Problem 1
Command of definitions, method choice, calculations, limitations, and ability to answer mathematical challenges.
Faculty use
Written Report and Oral Mathematical Defense
Reward correct mathematics, explicit dimensions/hypotheses, interpretation, and verification. Equivalent valid reasoning should receive credit.
Problem 2
Hidden assumptions, unexplained software output, missing units, no validation, or claims broader than the evidence.
Problem 3
Definitions should identify the vector/matrix/space/transformation, dimensions or domain/codomain, and the hypotheses behind communicating definitions, derivations, evidence, uncertainty, and limitations. Use the formulas claim supported by derivation and evidence; oral defense responds to assumptions and alternatives.
Problem 4
A strong error analysis identifies the first step that violates a definition, dimension, theorem hypothesis, or matrix-operation rule; then repairs that step and re-verifies the final result.
Problem 5
Application responses vary. Require defined variables, a compatible matrix/vector model connected to large systems, reproducible computation, research communication, ethical data modelling, and advanced mathematics, a complete computation, interpretation, and limitations.
Problem 6
Accept two independent checks appropriate to the task: reconstruction, residual, RREF comparison, determinant/rank test, orthogonality, substitution, eigenpair check Av=λv, factorization product, or a second method.
Scoring guidance
Six problems × 10 points: 5 mathematical accuracy, 2 structure/justification, 2 verification/interpretation, 1 notation and communication.