replace the authored argument.
Build from lesson evidence, compare alternatives, write an artifact, and tackle unfamiliar numerical cases. Use the rubric with a teacher, peer or colleague to assess the quality of your reasoning.
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