Math 385: Mathematical Logic (Spring 2024)

What, exactly, is a proof? This course begins with a precise definition specifying what counts as a mathematical proof. This definition makes it possible to carry out a mathematical study of what can be accomplished by means of deductive reasoning and, perhaps more interestingly, what cannot be accomplished. Topics will include the propositional and predicate calculi, completeness, compactness, and decidability. At the end of the course we will study Gödel’s famous Incompleteness Theorem, which shows that there are statements about the positive integers that are true but impossible to prove.

Time and location

• Monday, Wednesday, and Friday, 1:00-1:50am (SMUD 205)

Help hours

• My regular office hours in SMUD 401:
  • Tuesday 2:30-4:30
  • Wednesday 10:00-10:50
  • Friday 10:00-10:50

Handouts and links

• Syllabus
• Textbook, freely available in pdf
• Boardwork from days when I teach from a tablet
• Propositional calculus reference

Problem Sets

• Gradescope instructions for all problem sets. Our course code is NP7E7X.
• There is a course survey on Gradescope. Please fill it out during the first week of class.
• Problem Set 1 (due Wednesday 2/7 Friday 2/9 at 10pm)
• Problem Set 2 (due Friday 2/16 at 10pm)
• Problem Set 3 (due Wednesday 2/21 at 10pm)
• Problem Set 4 (due Wednesday 2/28 Friday 3/1 at 10pm)
• Problem Set 5 (due Wednesday 3/6 at 10pm)
• Problem Set 6 (due Wednesday 3/13 at 10pm)
• Problem Set 7 (due Friday 3/29 at 10pm)
• Problem Set 8 (due Wednesday 4/17 Friday 4/19 at 10pm)
• Problem Set 9 (due Wednesday 4/24 at 10pm)
• Problem Set 10 (due Wednesday 5/1 at 10pm)
• Problem Set 11 (due Tuesday 5/7 at 10pm)

Exams

There will be one take-home midterm exam and a take-home final exam. The format is largely similar to a problem set, except that you should complete it by yourself. Each exam will be distributed by a Dropbox link sent by email.

• The midterm exam will be distributed on Friday 3/29 and due on Friday 4/4 at 10pm.
• The final exam will be distributed on Thursday 5/9 and due on Friday 5/17 at noon.