LEARNING OUTCOMES
This course introduces you to the logical formalization of mathematical reasoning and to the mathematics of computational intractability. You learn to work with and reason using propositional logic and first-order logic. You learn how to prove that a computational problem is at least as hard as another computational problem by presenting an efficient reduction from the latter to the former. You know the problem classes P and NP, as well as the hardest problems in the class NP, namely the NP-complete problems. You learn how to prove that a computational problem is NP-complete.
Credits: 5
Schedule: 03.09.2024 - 14.11.2024
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Petteri Kaski
Contact information for the course (applies in this implementation):
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
Propositional logic and first-order logic. Formulas, models, validity, satisfiability; axioms and proofs, soundness and completeness; logic circuits. Computational hardness, reductions between problems, the classes P and NP; NP-completeness, the Cook-Levin Theorem.
Assessment Methods and Criteria
valid for whole curriculum period:
Points earned from weekly problem sets determine the course grade.
Workload
valid for whole curriculum period:
Lectures. Teaching in small groups. Independent work.
DETAILS
Study Material
valid for whole curriculum period:
Lecture notes and articles.
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language: English
Teaching Period: 2024-2025 Autumn I - II
2025-2026 Autumn I - II