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Industrial & Applied Mathematics Minor

College of Sciences / Mathematics and Statistics
Undergraduate minor

About The Program

The Industrial and Applied Mathematics Minor is a flexible program designed to enhance the quantitative capacities of students pursuing degrees in diverse fields. The minor integrates coursework in mathematics and statistics, including mathematical modeling and statistical programming. Two elective courses allow students to customize the program depending on their educational and career-related objectives.

Student outcomes

After completing the Industrial and Applied Mathematics Minor, students will be able to:

  • Use mathematical and statistical knowledge to formulate appropriate models and problem-solving approaches in diverse contexts
  • Utilize computing skills for problem-solving, data analysis, and visualization 

How to enroll

Current students: Declare this program

Once you’re admitted as an undergraduate student and have met any further admission requirements your chosen program may have, you may declare a major or declare an optional minor.

Future students: Apply now

Apply to Metropolitan State: Start the journey toward your Industrial & Applied Mathematics Minor now. Learn about the steps to enroll or, if you have questions about what Metropolitan State can offer you, request information, visit campus or chat with an admissions counselor.

Get started on your Industrial & Applied Mathematics Minor

Program eligibility requirements

Students interested in pursuing the Industrial and Applied Mathematics Minor must be formally admitted into this program. To be admitted, students must submit the online College of Sciences declaration form. Transfer coursework equivalency is determined by the Mathematics and Statistics Department.

Courses and Requirements

SKIP TO COURSE REQUIREMENTS

This minor is NOT open to students pursuing the Mathematics BA or the Industrial and Applied Mathematics BS degree. Students must complete at least 13 credits of the minor at Metropolitan State University. Students must take at least 8 credits in the minor that are not counted as part of their major or any other minor. All prerequisite and required courses must be completed with grades of C- or above. Work with your academic advisor to assure both major and minor requirements are met when planning your course load every semester towards graduation.

Minor Requirements

+ Core (16 - 18 credits)

This course covers the basic principles and methods of statistics. It emphasizes techniques and applications in real-world problem solving and decision making. Topics include frequency distributions, measures of location and variation, probability, sampling, design of experiments, sampling distributions, interval estimation, hypothesis testing, correlation and regression.

Full course description for Statistics I

Since its beginnings, calculus has demonstrated itself to be one of humankind's greatest intellectual achievements. This versatile subject has proven useful in solving problems ranging from physics and astronomy to biology and social science. Through a conceptual and theoretical framework this course covers topics in differential calculus including limits, derivatives, derivatives of transcendental functions, applications of differentiation, L'Hopital's rule, implicit differentiation, and related rates.

Full course description for Calculus I

This is a continuation of MATH 210 Calculus I and a working knowledge of that material is expected. Through a conceptual and theoretical framework this course covers the definite integral, the fundamental theorem of calculus, applications of integration, numerical methods for evaluating integrals, techniques of integration and series.

Full course description for Calculus II

Mathematical modeling is the process of using mathematics and computational tools to gain insights into complex problems arising in the sciences, business, industry, and society. Mathematical modeling is an iterative process which involves a computational approach to the scientific method. Assumptions are established, a mathematical structure consistent with those assumptions is developed, hypotheses are produced and tested against empirical evidence, and then the model is refined accordingly. The quality of these models is examined as part of the verification process, and the entire cycle repeats as improvements and adjustments to the model are made. This course provides an introduction to both the mathematical modeling process as well as deterministic and stochastic methods that are commonly employed to investigate time-dependent phenomena.

Full course description for Introduction to Mathematical Modeling

Select one of the following courses (2 or 4 credits)

An introduction to methods and techniques commonly used in data science. This course will use object-oriented computer programming related to the processing, summarization and visualization of data, which will prepare students to use data in their field of study and to effectively communicate quantitative findings. Topics will include basics in computer programming, data visualization, data wrangling, data reshaping, ethical issues with the use of data, and data analysis using an object-oriented programming language. Students will complete a data science project.

Full course description for Data Science and Visualization

This course covers advanced statistical programming techniques including data wrangling, data visualization and hypothesis testing using R. Topics of this course include R syntax, input and output in R, data visualization, interactive data graphics, data wrangling, tidy data, and hypothesis testing in R. This course builds on the knowledge learned in STAT201.

Full course description for Statistics Programming

+ Electives (8 credits)

Students must complete a minimum of two of the following courses.

This is a calculus-based probability course. It covers the following topics. (1) General Probability: set notation and basic elements of probability, combinatorial probability, conditional probability and independent events, and Bayes Theorem. (2) Single-Variable Probability: binomial, geometric, hypergeometric, Poisson, uniform, exponential, gamma and normal distributions, cumulative distribution functions, mean, variance and standard deviation, moments and moment-generating functions, and Chebysheff Theorem. (3) Multi-Variable Probability: joint probability functions and joint density functions, joint cumulative distribution functions, central limit theorem, conditional and marginal probability, moments and moment-generating functions, variance, covariance and correlation, and transformations. (4) Application to problems in medical testing, insurance, political survey, social inequity, gaming, and other fields of interest.

