General Information
| Course Code | XB_0083 |
|---|---|
| Credits | 6 EC |
| Period | P4 |
| Course Level | 100 |
| Language of Tuition | English |
| Faculty | Faculty of Science |
| Course Coordinator | prof. dr. K.S. Schlobach |
| Examiner | prof. dr. K.S. Schlobach |
| Teaching Staff |
prof. dr. K.S. Schlobach dr. I. Klang dr. P.S.H. Koopmann |
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Part of programme(s)
Bachelor
Premaster
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Practical Information
You need to register for this course yourself. The (de)registration deadlines can be found on VU.nl
| Teaching Methods | Seminar, Written partial exam, Lecture |
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Course Objective
After completing this course, the student can:
- express logical statements in propositional and predicate logic (Knowledge and understanding) (Applying knowledge and understanding)
- reason about the meaning of such formulas through truth tables and models (Applying knowledge and understanding) (Making judgements)
- argue formally whether one formula implies another one, or that they are equivalent (Applying knowledge and understanding) (Making judgements)
- reduce a propositional formula to disjunctive or conjunctive normal form (Applying knowledge and understanding)
- apply reasoning algorithms on propositional formulas (Applying knowledge and understanding)
- prove some basic theorem and propositions about propositional logic
Furthermore, the student is able to:
- reason about set constructions through Venn diagrams and the algebra of sets (Applying knowledge and understanding) (Making judgements)
- construct and interpret formal, graphic, and matrix representations of sets, relations and functions
- determine and argue whether (Applying knowledge and understanding) (Making judgements):
a. a relation is reflexive, transitive, symmetric or antisymmetric.
b. a relation is an ordering relation, equivalence relation, or a functionc.
c. a function is injective or surjective - construct and interpret compositions of relations (or functions) and their inverses (Applying knowledge and understanding) (Making judgements)
- construct a proof by mathematical induction (Applying knowledge and understanding)
Course Content
The sets part of the course starts by introducing the concepts of sets, Venn diagrams, product sets and relations. The student then learns the main characteristics and properties of three particular types of relation: ordering relations, equivalence relations and functions. The sets part concludes with a study of the principle of mathematical induction.
The logic part focuses in the first place on propositional logic: truth tables, boolean operators, functional completeness, logical puzzles, SAT-solving. In addition the student will learn the meaning and use formulas of predicate logic, to express mathematical properties and sentences from natural language.
Additional Information Teaching Methods
Every week, there is one 2-hour lecture and one 2-hour tutorial for the logic part of the course, and one 2-hour lecture and one 2-hour tutorial for the sets part of the course.
Method of Assessment
A written midterm exam (40% of the grade) and a written final exam (60% of the grade). For both the midterm and the final exam, at least a 5.0 must be achieved (and the overall mark must be at least 5.5.). The resit exam covers all material of the course. It is not possible to resit only the midterm exam or only the final exam of the course.