### Prerequisites for SSC 384 Topic 2 and SSC 384 Topic 3, Mathematical Statistics I and II

The two courses, Math Stat I and II, are two of the four statistics courses required for a Master of Science in Statistics at UT Austin. They are not introductory courses in statistics. The best preparation for Math Stat I is an undergraduate course in mathematical statistics, which had an undergraduate course in probability as a prerequisite. At UT, those courses are M362K , Probability I, and M378K, Introduction to Mathematical Statistics. The prerequisite for the probability course is calculus.

However, students come to this program with a variety of academic backgrounds. Some of these students have had other combinations of undergraduate courses and been successful in Math Stat I and II. The purpose of the further discussion here is to help students understand whether their background is minimally adequate to begin Math Stat I and, if not, what to do to prepare for it.

I will be happy to discuss the course and the prerequisite with any prospective student by email, telephone, or in person. (If you want to talk by telephone or in person, start with email to set up a time.) Email: Please send to both parker@math.utexas.edu and mary.mparker@gmail.com

Overview

In order to succeed in Math Stat I, every student must have strong current knowledge of calculus. Many homework problems require calculus and the calculus techniques will not generally be discussed in class.

In addition, a student should have done some reasonable amount of probability (in which calculus was used) and should have had at least one upper-division statistics course.

If a student has had substantial applied statistics (usually more than one course) and feels confident with that material, but not much probability, it is possible that he/she may be able to handle Math Stat I and II. Such a student should be prepared to do extra reading and background work from an undergraduate probability and mathematical statistics text. Here are suggestions for one such book. The topic lists given here for probability and statistics are a good place to start.

If a student has had a probability course but no statistics, this is a more serious problem. In Math Stat I and II, we do not go into detail about elementary statistics topics or applied statistics topics and so a student will not get a very balanced view of the field of statistics from these courses. If the student is taking other statistics courses concurrently with Math Stat I and II, and is willing to do some guided outside reading in an elementary statistics text and a mathematical statistics text, then it is possible that he/she could succeed in Math Stat I and II. The topic list given here for statistics is a good place to start.

Computer Software Skills

Although Math Stat I and II are very theoretical courses, sometimes the equation you need to solve cannot be conveniently solved analytically and so numerical methods are needed. You will occasionally need to determine some characteristics of the distribution of a statistic for which you cannot write the formula for the pdf/pmf. For these tasks, I encourage students to work together. (I find that saves students much time on computer work!) I will spend very little class time discussing how to do those. Since the R statistical software is free and it is easy to provide scripts for such tasks, I will provide scripts and a very brief introduction to how to read/modify them. When all the students use the same software for that, it is easy to worth together on these tasks.

Most students in Math Stat I and II have learned to use some software in their calculus class (or precalculus class) to graph a function, find a maximum or minimum value, and solve an equation. Also, they have usually used some statistical software to do applied statistics problems, such as t-tests and regression and possibly used this to simulate distributions. It is very useful to have those experiences before taking these courses. This preliminary assignment will allow you to explore your software and improve your skills with it.

Prerequisite for Math Stat II

The best preparation for Math Stat II is having just successfully completed Math Stat I. Some students who have just completed a graduate probability course in one of the engineering departments have been able to handle Math Stat II, but only with a substantial amount of outside work on the topics that were not covered in their other course. Those students also had substantial knowledge of mathematical statistics from other courses.

Other MS courses

There are two other specific required courses in the Master of Science in Statistics program at UT Austin. These are Regression and Design and Analysis of Experiments. These courses cover both theory and applications in those subjects. For that reason, the courses Math Stat I and II do not cover the topics of regression and analysis of variance.
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