The program is designed to prepare students to join 21st century business and industry in their growing needs for statistical analyses. An optimal mix of mathematical and computational background enables the graduates to contribute effectively in the educational institutions.
Program Requirements
Common Core
(0-8) credits
Simple and multiple regression, correlation, analysis of variance and covariance.
Prerequisites:
MATH 354 or STAT 354 or (MATH 455 or MATH 555) or (STAT 455 or STAT 555) with "C" (2.0) or better or consent.
A mathematical approach to statistics with derivation of theoretical results and of basic techniques used in applications. Includes probability, continuous probability distributions, multivariate distributions, functions of random variables, central limit theorem, and statistical inference. Same as MATH 555.
Prerequisites:
MATH 223 with "C" (2.0) or better or consent.
A mathematical approach to statistics with derivation of theoretical results and of basic techniques used in applications, including sufficient statistics, additional statistical inference, theory of statistical tests, inferences about normal models, and nonparametric methods. Same as MATH 556.
Prerequisites:
(MATH 455 or MATH 555) or (STAT 455 or STAT 555) with "C" (2.0) or better or consent.
A Common Core course is waived if credit has been received for an equivalent course with grade of C or better at the undergraduate or graduate levels. All Required Common Core courses, or their equivalents, must be completed before graduation. College of Graduate Study and Research Transfer policy applies.
Restricted Electives
Restricted Electives
500 Level Requirement - Choose 6 - 16 Credit(s).
The topology of Euclidean spaces, norms, classical inequalities, local and global properties of continuous functions, preservation of compactness and connectedness, sequences in Euclidean space and sequences of functions.
Prerequisites:
MATH 223 and MATH 290 with "C" (2.0) or better or consent.
This course presents topics from mathematical analysis of both discrete and continuous models taken from problems in the natural sciences, economics, and resource management.
Prerequisites:
MATH 223 and MATH 247 with "C" (2.0) or better or consent.
An in-depth study of linear operators and their related spaces, dimension, rank, matrix representation of linear operators, special matrices, determinants, eigenvectors, and eigenvalues.
Prerequisites:
MATH 345 with "C" (2.0) or better or consent.
This course provides an introduction to techniques and analysis involved with solving mathematical problems using technology. Topics included are errors in computation, solutions of linear and nonlinear equations, numerical differentiation and integration, and interpolation.
Prerequisites:
MATH 122 and MATH 247 with "C" (2.0) or better or consent.
Randomized complete block design, Latin squares design, Graco- Latin squares design, balanced incomplete block design, factorial design, fractional factorial design, response surface method, fixed effects and random effects models, nested and split plot design.
Prerequisites:
MATH 354 or STAT 354 or (MATH 455 or MATH 555) or (STAT 455 or STAT 555) with "C" (2.0) or better or consent.
Topics include: sampling distributions, means and variances; bias, robustness and efficiency; random sampling; systematic sampling methods including stratified random, cluster and two-state sampling; and ratio, regression, and population size estimation. Suitable software, such as MATLAB, R, SAS, etc., is introduced.
Prerequisites:
Either MATH/STAT 354 or both STAT 154 and MATH 121 with "C" (2.0) or better, or consent.
Topics on multivariate analysis for discrete data, including two/higher dimensional tables; models of independence; log linear models; estimation of expected values; model selection; and logistic models, incompleteness and regression. Suitable statistical software, such as MATLAB, R, SAS, etc., is introduced.
Prerequisites:
Either MATH/STAT 354 or both STAT 154 and MATH 121 with "C" (2.0) or better, or consent.
Topics include derivation and usage of nonparametric methods in univariate, bivariate, and multivariate data; applications in count, score, and rank data; analysis of variance for ranked data; and regression estimation. Suitable software, such as MATLAB, R, SAS, etc., is introduced.
Prerequisites:
Either MATH/STAT 354 or both STAT 154 and MATH 121 with "C" (2.0) or better, or consent.
600 Level Requirement - Choose 15 - 26 Credit(s).
Applications of discrete and continuous mathematics to deterministic problems in the natural sciences, computer science, engineering, and economics. Applied problems will be developed within the mathematical framework of dimensional analysis, asymptotic analysis, perturbation theory, stability, and bifurcation.
Prerequisites:
MATH 321 and (MATH 417 or MATH 517) and (MATH 447 or MATH 547) or consent.
Can be used for any graduate level applied mathematics course not offered as a regular course. Distinct offerings may be repeated for credit.
Prerequisites:
(MATH 417 or MATH 517) and (MATH 422 or MATH 522) and (MATH 447 or MATH 547) or consent.
Optimal conditions for constrained and unconstrained optimization problems, and a comprehensive description of the most powerful, state-of-the-art, techniques for solving continuous optimization problems. Large-scale optimization techniques are emphasized in the course.
