# Applied Statistics Immersion

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## Overview

Deepen your technical background and gain further appreciation for modern mathematical sciences and the use of statistics as an analytical tool.

• This immersion is closed to students majoring in applied statistics and actuarial science, applied mathematics, and computational mathematics.
• Students are required to complete at least one course at the 300-level or above as part of the immersion.

The program code for Applied Statistics Immersion is APSTAT-IM.

## Curriculum for Applied Statistics Immersion

Course
Prerequisites
MATH-181
Project-Based Calculus I
This is the first in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals. (Prerequisite: A- or better in MATH-111 or A- or better in ((NMTH-260 or NMTH-272 or NMTH-275) and NMTH-220) or a math placement exam score greater than or equal to 70 or department permission to enroll in this class.) Lecture 6 (Fall, Spring, Summer).
MATH-182
Project-Based Calculus II
This is the second in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates. (Prerequisites: C- or better in (MATH-181 or MATH-173 or 1016-282) or (MATH-171 and MATH-180) or equivalent course(s).) Lecture 6 (Fall, Spring, Summer).
(or equivalents)
Electives
Choose three of the following:*
MATH-251
Probability and Statistics I
This course introduces sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distributions of discrete and continuous random variables, joint distributions (discrete and continuous), the central limit theorem, descriptive statistics, interval estimation, and applications of probability and statistics to real-world problems. A statistical package such as Minitab or R is used for data analysis and statistical applications. (Prerequisites: MATH-173 or MATH-182 or MATH 182A or equivalent course.) Lecture 3 (Fall, Spring, Summer).
MATH-252
Probability and Statistics II
This course covers basic statistical concepts, sampling theory, hypothesis testing, confidence intervals, point estimation, and simple linear regression. The statistical software package MINITAB will be used for data analysis and statistical applications. (Prerequisites: STAT-251 or MATH-251 or equivalent course.) Lecture 3 (Fall, Spring).
MATH-505
Stochastic Processes
This course explores Poisson processes and Markov chains with an emphasis on applications. Extensive use is made of conditional probability and conditional expectation. Further topics, such as renewal processes, Brownian motion, queuing models and reliability are discussed as time allows. (Prerequisites: MATH-241 and MATH-251 or equivalent courses.) Lecture 3 (Spring).
STAT-205
Applied Statistics
This course covers basic statistical concepts and techniques including descriptive statistics, probability, inference, and quality control. The statistical package Minitab will be used to reinforce these techniques. The focus of this course is on statistical applications and quality improvement in engineering. This course is intended for engineering programs and has a calculus prerequisite. Note: This course may not be taken for credit if credit is to be earned in STAT-145 or STAT-155 or MATH 252.. (Prerequisite: MATH-173 or MATH-182 or MATH-182A or equivalent course.) Lecture 3 (Fall, Spring).
STAT-295
Statistical Analysis for Bioinformatics
This course is an introduction to the probabilistic models and statistical techniques used in computational molecular biology. Probabilistic and/or statistical techniques will be presented for the understanding of pairwise and multiple sequence alignment methods, gene and protein classification methods, and phylogenetic tree construction. (Prerequisites: MATH-173 or MATH-182 and MATH-190 or MATH-200 or equivalent courses.) Lecture 3 (Spring).
STAT-305
Regression Analysis
This course covers regression techniques with applications to the type of problems encountered in real-world situations. It includes use of the statistical software SAS. Topics include a review of simple linear regression, residual analysis, multiple regression, matrix approach to regression, model selection procedures, and various other models as time permits. (Prerequisites: MATH-241 and MATH-252 or equivalent courses.) Lecture 3 (Spring).
STAT-325
Design of Experiments
This course is a study of the design and analysis of experiments. It includes extensive use of statistical software. Topics include single-factor analysis of variance, multiple comparisons and model validation, multifactor factorial designs, fixed, random and mixed models, expected mean square calculations, confounding, randomized block designs, and other designs and topics as time permits. (Prerequisites: STAT-205 or MATH-252 or equivalent courses.) Lecture 3 (Fall).
STAT-335
Introduction to Time Series
This course is a study of the modeling and forecasting of time series. Topics include ARMA and ARIMA models, autocorrelation function, partial autocorrelation function, detrending, residual analysis, graphical methods, and diagnostics. A statistical software package is used for data analysis. (Prerequisites: STAT-205 or MATH-252 or equivalent courses.) Lecture 3 (Spring).
STAT-345
Nonparametric Statistics
This course is an in-depth study of inferential procedures that are valid under a wide range of shapes for the population distribution. Topics include tests based on the binomial distribution, contingency tables, statistical inferences based on ranks, runs tests and randomization methods. A statistical software package is used for data analysis. (Prerequisites: STAT-205 or MATH-252 or equivalent courses.) Lecture 3 (Fall).
STAT-405
Mathematical Statistics I
This course provides a brief review of basic probability concepts and distribution theory. It covers mathematical properties of distributions needed for statistical inference. (Prerequisites: STAT-205 or MATH-252 or equivalent courses.) Lecture 3 (Fall).
STAT-406
Mathematical Statistics II
This course is a continuation of STAT-405 covering classical and Bayesian methods in estimation theory, chi-square test, Neyman-Pearson lemma, mathematical justification of standard test procedures, sufficient statistics, and further topics in statistical inference. (Prerequisites: STAT-405 or equivalent course.) Lecture 3 (Spring).
STAT-521
Statistical Quality Control
This course presents the probability models associated with control charts, control charts for continuous and discrete data, interpretation of control charts, and some standard sampling plans as applied to quality control. A statistical software package will be used for data analysis. (Prerequisites: MATH-252 or equivalent course.) Lecture 3 (Fall, Spring).

* At least one courses must be taken at the 300-level or above.