Professor: Martin Bays
Office: HH-409
Telephone: (905) 525-9140, ext. 27031
Email Address: mbays@math.mcmaster.ca
Web page: http://www.math.mcmaster.ca/~mbays/
Lecture Times: Tu We Fr 12:30-13:20 HH217
Office Hours: TBA
Textbook: "Gödel, Escher, Bach: an Eternal Golden Braid", by Douglas Hofstadter, published by Basic Books Inc. Note that either the 1st or 20th-anniversary edition may be used (since except for a new introduction, they are essentially the same).
Kurt Gödel's famous First Incompleteness Theorem establishes that every sufficiently strong formal axiomatic system T is either inconsistent or incomplete; in other words, if T is consistent then there are sentences in the language of T which can neither be proved nor refuted in T. The Second Incompleteness Theorem establishes for such a consistent system T, that a statement formalizing the consistency of T is unprovable within T. The goal of this course is to present the proof of the First Incompleteness Theorem found in the course text. Along the way we will investigate formal systems, mathematical proofs, mathematical truth and the foundations of computability. We will also discuss results related to the incompleteness theorems, for example, Tarski's Theorem on the undefinability of truth within formal systems.
You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.
Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g. the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: "Grade of F assigned for academic dishonesty"), tutting, and/or suspension or expulsion from the university.
It is your responsibility to understand what constitutes academic dishonesty. For information on the various types of academic dishonesty please refer to the Academic Integrity Policy, located at www.mcmaster.ca/academicintegrity.
The following illustrates but three forms of academic dishonesty:
The instructor and university reserve the right to modify elements of the course during the term. The university may change the dates and deadlines for any or all courses in extreme circumstances. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster email and course websites weekly during the term and to note any changes.
Requests for Relief for Missed Academic Term Work for absences from classes lasting up to 5 days: Using the McMaster student absence form (MSAF) on-line, self-reporting tool, undergraduate students may report absences lasting up to 5 days and may also request relief for missed academic work. The submission of medical or other types of supporting documentation is normally not required. Students may use this tool to submit a maximum of one request for relief of missed academic work per term. Students must immediately follow up with their course instructors regarding the nature of the relief. Failure to do so may negate the opportunity for relief. It is the prerogative of the instructor of the course to determine the appropriate relief for missed term work in his/her course.
For absences from classes lasting more than five days: Students who are absent more than five days cannot use the on-line, self-reporting tool to request relief. They MUST report to their Faculty Office to discuss their situation and may be required to provide appropriate supporting documentation. If warranted, students will be approved to use a discretionary version of the MSAF on-line, self-reporting tool.
Usually, relief for missed work will take the form of a transferral of its weight to the final exam.