| CODE | MAT2005 | ||||||||
| TITLE | Introduction to Mathematical Logic | ||||||||
| UM LEVEL | 02 - Years 2, 3 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 5 | ||||||||
| ECTS CREDITS | 2 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | Mathematicians show that theorems about numbers, geometric objects, functions, sets, etc., are true by giving a proof. What exactly is a proof? Are all statements formulated in some mathematical language true or false? Philosophers have always been fascinated by questions such as these. Modern mathematical logic has provided tools to answer these questions. This is an introductory study unit on first order logic that includes a tangental review of propositional logic. The study unit will cover: 1. Propositional Logic: (a) Propositions, (b) Valuations and truth tables, (c) Semantics and syntactics of propositional logic, (d) Consistency, soundness and completeness. 2. First Order Logic: (a) Structures and languages, (b) Syntactics: terms, free variables, quantifiers, (c) Semantics: Tarski's definition of truth and logical implication, (d) Axioms, (e) Rules of inference, (f) Consistency, soundness and completeness of first order logic, (g) Compactness Theorem and its applications. Study-unit Aims: This study-unit will build the strong foundation necessary for the study of logic at a more advanced level. Students will learn to apply methods in mathematical logic to other areas of mathematics. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: - Appreciate the role and importance of the concept of proof in mathematics; - Describe the relationship between the syntax and semantics of first order logic. 2. Skills By the end of the study-unit the student will be able to: - Express statements in propositional and first order logic; - Explain the relationship between syntax and semantics of first order logic; - Recognise and analyse the use of logical quantifiers; - Apply the compactness theorem to relate statements involving infinite sets with statements involving finite sets; - Interpret first order formulas in a variety of mathematical structures; - Construct structures satisfying certain axioms in simple cases. Main Text/s and any supplementary readings: Michael L. O'Leary : A First Course in Mathematical Logic and Set Theory, Wiley, 2016. Christopher C. Leary and Lars Kristiansen : A Friendly Introduction to Mathematical Logic, 2nd Edition, Milne Library, 2015. Ian Chiswell and Wilfred Hodges : Mathematical Logic, Oxford University Press, 2017. Elliot Mendelson : Introduction to Mathematical Logic, Chapman and Hall, 1979. Reuben. L. Goodstein : Mathematical Logic, Leicester University Press, 1961. Georg Kreisel and Jean-Louis Krivine : Elements of Mathematical Logic, Elsevier Science Publishing, 1967. |
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| ADDITIONAL NOTES | Follows from: MAT1100 | ||||||||
| STUDY-UNIT TYPE | Lecture and Independent Study | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Beatriz Zamora-Aviles |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years. |
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