MATH 2040, Mathematical Logic I - arrangements for the module.

Lectures: Mondays 12.00–13.00 in RSLT 24, Thursdays 10.00–11.00 in RSLT22

Examples Class: Wednesdays 10.00–11.00 in RSLT 18. In week 1 (WednesdaySept 30) there will not be a formal Examples Class, but I will go along to thelecture room and discuss examples of logical inferences and fallacies.

Assessment: 85/100 2-hour exam at end of semester (January 2010). 15/100coursework (marked homework).

Coursework: I will hand out a problem sheet at the Thursday Lecture, eachweek. Only some questions from each homework (specified at the top of thehomework sheet) will be assessed. You should hand in homework at the Thursdaylecture in weeks 3,5,7,9,11. Thus, on Thursday October 15, you should hand insolutions to some (or if you like, all) questions on Homework Sheets 1 and 2.The homework will be marked, and the assessable homework given a grade outof 5, and should be returned to you the following Thursday (or in week 11, atthe beginning of the next week).

Lecturer: Prof. Michael Rathjen, School of Mathematics, Room: 8.22c,Phone: 0113 34 35109, E-mail: rathjen@maths.leeds.ac.ukHome page: http://www.maths.leeds.ac.uk/∼rathjen/teaching.html(from where course material can be downloaded)

Office Hours: Mondays 13.00–14.00.

Material to be covered (and approximate timing):1. Sets, functions, countability, induction (3 weeks, partly revision).2. Propositional Logic (4 weeks)3. Predicate logic (3–4 weeks).

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Syllabus and Book List for MATH2040Sem.1, 2009-10

Syllabus. (not necessarily in chronological order)

(1) Basic Set Theory. (to warm up)

• Sets, functions, power sets, countable/uncountable sets.

(2) Propositional Logic.

• Syntax, formulas

• Connectives, adequate sets of connectives

• Truth values, equivalence of formulas, tautologies

• Normal forms

• A formal proof system for propositional logic (The Resolutions Algorithm)

• The Compactness Theorem for propositional logic.

(3) Predicate/1st Order Logic

• Formal language/syntax

• Translating statements into 1st order logic

• Free variables

• Semantics: structures, interpretations, truth value

• Validity, satisfiability, models

• Consequence, equivalence, contradiction

• A proof system for predicate logic

Books. (For optional, additional reading.)WARNING: Definitions can vary considerably among different authors, including lecturers.

(1) For basic set theory and proof writing:

• Martin Liebeck, A Concise Introduction to Pure Mathematics

• J. Velleman, How to Prove it. A Stuctured Approach

(2) Books on logic:

• I. Chiswell, W. Hodges, Mathematical Logic

• A.G. Hamilton, Logic for Mathematicians

• S. Hedman, A First Course in Logic

• Uwe Schoning, Logic for Computer Scientists (for Resolution Algorithm, not in the library)

• Herbert Enderton, A Mathematical Introduction to Logic

• Elliott Mendelsohn, Introduction to Mathematical Logic

• H.D. Ebbinghaus, J. Flum, W. Thomas, Mathematical Logic

• C.C. Leary, A Friendly Introduction to Mathematical Logic

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