## Spring 2017

Important Information: The second midterm will be held on Wednesday April 19th. The final exam will be held on Tuesday May 9th.

Optional Textbook: Enderton, A mathematical introduction to logic, Academic Press.

Copies of my lectures notes from a previous year are posted at the bottom of this page. The homework exercises for this year's course will be assigned each week during the class.

Meeting times: The lecture will be held every Monday and Wednesday from 1:40pm until 3:00pm in the Science and Engineering Resource Center (SEC) room 218 on Busch Campus.

Lecturer:
 Name: Simon Thomas Office: Hill Center 730 (on the Busch Campus) Office hours: Monday 11 - 12, Wednesday 3:30 - 4:30 Phone: 848-445-6922 Email: Please cc: Webpage:

Course topics:

• Elementary set theory. After a review of the basic properties of functions and relations, we shall consider the notions of a countable and an uncountable set.
• Propositional logic. In this section, we shall study propositional languages. We shall concentrate on trying to understand the meaning of the Compactness Theorem for propositional logic. Numerous applications of the Compactness Theorem will be presented, including an infinite analogue of the Four Color Theorem.
• First order logic. In this section, we shall try to understand the relationship between the syntax and semantics of first order languages. This study will culminate in Godel's Completeness and Compactness Theorems for first order logic.
• Applications of the Compactness Theorem. In this section, we shall present various applications of the Compactness Theorem for first order logic, including the existence of nonstandard models of arithmetic.

The term grade will be based on the results of the examinations and the solutions of the homework problems. We will have 2 midterm (80 minute) exams and a final exam. Homework be assigned during most lectures and will be collected each Wednesday. Here are the weights of the different components:

 Component Percentage Midterm #1 20% Midterm #2 20% Final Exam 50% Homework 10%

Lecture Notes: