Courses / Mathematics / Discrete mathematics: logic, proof and algorithms / Project Build and defend your 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.
Choose an audience, investigate alternatives, copy evidence from your experiments, and produce an artifact. You can open this project at any time. Reports, numerical transfer checks and human review are separate outcomes.
Your project workspace Choose the kind of work you want to produce School investigation College investigation Workplace application Design a club-team counting problem and a route graph; write a counterexample and an induction proof with peer feedback.
1. Collect and compare evidence Required experiment sources:
Include every source above and at least one pair with different inputs from the same experiment. Explain confounding changes yourself; the presence check does not judge your interpretation.
Open an experiment and change an input or capture a trial to make evidence available here.
2. Write and revise your report Question, variables and assumptions State the domain, units, target claim or objective and assumptions.
Worked method and authored artifact Include a diagram, calculation, proof or runnable algorithm; explain each important step.
Comparison and evidence Compare captured settings, preserve failed cases and distinguish observations from general arguments.
Fresh case and verification Apply your method to a different case and verify it independently by substitution, enumeration or a justified argument.
Limitations and decision Explain when the method fails or changes and what further evidence is needed.
Your artifact: code, analysis, prototype or decision brief This field stores up to 12,000 characters of inert text. Code runs only through the explicit bounded editor in the relevant lessons; project attachments never execute.
Load a text artifact Review your work against the rubric The domain, logical predicates and outcome equivalence are stated. Counting rules correctly distinguish order and reuse. Counterexample belongs to the domain and falsifies the exact claim. Proof includes base/general cases or a valid induction step; finite tests are not presented as universal proof. Algorithm trace handles cycles and names its operation measure. 11 evidence requirements remain Capture evidence from Turn statements into sets and truth values. Capture evidence from Refute a claim—or justify every case. Capture evidence from Prove a recurrence pattern. Capture evidence from Explore a graph without getting trapped. Include two different input configurations from the same experiment to compare. Write your question, variables and assumptions. Write your worked method and authored artifact. Write your comparison and evidence. Write your fresh case and verification. Write your limitations and decision. Add your project artifact: code, analysis, prototype or decision brief. Record my report Download report and evidence Editing the report or evidence returns it to draft. Recording verifies field presence and input comparisons, not correctness of your reasoning or code.
3. Check transfer to unfamiliar cases These authored cases use different numbers or conditions from the lesson practice. They are public local checks, not secure certification. Each case permits three submissions. Opening, first responses and attempt counts survive imports; no reset creates fresh evidence.
Case choose Open case choose Case odds Open case odds Case edges Open case edges Case growth Open case growth
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