Math 114L: Mathematical Logic

General Information

Time and Place: MWF 9-9:50am

Instructor: Henry Towsner

E-mail address: hpt at

Mathematical Sciences Building 5634
Office Phone: (310) 825-2697
Office Hours: W 1:00-2:00, Th 10:30-11:30

Discussion Section: Th 9-9:50am,
Teaching Assistant: Justin Palumbo

Click here to download the course handout.

Final Exam information
Final Review Problem Solutions


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.


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 entertains a web page with errata and commentary.


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. Homeworks turned in no more than one class period after the due date will receive half credit. No homeworks will be accepted after that time. 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 10th)
  2. Homework 2 (Due Friday, April 17th)
  3. Homework 3 (Due Friday, April 24th)
  4. Extra Problems for Midterm 1
  5. Homework 4 (Due Friday, May 8th)
  6. Homework 5 (Due Friday, May 15th)
  7. Homework 6 (Due Friday, May 29th)
  8. Homework 7 (Due Friday, June 5th)


There will be two Midterm examinations in class. There will be a final exam.
Students with conflicts with the Midterm Exam in this course are responsible for discussing makeup examinations with me no later than two weeks prior to the exam.

No books, calculators, scratch paper or notes will be allowed during exams.

Grading policy: Homework: 20%. Midterm Exams: 20% each. Final Exam: 40%.

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