# MTP 621 Introduction to Mathematical Logic

## Summer Session II, 1996 July 8 -- August 8

This course meets from 10:40 AM to 12:40 PM on Mondays, Tuesdays, and Thursdays, in room 201 of the Business Building. We'll use the textbook The Language of First Order Logic, which comes with an accompanying software package for either Macintosh or Windows; you may use whichever you prefer. An official description of the course is in the bulletin.

The aforementioned textbook and software introduce the notation mathematicians use to formalize logical reasoning and to give a precise meaning to the notion of "truth". We'll discuss the notion of a "model" of a language (a miniature universe in which statements of the language are true or false) and the possibilities of a statement being true in one world and false in another, or true in several different worlds. We'll discuss the notion of logical consequence (under what circumstances one statement necessarily follows from another), its formalization in mathematical inference rules, and the correspondence of those formal rules to the informal principles of sound reasoning used by real human beings. We'll also mention some of the major paradoxes and problems in the history of logic, and some major breakthroughs of 20th-century logic.

## Homework assignments

Homework 1 assigned 9 July, due 16 July:
problems 2.3,2.4,2.5,2.19 to be turned in on floppy disk
problems 2.6,2.9,2.14,2.18,2.21,2.22,2.24 to be turned in on paper or by email
problems 2.1,2.2,2.15,2.16,2.17 to be done but not turned in or graded (if you specifically want feedback on one of them, turn it in on paper and write a comment in the margin telling me what you'd like me to look at).
Note: in problem 2.9, some of the sentences may be impossible to translate.
Note: in problem 2.19, you are required to build counterexample worlds for the invalid arguments. For the valid ones, try (as an "optional exercise") to write informal proofs of them.
Homework 2 assigned 16 July, due 23 July:
problems 3.24-3.26,3.32-3.34,3.42,3.43,3.56,3.59,3.60 to be turned in (on disk, paper, or email, as appropriate)
problems 3.5,3.12-3.14,3.18,3.19,3.30,3.31 to be done at your discretion, but not turned in unless you have a specific question.
Homework 3 assigned 23 July, due 30 July:
problems 4.11,4.14,4.16,4.23,5.8,5.10,5.12,5.18,5.19 to be turned in in groups if you wish. Turn in one disk, and one paper with the names of all the students who "contributed significantly" to the answers.
problems 4.3-4.8,4.18,4.23-4.28,5.1-5.7,5.9,5.11,5.13-5.15,5.21 to be done at your discretion. (Yes, this is a lot of optional problems. I really think they'll help you understand the material, but use your own judgment to decide how much time to spend on which.)
Homework 4 assigned 30 July, due 6 Aug:
problems 5.25,5.32,5.39,6.34,6.37,6.45 to be turned in in groups as above.
problems 5.23-32,5.36-41,6.2-4,6.11-12,6.18-21,6.29,6.32,6.35,6.52 to be done at your discretion. (Again, this is a lot of optional problems. Do as many as you think you need and have time for.)
Homework 5, aka Take-Home Final Exam to be assigned 5 Aug, due 8 Aug.

## Schedule and reading assignments

Date(s) Assignment Reading Lecture Subject
8 July Introduction, administrivia, history
9 July HW1 pp. 1-15, 283-293 Relationships among objects
11 July pp. 16-34 First Order languages and proofs
15 July pp. 35-66,293-295 Relationships among statements
16 July HW1 due; HW2 pp. 67-90 Formal proofs and other topics
18 July pp. 91-97 More relationships among statements
22 July pp. 97-106 More on conditionals and biconditionals
23 July pp. 106-122 Quantifiers
25 July I'll be at a conference on teaching logic
29 July pp. 123-134 Translating and using quantifiers
30 July HW3 due; HW4 pp. 134-153 Proofs with quantifiers
1 Aug pp. 154-171 Multiple Quantifiers
5 Aug HW5 pp. 172-184 Proofs with multiple quantifiers
6 Aug HW4 due Review and catch up
8 Aug HW5 due pp. 227-240 Mathematical Induction

Last modified: Tue Jul 30 10:31:27 EDT 1996
Stephen Bloch / sbloch@boethius.adelphi.edu