Math 414: Mathematical Logic

Basic Information

Text

Ebbinghaus, Flum, and Thomas, Mathematical Logic, Second Edition, 1994, Springer.

Grading

Grading policy is summarized in the following table.

what? when? how much?
Homework weekly, due Fridays 20%
Exam 1 Friday, Feb 24th 25%
Exam 2 Friday, April 14th 25%
Final exam Friday, May 5th, 8:00 to 11:00 am 30%

Homework: .

Homeworks are due at the beginning of class each Friday. Late homeworks will not be accepted. However, the lowest two homework grades will be dropped.

Exams: Each exam will have a take-home component, and an in-class component. The take-home portion will be due a week after the day listed in the table above, and the in-class portion will also be held on that day.

Final: If you do better on the final than on the your lowest scoring exam, the exam grade will be replaced with the final grade.

Homework

  • Homework #1
  • Homework #1 -- Solutions
  • Homework #2
  • Homework #2 -- Solutions
  • Homework #3
  • Homework #3 -- Solutions
  • Homework #4
  • Homework #4 -- Solutions
  • Homework #5
  • Homework #5 -- Solutions
  • Notes for the in class part of the first exam
  • Takehome Exam #1
  • Takehome Exam #1 -- Solutions
  • Homework #6
  • Homework #6 -- Solutions
  • Homework #7
  • Homework #7 -- Solutions
  • Homework #8
  • Homework #8 -- Solutions
  • Homework #9
  • Homework #9 -- Solutions
  • Notes for the in class part of the second exam
  • Takehome Exam #2
  • Takehome Exam #2 -- Solutions
  • Homework #10
  • Homework #10 -- Solutions
  • Homework #11
  • Homework #11 -- Solutions
  • Final -- Takehome Section

    Tentative Course Outline

  • Introduction

    History:
    Basics of Set Theory: Countability, Uncountability
    Propositional Logic
    Some Examples

  • Model Theory

    Syntax of First Order Logic
    Semantics of First Order Logic
    A Sequent Calculus
    The Completeness Theorem
    The Limitations of First Order Logic

  • Computability

    Turing Machines
    Decidable Sets
    Computable Sets
    The Halting Problem
    The Undecidability of First Order Logic