Department of Mathematics, Statistics
and Computer Science
Wim Ruitenburg's Fall 2014 MATH 4995-XXX. Mathematical Logic
Last updated: September 2014
Comments and suggestions: Email wimr@mscs.mu.edu
Always under construction.
About this class:
- Objective: Learn precise and correct reasoning about precise and
correct reasoning.
Be able to use the completeness theorem of predicate logic in applications
within mathematical logic as well as in mathematics more generally.
Develop the ability to independently investigate questions about mathematical
logic and its applications.
This includes the ability to create relevant questions.
- We meet once a week for 1.5 hours, usually in CU 384.
Extra times may be set aside when the need arises.
- Book: Dirk van Dalen, Logic and Structure, fourth edition, Universitext,
Springer 2004.
- Both the mathematical as well as the meta-mathematical levels of the
study start off with traditional (usually called classical) mathematics.
As the class progresses, we will investigate alternates at the mathematical
level, including intuitionistic mathematics.
- Grades:
We maintain a cross between a journal and a report.
In particular, the student will update `earlier' sections of the report while
adding new material at its end.
As a safety zone the student does exercises from the book in the usual and
expected way, and records the work in the report.
Besides that, we consider challenge questions and tasks about details of the
book, like:
Could this part be more precise?
Can this part be done more general?
Look in the literature for applications.
It is important that this is done in a dynamic way, as the student moves
through the material in the book.
As a safety structure, we cover the book through Chapter 3, which includes the
completeness theorem for classical predicate logic.
The student will look into Chapter 5 on intuitionistic predicate logic, and
investigate possible generalizations from traditional (classical) predicate
logic to intuitionistic predicate logic.