Basic Courses

Pure Math graduate students are required to pass (or exempt from) the following sequence of courses. Algebra: Groups, rings, and vector spaces (GRV) I, II, III (MAS5307, MAS5308, MAS5311); Topology: Topology I, II(MTG5326, MTG5327) Algebraic topology (Top IIIa) (MTG5346) and Differential topology (Top IIIb) (MTG5392) ; Complex Analysis: Theory of functions of a complex variable I, II (MAA5406, MAA5407); Real Analysis: Measure & integration I, II (MAA5616, MAA5617). Students may exempt from a part or all of a course sequence by doing well on the corresponding qualifier exam. The qualifier exams are typically offered in the August and January at the beginning of the fall and spring semesters. Typically, the courses are offered as follows: Fall: GRV I,III Topology I,IIIa* Complex Analysis I Measure & Integration I Spring: GRV II Topology II,IIIb* Complex Analysis II Measure & Integration II *The order in which Topology IIIa and Topology IIIb is offered may depend on the year. Most students are only required to take one of the two Topology III courses, but some major professors may require their students to take both.

Three Examples: Course grids for an entering student taking 9 credit hours. Example 1: a student geared toward Algebra and Topology. (Here the roles of real and complex analysis may be exchanged.) 1st year F Complex Analysis I GRV I Topology I S Complex Analysis II GRV II Topology II 2nd year F Measure and integration I GRV III (Topology IIIa*) S Measure and Integration II (Topics course) (Topology IIIb*) Example 2: a student geared toward real and complex analysis. 1st year F Complex Analysis I GRV I Measure and Integration I S Complex Analysis II GRV II Measure and Integration II 2nd year F Topology I GRV III (Topics course) S Topology II Topology IIIb* (Topics course) Example 3: a student who needs extra preparation in real analysis. 1st year F Complex Analysis I GRV I Advanced Calculus I S Complex Analysis II GRV II Advanced Calculus II 2nd year F Topology I GRV III Measure and Integration I S Topology II Topology IIIb* Measure and Integration II It is not uncommon that a student begins graduate work at FSU with previous exposure to some of the topics covered by the core sequences, at a comparable level of depth. With the permission of the instructor, these students may skip the first one or two semesters in a sequence. In any case, students have the option of taking qualifying exams in these areas in the week preceding the beginning of the semester. Their performance on a qualifying exam may warrant placement into a more advanced course in the sequence, or allow them to skip the corresponding sequence altogether. Alternatively, students whose background does not include a solid preparation in undergraduate Advanced Calculus should take Advanced Calculus I and II (MAA5306/7) in their first year, and plan to enroll in Measure & Integration in their second year. Students should keep in mind that they are expected to find a major professor by the end of their second year. To help students find an area in which to specialize, the grid of a first- or second-year student will normally have room for courses outside the core sequences. Typically, this will include topics courses offered by the department in that semester, seminars, or DIS (Directed Individual Studies) courses in areas of particular interest to that student.

(latest update: 7/21/09)