A student beginning graduate study in mathematics as a doctoral student is expected to have had, as an undergraduate or master's student a rigorous course in analysis covering the material in texts such as Mathematical Analysis by T.M. Apostol, Advanced Calculus by R.C. Buck, or Principles of Mathematical Analysis by Walter Rudin, a rigorous course in algebra covering the material in texts such as Introduction to Abstract Algebra by E.A. Walker, Topics in Algebra by I.N. Herstein, or Abstract Algebra by D. Saracino. An applicant whose preparation is deficient may be admitted to the program, if otherwise qualified, but will be required to correct the deficiency, increasing somewhat the time required to complete work for the degree. Prospective graduate students are advised to take at least introductory courses in related fields such as physics, statistics, and computer science.
The comprehensive exams are meant to test students on breadth in mathematics. They cover material from several general areas. The qualifying exam determines the student's readiness to write a thesis. The thesis itself is of integral importance to both doctoral degrees. It is the culmination of a major research project and exhibits the student's expertise in a very specific field of study. The Ph.D. thesis is an original piece of significant mathematical research or research in mathematics education.
Beginning students concentrate on gaining general knowledge in the core areas of algebra, topology, complex analysis, and real analysis. Students in the mathematics education program are required to take courses in at least three of these core areas, statistics and in education. All students also take courses on more specific topics and attend seminars to gain greater understanding of particular research topics. The actual course sequences taken by a doctoral candidate will vary greatly depending on the preparation received in their Master's work. The sample plans of study given are typical of students entering with a Master's degree similar to that given at OSU. After the core courses have been completed students take their comprehensive exams. The next step is to gain specific knowledge about an area of interest which might lead to a thesis topic. Under the direction of a faculty member, the doctoral student will continue with topics courses, work on outside readings, and become actively involved in seminars. When the student has gained the background to begin serious research for a thesis, a qualifying exam is administered by his/her advisory committee. This exam determines if the student is ready to conduct the necessary research. Upon completion of the qualifying exam, the student devotes a major portion of his/her time to research for a thesis.