Industrial & Applied Mathematics BS

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 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

This is a continuation of Math 211 Calculus II and covers calculus as it applies to functions of several variables. Topics include vectors and plane curves, partial differentiation, curves and vectors in space, multiple integrals, vector fields, line integrals, and Stokes Theorem.

Full course description for Calculus III: Multivariable Calculus

The need to solve systems of linear equations frequently arises in mathematics, the physical sciences, engineering and economics. In this course we study these systems from an algebraic and geometric viewpoint. Topics include systems of linear equations, matrix algebra, Euclidean vector spaces, linear transformations, linear independence, dimension, eigenvalues and eigenvectors.

Full course description for Linear Algebra and Applications

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 addresses the theory and practice of using algorithms and computer programming to solve mathematical problems. Possible topics include roundoff and truncation errors, solution of nonlinear equations, systems of linear and nonlinear equations, interpolation and approximation, numerical differentiation and integration, numerical solution of ordinary differential equations.

Full course description for Computational Mathematics

Statistical machine learning (often referred to simply as statistical learning) has arisen as a recent subfield of statistics. It emphasizes the interpretability, precision, and uncertainty of machine learning models. This course assesses the accuracy of several supervised and unsupervised machine learning models for both regression and classification. Topics include the bias-variance trade-off, training and test datasets, resampling methods, shrinkage and dimension reduction methods, non-linear modeling techniques such as regression splines and generalized additive models, and decision tree-based methods. Applications include examples from medicine, biology, marketing, finance, insurance, and sports.

Full course description for Applied Machine Learning

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

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

This advanced workshop will give students exposure to the statistical and non-statistical issues that arise in statistical problem solving, and provide an experiential background in statistical consulting. Students will develop the knowledge, skills, and professional rapport necessary to interact with clients, including the skills necessary for communicating technical statistical content with non-statisticians.

Full course description for Statistical Consulting

This course integrates reading of the mathematical literature with presentation of student developed projects.

Full course description for Mathematics Capstone

Students obtain internships in selected areas of study to gain deeper understand of knowledge, skills and the context of a given field. Site supervisors give guidance and direction to customized internship projects. Faculty members serve as liaisons between the internship sites and the university, providing information to students and potential supervisors and supervising the learning experience. Students should contact the Institute for Community Engagement and Scholarship (ICES) at Metropolitan State University for more information.

Full course description for Statistics Internship

Internships offer students opportunities to gain deeper knowledge and skills in their chosen field. Students are responsible for locating their own internship. Metro faculty members serve as liaisons to the internship sites¿ supervisors and as evaluators to monitor student work and give academic credit for learning. Students are eligible to earn 1 credit for every 40 hours of work completed at their internship site. Students interested in internships within the Mathematics and Statistics Department should work with their advisor and/or faculty internship coordinator to discuss the process for your specific major.

Full course description for Mathematics Internship

Internships offer students opportunities to gain deeper knowledge and skills in their chosen field. Students are responsible for locating their own internship. Metro faculty members serve as liaisons to the internship sites¿ supervisors and as evaluators to monitor student work and give academic credit for learning. Students are eligible to earn 1 credit for every 40 hours of work completed at their internship site. Students interested in internships within the Mathematics and Statistics department should work with their advisor and/or faculty internship coordinator to discuss the process for your specific major.

Full course description for Data Science Internship

This is an introductory course in real analysis. Starting with a rigorous look at the laws of logic and how these laws are used in structuring mathematical arguments, this course develops the topological structure of real numbers. Topics include limits, sequences, series and continuity. The main goal of the course is to teach students how to read and write mathematical proofs.

Full course description for Introduction to Analysis

This course develops the more advanced mathematical tools necessary for an in-depth analysis of dynamic models. Topics include first order differential equations, first order systems, linear systems, nonlinear systems and numerical methods.

Full course description for Ordinary Differential Equations

Starting with an introduction to the complex plane, this course covers holomorphic functions and power series, Cauchy's Theorem, contour integration and its applications.

Full course description for Complex Variables

This course covers the theory of initial and boundary value problems for linear parabolic, elliptic, and hyperbolic partial differential equations. Topics may include first order equations, second order equations, separation of variables, the Sturm-Liouville problem, transform methods, Green's functions, Fourier series, numerical methods and modeling applications.

Full course description for Partial Differential Equations

By extending the familiar concepts of arithmetic, this course introduces abstract algebraic structures. Topics include an introduction to number theory; group theory, including the classification of all finite abelian groups; rings, integral domains, and fields.

Full course description for Abstract Algebra

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 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

This is the first course of a two semester sequence covering the fundamental concepts of physics. This course covers Newton's laws of motion, work, energy, linear momentum, rotational motion, gravity, equilibrium and elasticity, periodic motion, fluid mechanics, temperature, heat, and the laws of thermodynamics. Laboratories emphasize application of physics concepts and quantitative problem solving skills. Intended for science majors and general education students with strong mathematical background.

Full course description for Calculus Based Physics I

This is the second course of a two semester sequence covering the fundamental concepts of physics. This course covers oscillatory motion, waves, superposition and interference of waves, diffraction, electricity and magnetism, electric circuits, light, mirrors and lenses. Laboratories emphasize application of physics concepts and quantitative problem solving skills. Intended for science majors.

