Theoretical Minimums (TMs) are comprehensive oral/written examinations testing deep understanding of mathematical theory and proof techniques. Called “minimums” because passing them is a minimum requirement for course completion.
⚠️ Critical Requirement : You must pass both TMs (score ≥50%) to receive credit for the course, regardless of your other grades.
Detail Information
Number of TMs 4 total (2 per semester) Points Each 10 points Total Points 40 points (20% of final grade) Duration 120 minutes each Format Closed book, written + possible oral component Passing Requirement ≥5/10 on each TM
Exam Coverage Week Topics Passing Threshold
TM1 📐🔗Modules 1–2 Week 7 Set Theory + Binary Relations ≥5/10 TM2 ⚡🧠Modules 3–4 Week 15 Boolean Algebra + Formal Logic ≥5/10
Exam Coverage Week Topics Passing Threshold
TM3 🌐💧Modules 5–6 Week 7 Graph Theory + Flow Networks ≥5/10 TM4 🤖🎲Modules 7–8 Week 15 Automata + Combinatorics ≥5/10
TMs ensure you can:
✓ State definitions and theorems precisely – word-perfect recall
✓ Construct rigorous proofs – logical, complete arguments
✓ Explain concepts clearly – demonstrate understanding, not memorization
✓ Make connections between topics – see the big picture
✓ Demonstrate mathematical maturity – write like a mathematician
💡 Key Insight : You cannot pass this course through computation alone. Theoretical understanding is mandatory .
Aspect Regular Tests Theoretical Minimums
Focus Computation, problem-solving Theory, definitions, proofs Resources Open book (notes, textbook) Closed book (nothing allowed) Duration 90 minutes 120 minutes Partial Credit Generous (60% method, etc.) Limited (correctness emphasized) Passing No minimum threshold Must score ≥50% Coverage 1 module (2–5 weeks) 2 modules (7–8 weeks) Format Written only Written + possible oral Question Types Calculations, applications Definitions, theorem statements, proofs
Detail Information
Retakes Allowed One retake per TM Scheduling 1–2 weeks after original exam Format May be oral instead of written Difficulty Expect different (possibly harder) questions Score Retake score is final (does not average)
⚠️ Retake Strategy
Take retake seriously – it may be more challenging
Oral format requires explaining concepts verbally
Study gaps identified in original attempt
Schedule retake ASAP while material is fresh
Use office hours/mentors before retake
Memorization (❌) Understanding (✅)
“Learn” definitions word-by-word Understand why definitions are structured that way Memorize proof steps Grasp proof strategy and key ideas Recite theorem statements Know when/how to apply theorems Copy examples from notes Generate your own examples
When What to Do
4 weeks before Start reviewing notes systematically 3 weeks before Create definition/theorem summary sheets 2 weeks before Practice proofs without looking at solutions 1 week before Form study groups, quiz each other 3 days before Review all definitions, theorem statements 1 day before Light review, get good sleep
Category Weight Example
Definitions ~30% “Define equivalence relation. Provide an example and a non-example.” Theorem Statements ~20% “State Cantor’s theorem precisely.” Proofs ~40% “Prove that ℝ is uncountable.” Conceptual ~10% “Explain why Russell’s paradox matters for set theory.”
Precision : Definitions and statements must be exactRigor : Proofs must be logically completeClarity : Explanations must be clear and well-organizedCorrectness : Right answers with valid justification
💡 Partial Credit : While more limited than regular tests, you can still earn points for:
Correct definitions even if proof fails
Valid proof strategies even if details are wrong
Clear explanations of concepts
Good luck on your TMs! Remember: deep understanding is the goal. 🎓