We list what would usually be considered adequate and excellent preparation for the prelim courses. Note that there are many other advanced undergraduate and beginning graduate courses which help with developing the necessary mathematical sophistication needed to do well in a prelim course.  Consult with an advisor to find out which topics courses are offerred each semester which would be suitable.

Algebra (prelim sequence M380C & D):
 Expected: undergraduate algebra I and II (M373K & L at UT)
 Excellent: several advanced undergraduate courses in group theory, number theory, coding theory ,or experience in a graduate algebra course at another university
 Prelim course preparation: M343L (applied number theory; cryptography in fall semesters, coding theory in spring semesters) and certain topics courses which vary from semester to semester.

 Analysis (prelim sequence M381C & D):
Expected: undergraduate real analysis I and II (M365C & D at UT)
 Excellent: Undergraduate complex analysis (M361 at UT) and one or more undergraduate courses beyond real analysis, or experience in a graduate analysis course at another university. Note that it is possible to take the complex analysis prelim class (M381D, spring semesters) before taking the real analysis prelim course (M381C, fall semesters).
Prelim course preparation:  Certain graduate topics courses which vary from semester to semester.

Topology (prelim sequence M382C & D):
 Expected: an undergraduate topology course (M367K at UT); good knowledge of linear algebra (for both M382C & D); advanced calculus and some differential equations for differential topology (M382D).
Excellent: a curves and surfaces course or experience in a graduate topology course at another university.
Prelim sequence preparation: Curves and surfaces (usually taught as a M375 topics course at UT)  and certain topics courses which vary from semester to semester.

Applied Mathematics ( prelim sequence M383C & D):
Expected: differential equations and Fourier series
Excellent: undergraduate course in partial differential equations (M372 at UT), the graduate real analysis course (M381C), or a beginning graduate course in any of a number of subjects.
Prelim sequence preparation: M346K (applied linear algebra) M362M (Markov processes and an introduction to stochastic analysis) and certain topics courses which vary from semester to semester.