Math 114L: Mathematical Logic
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General Information
Time and Place: MWF 9-9:50am, 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: W 1:00-3:00, Th 10:30-11:30
Teaching Assistant: Victoria Noquez
Click here to download the course handout.
Homework 1 Solutions
Homework 2 Solutions
Homework 3 Solutions
Homework 4 Solutions
Homework 5 Solutions
Homework 6 Solutions
Homework 7 Solutions
Extra Credit Solutions
Midterm 1 from 2009
Midterm 2 from 2009
Final from 2009
Review sheet for last year (Note that we covered slightly different sections this year! In particular, ignore question 7.)
Answers to last year's review problems
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
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.
- Homework 1, Due Friday April 9th: Section 1.1, Problems 1, 5; Section 1.2, Problems 1, 2, 4, 5, 7, 10
- Homework 2, Due Friday April 16th: Section 1.4, Problems 1, 2; Section 1.5, Problems 3, 4, 7, 8
- Homework 3, Due Friday April 30th: Section 1.7, Problems 8, 10 (clarification: in part b, assume that there is at least one τ such that both happen), 11; Section 2.1, Problem 10
- Homework 4, Due Friday May 7th: Section 2.2, Problems 1, 4, 9, 10, 12, 17a, 18
- Homework 5, Due Friday May 21st: Section 2.5, Problems 1, 2, 4, 7
- Homework 6, Due Friday May 28st: Section 2.5, Problems 6, 8, 9; Section 2.6, Problems 1, 4
- Homework 7, Due Friday June 4th: Section 2.6, Problems 2, 7, 8, 9, 10
- Extra Credit
Exams
There will be two
Midterm examinations in class. There will be a final exam. No make-up exams will be given.
All scores and final grades will be available on the MyUCLA gradebook.