Teachers with a BS in math from the University of Texas at Austin will be expected to be among the most mathematically qualified in the state. Therefore they will be likely to be asked to teach Advanced Placement courses. The purpose of the depth requirement is to give you additional depth of mathematical background in one of the two fields in which Advanced Placement math courses are taught: calculus and statistics.

The Depth Course is listed as Requirement 14 (f) in the catalogue. Your choices are M 427K: Advanced Calculus for Applications I and M 378K: Introduction to Mathematical Statistics.

• M 427K is a course in differential equations. Differential equations are equations involving functions and their derivatives. Many of the applications of calculus involve differential equations, so taking M 427K should give you additional background on areas in which calculus is applied. The course will also give you good practice in using many calculus concepts.
• M 378K is an introduction to the mathematical theory of statistics. It will help give you more of an idea of how and why some of the techniques you studied in M 358K are developed. It will also help you review and understand the important statistical concepts of sampling distribution, hypothesis test, and confidence interval, as well as broaden your statistical knowledge beyond the subject matter of M 358K. M 378K also uses a lot of calculus, so can help strengthen your calculus background as well.

You should wait until you have taken M 358K to decide which depth course to take.

Yes. You can count one toward the depth course requirement and one toward the additional hours of upper division math requirement, or as an elective.

If you can take both M 427K and M 378K, do that. If you can't fit both courses into your schedule, M 378K is the best choice, since it gives you depth of background in calculus as well as statistics.

Yes.

• See the web page on the supporting course for suggestions for supporting courses to give you additional background for teaching P courses. Although you are only required to take one supporting course, you can take more of these courses as electives if you wish.
• Additional math courses that you can take to gain depth of background in calculus are: M427L (Advanced Calculus for Applications II), M 361 (Theory of Functions of a Complex Variable), M 364k (Vector and tensor Analysis I), M 364C and D (Real Analysis I and II), M 372 (Fourier and Boundary value Problems), M 374 (Fourier and Laplace Transforms), M 374M (Introduction to Mathematical Modeling and Industrial Mathematics) Most of these are not listed among the courses specified for the additional math upper division hours required for your degree, but in some cases they might be counted with permission of the faculty advisor, Dr. Smith (mks@math.utexas.edu). Also, sometimes courses are offered under the number M 375 that might be appropriate.
• Additional math courses that you can take to gain depth of background in probability and statistics are: M 439J (Probability Models with Actuarial Applications), 339U ( Actuarial Contingent Payments I), M 362M (Introduction to Stochastic Processes), M 374G (Linear Regression Analysis). All but the last of these are included in the list of courses specified for the additional math upper division hours required for your degree; it might be able to count M 374G toward this requirement; contact the faculty advisor, Dr. Smith (mks@math.uteas.edu) to pursue this possibility. Also, sometimes courses are offered under the number M 375 that might be appropriate (One example is Introduction to Risk Analysis in Fall, 2001.)