Full course description for Probability

Optimization covers a broad range of problems that share a common goal - determining the values for the decision variables in a problem that will maximize (or minimize) some objective function while satisfying various constraints. Using a mathematical modeling approach, this course introduces mathematical programming techniques and concepts such as linear programming, sensitivity analysis, network modeling, integer linear programming, goal programming, and multiple criteria optimization. Software is used to solve real-world problems with an emphasis on interpretability of results. Applications include determining product mix, routing and logistics, and financial planning.

Full course description for Optimization

Stochastic processes involve sequences of events governed by probabilistic laws. Many applications of stochastic processes occur in biology, medicine, psychology, finance, telecommunications, insurance, security, and other disciplines. This course introduces the basics of applied stochastic processes such as Markov chains (both discrete-time and continuous-time), queuing models, and renewal processes. Software is used to solve real-world problems with an emphasis on interpretation of results and the role of stochastic processes in management decision-making.

Full course description for Introduction to Stochastic Processes

This course provides students with significant problem-solving experience through investigating complex, open-ended problems arising in real-world settings. Working in teams, students apply mathematical modeling processes to translate problems presented to them into problems that can be investigated using the mathematical, statistical, and computational knowledge and thinking they have gained from previous coursework. Significant emphasis is placed on justifying approaches used to investigate problems, coordinating the work of team members, and communicating analyses and findings to technical and non-technical audiences.

Full course description for Advanced Mathematical Modeling

This course covers introductory and intermediate ideas of the analysis of variance (ANOVA) method of statistical analysis. The course builds on the ideas of hypothesis testing learned in STAT201 (Statistics I). The focus is on learning new statistical skills and concepts for real-world applications. Students will use statistical software to do the analyses. Topics include one-factor ANOVA models, two-factor ANOVA models, repeated-measures designs, random and mixed effects, principle component analysis, linear discriminant analysis and cluster analysis.

Full course description for Analysis of Variance and Multivariate Analysis

This course covers fundamental to intermediate regression analysis. The course builds on the ideas of hypothesis testing learned in STAT201 (Statistics I). The focus is on learning new statistical skills and concepts for real-world applications. Students will use statistical software to do the analyses. Topics include simple and bivariate linear regression, residual analysis, multiple linear model building, logistic regression, the general linear model, analysis of covariance, and analysis of time series data.

Full course description for Regression Analysis

This course covers fundamental and intermediate topics in biostatistics, and builds on the ideas of hypothesis testing learned in STAT 201 (Statistics I). The focus is on learning new statistical skills and concepts for real-world applications. Students will use SPSS to do the analyses. Topics include designing studies in biostatistics, ANOVA, correlation, linear regression, survival analysis, categorical data analysis, logistic regression, nonparametric statistical methods, and issues in the analysis of clinical trials.

Full course description for Biostatistics

This course covers the fundamental to intermediate ideas of nonparametric statistical analysis. The course builds on the ideas of hypothesis testing learned in STAT201 (Statistics I). The focus is on learning new statistical skills and concepts for real-world applications. Students will use statistical software to do the analyses. Topics include nonparametric methods for paired data, Wilcoxon Rank-Sum Tests, Kruskal-Wallis Tests, goodness-of-fit tests, nonparametric linear correlation and regression. Completion of STAT201 (Statistics I) is a prerequisite for this course.

Full course description for Nonparametric Statistical Methods

This course covers the fundamental to intermediate ideas of the statistical analysis of categorical data. The course builds on the ideas of hypothesis testing learned in STAT201 (Statistics I). The focus is on learning new statistical skills and concepts for real-world applications. Students will use statistical software to do the analyses. Topics include analysis of 2x2 tables, stratified categorical analyses, estimation of odds ratios, analysis of general two-way and three-way tables, probit analysis, and analysis of loglinear models. Completion of STAT201 (Statistics I) is a prerequisite.

Full course description for Analysis of Categorical Data

This course covers the intermediate statistical methods in analyzing environmental and biological datasets. This course is built on the knowledge of an introductory statistics and hypothesis testing. The contents of the course include paired T-test, unpaired T-test, F-tests, one-way and two-way ANOVA, multivariate ANOVA, repeated measures, regression, principle component analysis and cluster analysis. Students will learn how to use statistical software to perform all the analyses.

Full course description for Environmental Statistics

A time series is a sequence of observations on a variable measured at successive points in time or over successive periods of time. This course provides an introduction to both standard and advanced time series analysis and forecasting methods. Graphical techniques and numerical summaries are used to identify data patterns such as seasonal and cyclical trends. Forecasting methods covered include: Moving averages, weighted moving averages, exponential smoothing, state-space models, simple linear regression, multiple regression, classification and regression trees, and neural networks. Measures of forecast accuracy are used to determine which method to use for obtaining forecasts for future time periods.

Full course description for Time Series Analysis and Forecasting