Applied Statistics Minor

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. (Prerequisites: MATH-111 or (NMTH-220 and NMTH-260 or NMTH-272 or NMTH-275) or equivalent courses with a minimum grade of B-, or a score of at least 60% on the RIT Mathematics Placement Exam.) Lecture 4 (Fall, Spring).

This is the second in a two-course sequence. 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-181A or equivalent course.) Lecture 4 (Fall, Spring).

This is the first course in a three-course sequence (COS-MATH-171, -172, -173). This course includes a study of precalculus, polynomial, rational, exponential, logarithmic and trigonometric functions, continuity, and differentiability. 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. (Prerequisites: Completion of the math placement exam or C- or better in MATH-111 or C- or better in ((NMTH-260 or NMTH-272 or NMTH-275) and NMTH-220) or equivalent course.) Lecture 5 (Fall, Spring).

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. (Prerequisites: C- or better in MATH-171 or 1016-171T or 1016-281 or 1016-231 or equivalent course.) Lecture 5 (Fall, Spring).

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. (Prerequisites: C- or better in MATH-172 or equivalent course.) Lecture 5 (Fall, Spring).

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, Recitation 1 (Fall, Spring, Summer).

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 or MATH-241H) and MATH-251 or equivalent courses.) Lecture 3 (Spring).

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).

Learn how data furthers understanding of science and engineering. This course covers basic statistical concepts, sampling theory, hypothesis testing, confidence intervals, point estimation, and simple linear regression. A statistical software package such as MINITAB will be used for data analysis and statistical applications. (Prerequisites: MATH-251. NOTE: Students cannot receive credit for both MATH-252 and STAT-257 nor for both STAT-205 and STAT-257.) Lecture 3 (Fall, Spring).

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 STAT-205 or STAT-257) or equivalent courses.) Lecture 3 (Fall).

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 STAT-257 or equivalent course.) Lecture 3 (Spring).

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 STAT-257 or equivalent course.) Lecture 3 (Fall).

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 STAT-257 or equivalent course.) Lecture 3 (Spring).

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 STAT-257 or equivalent course.) Lecture 3 (Fall).

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).

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: STAT-205 or MATH-252 or STAT-257 or equivalent course.) Lecture 3 (Fall, Spring).

This course is an introduction to the statistical-software package R, which is often used in professional practice. Some comparisons with other statistical-software packages will also be made. Topics include: data structures; reading and writing data; data manipulation, subsetting, reshaping, sorting, and merging; conditional execution and looping; built-in functions; creation of new functions; graphics; matrices and arrays; simulations and app development with Shiny. (Prerequisites: MATH-252 or STAT-257 or equivalent course.) Lecture 3 (Fall, Spring).

The use of statistical models in computer algorithms allows users to make decisions and predictions, and to perform tasks that traditionally require human cognitive abilities. Data mining and Machine learning are interdisciplinary fields at the intersection of statistics, computer science, applied mathematics which develops such statistical models and interweaves them with computer algorithms. It underpins many modern technologies, such as speech recognition, Internet search, bioinformatics and computer vision. The course will provide an introduction to Statistical Machine Learning and its core models and algorithms. (Prerequisites: STAT-305 or equivalent courses.) Lecture 3 (Spring).

This course is an introduction to sample survey design with emphasis on practical aspects of survey methodology. Topics include: survey planning, sample design and selection, survey instrument design, data collection methods, and analysis and reporting. Application areas discussed will include program evaluation, opinion polling, customer satisfaction, product and service design, and evaluating marketing effectiveness. Data collection methods to be discussed will include face-to-face, mail, Internet and telephone. (Prerequisites: MATH-252 or STAT-257 or equivalent course.) Lecture 3 (Fall).

This course is intended to introduce students to categorical data analysis. Topics include: contingency tables, matched pair analysis, Fisher's exact test, logistic regression, analysis of odds ratios, log linear models, multi-categorical logit models, ordinal and paired response analysis. (Prerequisites: STAT-305 or equivalent courses.) Lecture 3 (Spring).