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MATH3066 Algebra and Logic > 10 - Quotient constructions. Field extensions. Irreducible polynomials and finite fields > Flashcards

10 - Quotient constructions. Field extensions. Irreducible polynomials and finite fields Flashcards

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MATH3066 Algebra and Logic (13 decks)

1 - Introduction to logic and impossibility. Mathematical Implication. Truth tables

2 - Russell’s Paradox. Cardinality. Uncountability. Integers and modular arithmetic

3 - Polynomials and factorisation. Introduction to groups, rings and fields

4 - Deduction and proof in the propositional calculus

5 - Metaproofs. Soundness in the propositional calculus

6 - Syntax and semantics. Completeness of the propositional calculus

7 - Quantifiers. Predicate calculus

8 - Deduction and proof in the Predicate calculus

9 - Soundness and completeness of the predicate calculus

10 - Quotient constructions. Field extensions. Irreducible polynomials and finite fields

11 - Construction of the real numbers, the completeness axiom

12 - Unsolvability of ancient problems of the Greeks

13 - The Halting Problem and undecidability of First Order Logic

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