Difference between revisions of "MAT5001"

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(Created page with "(1) Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms. (2) Predicat...")
 
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(1) Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms.
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(2) Predicate Logic: Existential and universal quantification, free variables and substitutions. Discussion of the various axiomatic systems for first-order logic (including axioms and rules of inference). The power and the limitations of axiomatic systems for logic: Informal discussion of the completeness and incompleteness theorems.
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! Week !! Topics !! Prerequisite Skills !! Student Learning Outcomes
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(3) Sets: Operations on sets. Correspondence between finitary set operations and propositional logic. Correspondence between infinitary operations and quantifiers. The power and limitations of the language of set theory: Informal discussion of the set-theoretic paradoxes and the need for axiomatic systems for set theory.
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(4) Relations: Properties of relations. Special relations: Equivalence relations, partially ordered sets, totally ordered sets.
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| Week 1 || Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms. ||  ||
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(5) Functions: Operations of functions, direct image and inverse image.
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(6) Well-ordered sets: Correspondence between well-ordering relations and induction. Correspondence between well-ordering relations and choice functions.
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| Week 2 || Predicate Logic: Existential and universal quantification, free variables and substitutions. Discussion of the various axiomatic systems for first-order logic (including axioms and rules of inference). The power and the limitations of axiomatic systems for logic: Informal discussion of the completeness and incompleteness theorems. ||  ||
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(6) Introduction to computability. Classical models of computation (recursive functions, and Turing models).  
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(7) Limitations of computation. Contemporary models of computation: Digital vs analog vs quantum computing.
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| Week 2 || Sets: Operations on sets. Correspondence between finitary set operations and propositional logic. Correspondence between infinitary operations and quantifiers. The power and limitations of the language of set theory: Informal discussion of the set-theoretic paradoxes and the need for axiomatic systems for set theory. ||  ||
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|-
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| Week 3 || Relations: Properties of relations. Special relations: Equivalence relations, partially ordered sets, totally ordered sets. ||  ||
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| Week 3 || Functions: Operations of functions, direct image and inverse image. ||  ||
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|-
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| Week 4 || Well-ordered sets: Correspondence between well-ordering relations and induction. Correspondence between well-ordering relations and choice functions. (6) Introduction to computability. Classical models of computation (recursive functions, and Turing models). ||  ||
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| Week 4 || Limitations of computation. Contemporary models of computation: Digital vs analog vs quantum computing. ||  ||
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Latest revision as of 09:55, 10 March 2023

Week Topics Prerequisite Skills Student Learning Outcomes
Week 1 Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms.
Week 2 Predicate Logic: Existential and universal quantification, free variables and substitutions. Discussion of the various axiomatic systems for first-order logic (including axioms and rules of inference). The power and the limitations of axiomatic systems for logic: Informal discussion of the completeness and incompleteness theorems.
Week 2 Sets: Operations on sets. Correspondence between finitary set operations and propositional logic. Correspondence between infinitary operations and quantifiers. The power and limitations of the language of set theory: Informal discussion of the set-theoretic paradoxes and the need for axiomatic systems for set theory.
Week 3 Relations: Properties of relations. Special relations: Equivalence relations, partially ordered sets, totally ordered sets.
Week 3 Functions: Operations of functions, direct image and inverse image.
Week 4 Well-ordered sets: Correspondence between well-ordering relations and induction. Correspondence between well-ordering relations and choice functions. (6) Introduction to computability. Classical models of computation (recursive functions, and Turing models).
Week 4 Limitations of computation. Contemporary models of computation: Digital vs analog vs quantum computing.
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