March 18, 1998
The Department of Mathematics proposes to institute a Logic and Foundations Option within its Ph.D. program. This option was approved by the mathematics faculty on September 23, 1997.
The creation of a new Logic and Foundations Option within the current mathematics graduate program is aimed towards creating an environment where research and education in mathematical logic and foundations of mathematics can prosper and thrive beyond the current level.
Typical candidates for the Logic and Foundations Option would be students with a strong undergraduate mathematics background who are interested in mathematical logic and foundations of mathematics. The Logic and Foundations Option would allow such students to pursue a Ph.D. in mathematics with a concentration in these areas.
The design of the new option takes into account the success of the current mathematics Ph.D. program in providing an excellent doctoral education. However it also acknowledges its limitations in supporting some areas of graduate education in mathematical logic and foundations of mathematics. Within such a context, the establishment of the new Logic and Foundations Option is intended to augment and enrich the current graduate program rather than alter it.
For the Logic and Foundations Option to succeed, it is essential to ensure a stable supply of graduate students. Because of realistic constraints in personal resources and time, the present qualifying exam system has negatively impacted recruitment of candidates. Discussion with department faculty in all areas reveals that a reasonable solution to accommodate the Logic and Foundations Option can be found without jeopardizing the present one, while simultaneously ensuring and strengthening the quality level of the current system.
None. We are not proposing any new courses. The Department of Mathematics currently offers several courses in logic and foundations; see appendix 4. The resources needed to offer the Logic and Foundations option are already in place.
The new program is called the Logic and Foundations Option. It is an option within the existing Ph.D. program in the department of mathematics.
Students who have been admitted to the mathematics Ph.D. program will be allowed to select the Logic and Foundations Option by filing a petition with the departmental graduate studies committee at any time during the interval between admission to the Ph.D. program and the add/drop deadline for the student's first semester in the Ph.D. program. Degree requirements and procedures for the Logic and Foundations Option will be exactly the same as for the standard mathematics Ph.D. program (see section 6.2 in appendix 6). The only difference is that candidates under the Logic and Foundations Option will take a written qualifying examination in Logic/Foundations, instead of Geometry/Topology as in the standard mathematics Ph.D. program. A first-year graduate sequence of two 3-credit courses, Math 557-558, will prepare students for the Logic/Foundations qualifying examination. The content of these courses will be as currently offered and listed in the graduate catalog (see appendix 5). The written qualifying examinations in Algebra and Analysis and all other requirements will be administered under the standard mathematics Ph.D. program. Candidates under the Logic and Foundations Option will graduate with the same title of Ph.D. in Mathematics as those in the standard mathematics Ph.D. program.
It is anticipated that the Logic and Foundations Option will have a large positive impact in research and education in various branches of mathematical logic, including recursive function theory, set theory, proof theory, and model theory. Since a major goal of such research is to obtain insight into the foundations of mathematics, such kinds of research are very unlikely to be pursued in other departments of the University.
It is relevant to point out that Penn State Mathematics Department has a long history of research and graduate education in mathematical logic and foundations of mathematics, going back to key figures such as Haskell Curry. (See appendix 1.) For many years, Penn State was considered one of the best places in the world to study these subjects. Unfortunately, our ability to recruit and develop students in these areas has been negatively impacted by the system of Ph.D. qualifying examinations which the Department of Mathematics instituted in 1990. The Logic and Foundations Option would help to restore our ability to develop Ph.D. students in these area.
No other departments are affected.
The mathematics department graduate faculty currently numbers about 60 including three specialists in mathematical logic: Thomas Jech, Richard Mansfield, and Stephen G. Simpson. Professors Jech, Mansfield, and Simpson have made substantial contributions to the graduate program, by supervising Ph.D. students in mathematical logic and set theory and in other ways. (See appendices 2 and 3.) Therefore, we anticipate that the current faculty in mathematical logic will be able to sustain the Logic and Foundations Option for at least the next five years. Although additional faculty would be desirable, this is not a requirement for restarting the Logic and Foundations Option. As noted in item B above, the resources needed to offer the Logic and Foundations Option are already in place.
The Logic and Foundations Option has been narrowly drawn so that it will have no effect on the existing standard Ph.D. program in mathematics. (See appendices 5, 6 and 7.) It will also have no effect on any other program, option, or minor.
The Logic and Foundations Option will not require the dropping of any program, option, or minor.