Full course description for Calculus Based Physics II

This course introduces the concepts of thermodynamics. Topics include the first law of thermodynamics, the second law of thermodynamics, entropy, statistical mechanics, specific heat capacities of gases and solids, efficiency and the Carnot cycle, chemical potential, chemicals and phase equilibriums, etc. Applications explored will include the behavior of gases and the operation of heat engines. Laboratories emphasize real world applications of the concepts and problem solving skills taught in this course.

Full course description for Thermodynamics

This course covers special relativity, elementary quantum theory, atomic structure and spectra. It is intended for students pursuing chemistry and physics major/minor.

Full course description for Modern Physics

This course provides laboratory activities to test the major theories that lead to the understanding of atomic structure and their spectra. It is intended for students pursuing chemistry and physics major/minor.

Full course description for Modern Physics Lab

Covers concepts and methods in the definition, creation and management of databases. Emphasis is placed on usage of appropriate methods and tools to design and implement databases to meet identified business needs. Topics include conceptual, logical and physical database design theories and techniques, such as use of Entity Relationship diagrams, query tools and SQL; responsibilities of data and database administrators; database integrity, security and privacy; and current and emerging trends. Use of database management systems such as MySQL. Coverage of HCI (Human Computer Interaction) topics and development of front ends to databases with application of HCI principles to provide a high level usability experience. Overlap: ICS 311T Database Management Systems.

Full course description for Database Management Systems

Exploration of the design and implementation of data structures and algorithms fundamental to computer systems and applications and to software engineering. Topics include trees, graphs, basic analysis of algorithmic complexity, fundamental questions of computability, and introduction to the algorithmic basis of intelligent systems. Programming projects.

Full course description for Algorithm Design and Analysis

This course is a comprehensive introduction to the principal features and design of programming languages. It provides a comparative study of programming paradigms including structured programming, object-oriented programming, functional programming and logic programming. This course is a survey of programming concepts and constructs including data types, control structures, subprograms and parameter passing, nesting and scope, derived data types, input and output, and dynamically varying structures. Also covered are the principles of lexical and semantics analysis.

Full course description for Organization of Programming Languages

System development using the object-oriented paradigm. Programming topics include: inheritance, polymorphism, dynamic linking, generics, Graphical User Interfaces, and data serialization. Use-case and state-based approaches for the discovery of conceptual classes. Design principles including the Liskov Substitution Principle, Open Closed Principle, and Stable Dependencies Principle. Design patterns such as Factory, Iterator, Adapter, Facade, Bridge, Observer, Command, State, Composite, Singleton, and Mediator. Employment of design principles, design patterns, and the Model View Controller in the design of object-oriented systems. System implementation. Refactoring. Group projects.

Full course description for Object-Oriented Design and Implementation

Covers the concepts and approaches that are used by big-data systems. Topics covered include: fundamentals of big data storage and processing using distributed file systems, the map-reduce programming paradigm, and NoSQL systems. Students will gain hands-on experience by implementing solutions to big data problems using tools like Hadoop, Apache Pig Latin, Hive, Impala, MongoDB, Cassandra, Neo4J, or Spark.

Full course description for Big Data Storage and Processing

Covers design and development of parallel and distributed algorithms and their implementation. Topics include multiprocessor and multicore architectures, parallel algorithm design patterns and performance issues, threads, shared objects and shared memory, forms of synchronization, concurrency on data structures, parallel sorting, distributed system models, fundamental distributed problems and algorithms such as mutual exclusion, consensus, and elections, and distributed programming paradigms. Programming intensive.

Full course description for Parallel and Distributed Algorithms

Principles and practices of the OSI and TCP/IP models of computer networks, with special emphasis on the security of these networks. Coverage of general issues of computer and data security. Introduction to the various layers of network protocols, including physical, data link, network, and transport layers, flow control, error checking, and congestion control. Computer system strengths and vulnerabilities, and protection techniques: Topics include applied cryptography, security threats, security management, operating systems, network firewall and security measures. Focus on secure programming techniques. Programming projects.

Full course description for Networks and Security

Principles, techniques, and algorithms for the design and implementation of modern operating systems. Topics include operating system structures, process and thread scheduling, memory management including virtual memory, file system implementation, input output systems, mass storage structures, protection, and security. Students will implement process, memory, and file management algorithms.

Full course description for Operating Systems

This course introduces the application to financial decision-making of mathematics, statistics, economic theory, and accounting procedures. The two central ideas are time value of money and the relationship between expected return and risk, and how these ideas are used to value bonds, stocks, and other financial securities, and to make capital investment decisions.

Full course description for Principles of Finance

Business Intelligence is the user-centered process of exploring data, data relationships and trends - thus helping to improve overall decision making for enterprises. This course addresses the iterative processes of accessing data (ideally stored in the enterprise data warehouse) and analyzing data in order to derive insights and communicate findings. Moreover, the course also addresses the use of software tools for analysis and visualization of data, especially report design along with the use of dashboards.

Full course description for Business Intelligence and Analytics

This course builds upon prior coursework related to analytical thinking and competence in business intelligence and analytics approaches. The course serves to advance and refine expertise on theories, approaches, tools and techniques related to prediction and forecasting in business. Students will gain practical experience in analyzing a variety of business analytics cases and scenarios using industry-standard tools and platforms. The course prepares learners to help organizations make more effective business decisions based on the gathering and analysis of data. The design and delivery of the course enables an engaged learning environment.

Full course description for Predictive Analytics