Math 114L: Mathematical Logic

General Information

Time and Place: MWF 10-10:50am, MS 7608

Instructor: Henry Towsner

E-mail address: hpt at math.ucla.edu

Office:
Mathematical Sciences Building 5634
Office Phone: (310) 825-2697
Office Hours: Monday 12:30-1:30, Thursday 11:00-1:00

Teaching Assistant: Sherwood Hachtman

Final Exam

Solution to 5b, 5c

Click here to download the course handout.

Previous midterms: 1 2

Previous second midterms: 1 2

Description

The main objective of this course is to introduce you to mathematical logic through the study of two of its aspects:

1. Pure logic: Sentential logic and first-order logic, culminating in the proof of Gödel's Completeness Theorem (not to be confused with Gödel's Incompleteness Theorems).

2. Basic model theory: Applications of the Completeness Theorem, including the Löwenheim-Skolem Theorems, the Compactness Theorem; and a discussion of elementary equivalence.

Prerequisities

The ability to formulate mathematical proofs. For this reason, you should have had some exposure to proof-writing before taking this course. Some knowledge of linear algebra or abstract algebra would also be useful, but is not strictly necessary. Please feel free to contact me if you'd like to take this course, but are unsure whether you have the right preparation.

Course Text

We will try to cover Chapters 1 and 2 of the book A Mathematical Introduction to Logic, Second Edition, by Herbert B. Enderton, Academic Press, 2001. The author of the textbook maintains a web page with errata and commentary.





Homework

There will be a problem set assigned every week. The problems will range in difficulty from routine to more challenging. Completed solutions are to be handed in at the beginning of class on the due date specified on the respective homework set. No late homeworks will be accepted. You are encouraged to work together on the exercises, but any graded assignment should represent your own work.

Put the following information in the upper right hand corner of the first page:

   Your Name
   Math 114L, Homework # number.

On each additional page, put your name in the upper right-hand corner. STAPLE any homework that is more than one page long. Remove all perforation before submitting. Write legibly. Homework that fails to meet the above requirements will be marked "Unacceptable'' and returned unread.
  1. Homework 1, Due Friday, April 8th: Section 1.1, Problems 1, 2, 5; Section 1.2, 1, 3, 4, 9, 10, 14. Also: Prove that "(A1)" is not a wff. (solutions)
  2. Homework 2, Due Friday, April 14th: Section 1.5, Problems 1, 3, 4, 5, 7, 9, 12 (solutions)
  3. Suggested problems before Midterm 1: Section 1.7, Problems 2, 3, 10, 11, 12 (solutions)
  4. Homework 3, Due Friday, May 6th: Section 2.1, Problems 1, 4, 10; Section 2.2, Problems 1, 2, 3, 6, 9 (solutions)
  5. Homework 4, Due Wednesday, June 1st: Section 2.4, Problems 2, 4, 6, 10, 14; Section 2.5, problems 2, 4

Exams

There will be two Midterm examinations in class. There will be a take-home final exam. No make-up exams will be given.


All scores and final grades will be available on the MyUCLA gradebook.