MATH-16 · Undergraduate · ENGLISH · PLANNED
Build the picture, explain the rule, work an example, then justify it.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Mathematics | Discrete Mathematics and Proof
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Sign in to save this learning pathPractical outcome: Verify a scheduling rule with a proof and a counterexample.
Explain propositions using a visual and one worked real-world example. Context: Verify a scheduling rule with a proof and a counterexample. End with a prediction or check-for-understanding.
Explain logical connectives using a visual and one worked real-world example. Context: Verify a scheduling rule with a proof and a counterexample. End with a prediction or check-for-understanding.
Explain quantifiers using a visual and one worked real-world example. Context: Verify a scheduling rule with a proof and a counterexample. End with a prediction or check-for-understanding.
Explain direct proof using a visual and one worked real-world example. Context: Verify a scheduling rule with a proof and a counterexample. End with a prediction or check-for-understanding.
Use the first concepts from this section. Verify a scheduling rule with a proof and a counterexample. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain contrapositive using a visual and one worked real-world example. Context: Verify a scheduling rule with a proof and a counterexample. End with a prediction or check-for-understanding.
Explain contradiction using a visual and one worked real-world example. Context: Verify a scheduling rule with a proof and a counterexample. End with a prediction or check-for-understanding.
Explain induction using a visual and one worked real-world example. Context: Verify a scheduling rule with a proof and a counterexample. End with a prediction or check-for-understanding.
Explain strong induction using a visual and one worked real-world example. Context: Verify a scheduling rule with a proof and a counterexample. End with a prediction or check-for-understanding.
Verify a scheduling rule with a proof and a counterexample. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Propositions, Logical connectives, Quantifiers and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Count feasible passwords without generating personal credentials.
Explain sets using a visual and one worked real-world example. Context: Count feasible passwords without generating personal credentials. End with a prediction or check-for-understanding.
Explain functions as relations using a visual and one worked real-world example. Context: Count feasible passwords without generating personal credentials. End with a prediction or check-for-understanding.
Explain equivalence relations using a visual and one worked real-world example. Context: Count feasible passwords without generating personal credentials. End with a prediction or check-for-understanding.
Explain partial orders using a visual and one worked real-world example. Context: Count feasible passwords without generating personal credentials. End with a prediction or check-for-understanding.
Explain sum and product rules using a visual and one worked real-world example. Context: Count feasible passwords without generating personal credentials. End with a prediction or check-for-understanding.
Use the first concepts from this section. Count feasible passwords without generating personal credentials. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain permutations using a visual and one worked real-world example. Context: Count feasible passwords without generating personal credentials. End with a prediction or check-for-understanding.
Explain combinations using a visual and one worked real-world example. Context: Count feasible passwords without generating personal credentials. End with a prediction or check-for-understanding.
Explain inclusion-exclusion using a visual and one worked real-world example. Context: Count feasible passwords without generating personal credentials. End with a prediction or check-for-understanding.
Explain pigeonhole principle using a visual and one worked real-world example. Context: Count feasible passwords without generating personal credentials. End with a prediction or check-for-understanding.
Explain recurrence relations using a visual and one worked real-world example. Context: Count feasible passwords without generating personal credentials. End with a prediction or check-for-understanding.
Count feasible passwords without generating personal credentials. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Sets, Functions as relations, Equivalence relations and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Find a low-cost route through a delivery network.
Explain vertices and edges using a visual and one worked real-world example. Context: Find a low-cost route through a delivery network. End with a prediction or check-for-understanding.
Explain paths and cycles using a visual and one worked real-world example. Context: Find a low-cost route through a delivery network. End with a prediction or check-for-understanding.
Explain trees using a visual and one worked real-world example. Context: Find a low-cost route through a delivery network. End with a prediction or check-for-understanding.
Explain bipartite graphs using a visual and one worked real-world example. Context: Find a low-cost route through a delivery network. End with a prediction or check-for-understanding.
Explain euler paths using a visual and one worked real-world example. Context: Find a low-cost route through a delivery network. End with a prediction or check-for-understanding.
Use the first concepts from this section. Find a low-cost route through a delivery network. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain planar graphs using a visual and one worked real-world example. Context: Find a low-cost route through a delivery network. End with a prediction or check-for-understanding.
Explain graph colouring using a visual and one worked real-world example. Context: Find a low-cost route through a delivery network. End with a prediction or check-for-understanding.
Explain shortest paths using a visual and one worked real-world example. Context: Find a low-cost route through a delivery network. End with a prediction or check-for-understanding.
Explain spanning trees using a visual and one worked real-world example. Context: Find a low-cost route through a delivery network. End with a prediction or check-for-understanding.
Explain asymptotic notation using a visual and one worked real-world example. Context: Find a low-cost route through a delivery network. End with a prediction or check-for-understanding.
Find a low-cost route through a delivery network. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Vertices and edges, Paths and cycles, Trees and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Find a low-cost route through a delivery network. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Discrete Mathematics and Proof, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Visual constructions, worked problems and proofs. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
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