MTHT 490 Summer 1999

John Baldwin

This is intended as a reading course. Our general plan is to meet twice a week during the summer -once with me, once just the students. The text is Barwise and Etchemendy: The language of first order logic.

The basic course work is: do the problems. The default is to do all of them. As we progress, we will decide that not all are necessary. I will grade some of the problems; in many cases you will grade each others problems. I may decide that there needs to be a final exam. But this will not be necessary if everyone is doing the problems.

The intended coverage is: definitely parts I and II of the text. If there is interest in Part III we may continue with it. We will also want to have a deeper understanding of Chapter

11.7 than is provided by this text; I will give further reading assignments on it. I will also provide some additional material illustrating how some of the concepts raised in this

book are relevant to the classroom.

Rough syllabus.

Each week for the meeting with Baldwin,

you will have two separate tasks.

1. Read the new chapter and begin to do the problems.

2. Complete the problems for the preceding week.

First meeting May 15: Lecture and assignment.

Second meeting 4:30 PM Wednesday June 2 with Baldwin. Bob Vivallis may get in touch with you sooner to set a meeting with the students.

3rd meeting week of June 4-students only

Assignments:

For June 2: Chapter 2: pages 9-33; attempt all problems.

June 2: discussion of these problems; bring in ones you have not been able to do.

Thereafter:

week 2: 3.1-3.7

week 3: 3.8-3.12

week 4: chapter 4

week 5: chapter 5

week 6: chapter 6

week 7: chapter 7

week 8: The completeness Theorem.

Lecture 1

The following are terms that I have made up for use in this course:

informal reasoning: People trying to `think straight'.

Mathematical reasoning: Ordinary discourse about mathematics-by students or experts. Hypotheses are specified and `in principle' reduce to a few basic hypotheses for all of

mathematics (e.g. Zermelo-Fraenkel set theory) or for a particular subject ( Euclid's axioms (geometry); or the axioms of complete real closed ordered fields (analysis)).

symbolic logic: formal language; formal rules of inference;

We are going to study symbolic logic in order to clarify our normal exposition of mathematical reasoning.

Syntax, semantics, and completeness.