Trent University, Fall 2012

Mathematics-Computing & Information Systems 4215H

Mathematical logic

**Prerequisite:** MATH-COIS 2600H, or the permission of the instructor.

I have a jury summons to respond to on Monday, 19 November. It is likely that classes on one or two days that week, and perhaps on one or two days the week after, will have to be cancelled even if I do not get put on a jury. (If I do end up on a jury, even more may be missed.) More information will be posted here as it becomes available...

In the meantime, all the remaining problem sets and the take-home final exam have been posted below in Handouts & Work, just in case.

Instructor | Text | Meetings | Marking | Content | Honour & Help! | Other sources | Handouts & Work

Stefan Bilaniuk

*office:* GCS 337

*Winter hours:* Tuesday and Friday 11:00-11:50, Wednesday and Thursday 12:00-12:50, or by appointment, or just drop by!

*phone:* 705 748-1011 x7474

*home phone:* 705 742-7862 [Do *not* call between 10 p.m. and 8 a.m. unless it's an emergency.]

*e-mail:* `sbilaniuk{at}trentu{dot}ca`

and `stefanbilaniuk{at}cogeco{dot}ca`

[E-mail sent to my Trent address all too frequently vanishes. If it's important, send it to both.]

*web:* `http:/euclid.trentu.ca/math/sb/`

A Problem Course in Mathematical Logic, Version 1.6, Stefan Bilaniuk, 2003. (We will only use Parts I and II.) It's free, O guinea pigs and can be downloaded from the link above.

*Lectures:* Wednesday 11:00-11:50 in SC W3, Thursday 11:00-11:50 in CC K1, and Friday 12:00-12:50 in CC K1.

*Seminars:* Friday 13:00-13:50 in CC K1.

(In practice, we will use our class time as lectures or seminars as necessary.)

TThere will be eleven weekly problem sets, with problems taken from the text, which will be mostly be due on Fridays, and a take-home final examination. The final examination will be distributed on Wednesday, 21 November, and will be due on Wednesday, 19 December. The final mark will be calculated as follows:

Best 10 problem sets (7% ea.) | 70% |

Final Examination | 30% |

Problem sets will not normally be accepted after the due date. Students who cannot submit work on time for reasons beyond their control should contact the instructor as soon as possible.

This scheme may be modified for students in exceptional circumstances. Any such modification will require the agreement of both the student and the instructor.

This course is an introduction to the study of logic as a mathematical object(s) in its own right. The objective is to acquire a knowledge of the basic language(s) of formal logic and techniques for analyzing their capabilities and limitations. In particular, we will cover the following topics:

- Propositional logic: language, truth assignments, deduction
- Propositional logic: Soundness, Completeness, and Compactness
- First-order logic: languages, structures and models, deduction
- First-order logic: Soundness, Completeness, and Compactness

The obligatory statement concerning **academic integrity** reads as follows:

Academic dishonesty, which includes plagiarism and cheating, is an extremely serious academic offence and carries penalties varying from a 0 grade on an assignment to expulsion from the University. Definitions, penalties, and procedures for dealing with plagiarism and cheating are set out in Trent UniversityÕs Academic Integrity Policy. You have a responsibility to educate yourself - unfamiliarity with the policy is not an excuse. You are strongly encouraged to visit Trent's Academic Integrity website to learn more -www.trentu.ca/academicintegrity.

For clarity, the following guidelines will apply in MATH-COIS 4215H:

You are permitted and encouraged to work together and ask anyone willing (especially the instructor!) for explanations, hints, and suggestions on the problem sets, and to consult whatever sources you wish, with the exception that

you may not consult anyone who has taken a similar course recently or their work. However,all work submitted for credit must be written up entirely by you, giving due credit to all relevant sources of help and information. The restrictions for the take-home final exam will be spelled out on the exam.

In some circumstances you may also be eligible for special help or accommodation. The obligatory statement concerning **access to instruction** reads as follows:

It is Trent University's intent to create an inclusive learning environment. If a student has a disability and/or health consideration and feels that he/she may need accommo- dations to succeed in this course, the student should contact the Disability Services Office (Blackburn Hall Suite 132, 705 748-1281,disabilityservices@trentu.ca) as soon as possible.

Some mathematical logic notes and resources available online:

- Mathematical Logic around the world, an extensive list of links related to mathematical logic.
- Mathematical logic and foundations, overview at The Mathematical Atlas.
- Mathematical logic, article at Wikipedia.
- Elementary Calculus: An Approach Using Infinitesimals, a calculus text using non-standard analysis by H. Jerome Keisler.
- Mathematical Logic [pdf], notes for a logic course by Helmut Schwichtenberg.
- Mathematical Logic [pdf], notes for a logic course by Stephen G. Simpson.
- math.LO Logic, a specialized-for-logic front end for the arXiv.org E-print archive.

- MATH-COIS 4215H Course outline [With minor corrections made 2012.09.10.]
- Readings & Schedule
- Problem sets
- Take-Home Final Examination

Department of Mathematics Trent University

Maintained by Stefan Bilaniuk. Last updated 2012.11.13.