# Applied Statistics Minor

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## Overview

The applied statistics minor provides an opportunity for students to deepen their technical background and gain further appreciation for modern mathematical sciences and the use of statistics as an analytical tool.

• The minor is closed to students majoring in applied statistics and actuarial science.
• Posting of the minor on the student's academic transcript requires a minimum GPA of 2.0 in the minor.

## Curriculum

Course
Prerequisites
Choose one of the following course sequences:
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.
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.
or

MATH-181A
Calculus I
MATH-182A
Calculus II
or

MATH-171
Calculus A
This is the first course in a three-course sequence (COS-MATH-171, -172, -173). This course includes a study of functions, continuity, and differentiability. The study of functions includes the exponential, logarithmic, and trigonometric functions. Limits of functions are used to study continuity and differentiability. The study of the derivative includes the definition, basic rules, and implicit differentiation. Applications of the derivative include optimization and related-rates problems.
MATH-172
Calculus B
This is the second course in three-course sequence (COS-MATH-171, -172, -173). The course includes Riemann sums, the Fundamental Theorem of Calculus, techniques of integration, and applications of the definite integral. The techniques of integration include substitution and integration by parts. The applications of the definite integral include areas between curves, and the calculation of volume.
MATH-173
Calculus C
This is the third course in three-course sequence (COS-MATH-171, -172, -173). The course includes sequences, convergence and divergence of series, representations of functions by infinite series, curves defined by parametric equations, and polar coordinates. Also included are applications of calculus to curves expressed in parametric and polar form.
Electives
Choose five 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.
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.
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.
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..
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.
STAT-315
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.
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.
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.
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.
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.
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.
STAT-415
Statistical Sampling
This course provides a basis for understanding the selection of the appropriate tools and techniques for analyzing survey data. Topics include design of simple surveys, methods of data collection, a study of standard sampling methods. A statistical software package is used for data analysis.
STAT-425
Multivariate Analysis
This course is a study of the multivariate normal distribution, statistical inference on multivariate data, multivariate analysis of covariance, canonical correlation, principal component analysis, and cluster analysis. A statistical software package such as Excel or SAS is used for data analysis.
STAT-435
Statistical Linear Models
This course is an introduction to the theory of linear models. Topics covered are least squares estimators and their properties, matrix formulation of linear regression theory, random vectors and random matrices, the normal distribution model and the Gauss-Markov theorem, variability and sums of squares, distribution theory, the general linear hypothesis test, confidence intervals, confidence regions, correlations among regressor variables, ANOVA models, geometric aspects of linear regression, and less than full rank models.