Prerequisites:
MATH 517 and MATH 547
This course is an in-depth study of solving ordinary differential equations and partial differential equations numerically. Runge-Kutta methods and general multi-step methods are developed for ordinary differential equations. Finite Difference Method and Finite Element methods are developed for partial differential equations. Error control and step size changing for both stiff and non-stiff equations are analyzed.
Prerequisites:
MATH 321 and (MATH 470 or MATH 570) or consent.
This course is an in-depth study of solving algebraic eigenvalue problems, least-square problems, direct and iterative methods for solving linear systems, and their applications.
Prerequisites:
(MATH 447 or MATH 547) and (MATH 470 or MATH 570) or consent.
Bayesian Statistics is an alternative to Frequentist statistics. Bayesian inference uses probability for both hypotheses and data. In Bayesian statistics, population parameters are considered random variables having probability distributions. The probabilities measure a degree of belief in the parameters. Bayes¿ theorem is used to reformulate the beliefs using observed data. This course introduces the Bayesian approach to statistical inference and describes effective approaches to Bayesian modeling and computation.
Prerequisites:
MATH/STAT 455/555 and STAT 450/550, or consent
Most statistical analysis and modeling techniques involve assumptions about the independence of the data. However, many real life data occur in the form of time series where observations are dependent. In this course, we will concentrate on both univariate and multivariate time series analysis and model building strategies with time dependent data. Available software will be used to complete the data analysis projects with a balance between theory and applications.
Prerequisites:
MATH/STAT 455/555 and MATH/STAT 450/550, with "C" (2.0) or better, or consent.
Matrix theory, multivariate normal distribution of quadratic forms, estimation and hypothesis testing in the general linear model, and applications of linear models.
Prerequisites:
MATH/STAT 455/555 and STAT 450/550 with "C" (2.0) or higher, or consent.
Statistical tools used to analyze data in biological and medical research. Topics covered are Statistical Theory, Concepts of Statistical Inference, Regression and Correlation Methods, Analysis of Variance, Survival Analysis and Study Designs. Applications to medical problems.
Prerequisites:
STAT 450/550 with "C" (2.0) or higher, or consent.
This course will cover the basic concepts of big data with an emphasis on the statistical techniques for analyzing structured and unstructured data. Students will learn concepts, techniques and tools that are necessary for working with the various facets of data science practice, including data collection and integration, exploratory data analysis, predictive modeling, descriptive modeling, data product creation, evaluation, and effective communication. The course has applications across many disciplines such as engineering, computer science, statistics, mathematics, economics and management. Prerequisite: MATH 247 and STAT 354 or instructor consent
Prerequisites:
STAT 450/550 with "C" (2.0) or higher, or consent.
A graduate course in a particular area of statistics not regularly offered. May be repeated for credit on each new topic.
Prerequisites:
none
Statistical package programs used in data collection, transformation, organization, summarization, interpretation and reporting, statistical description and hypothesis testing with statistical inference, interpreting outputs, chi-square, correlation, regression, analysis of variance, nonparametrics, and other designs, accessing and using large files (U.S. Census data, National Health Survey, etc.) Same as COMS 696
Prerequisites:
STAT 450/550 with "C" (2.0) or higher, or consent.
Other Graduation Requirements
Comprehensive Exam: Four courses chosen from STAT 555, STAT 556, STAT 550, STAT 551, MATH 570, MATH 517, or MATH 547. Advisor approval is required.
Thesis or Alternate Plan Paper - Choose 1 - 4 Credit(s).
Research under the supervision of the student's advisor leading to an alternate plan paper.
Prerequisites:
Consent
Research under the supervision of the student's advisor leading to a thesis.
Prerequisites:
Consent
Degree Plan
The Degree Plan is a model for completing your degree in a timely manner. Your individual degree plan may change based on a number of variables including transfer courses and the semester/year you start your major. Carefully work with your academic advisors to devise your own unique plan. * Please meet with your advisor on appropriate course selection to meet your educational and degree goals.
First Year
Fall - 8 Credits
This course provides an introduction to data science, discusses opportunities and challenges associated with data science projects, and develops competencies related to data collection, data cleaning, data analysis, and model evaluation. The course focuses on hands-on exercises using data analytics tools.
Prerequisites:
CIS 223, CIS 340
This course discusses concepts and techniques for design, development and evaluation of user interfaces. Students will learn the principles of interaction design, interaction styles, user-centered design, usability evaluation, input/output devices, design and analysis of controlled experiments and principles of perception and cognition used in building efficient and effective interfaces. Group project work.
Prerequisites:
none
Spring - 10 Credits
Research methodology in general and in computer science. Data and research sources. Analysis of existing research. Preliminary planning and proposals. Conceptualization, design, and interpretation of research. Good reporting. Same as CS 600. Pre-req: An elementary statistics course.
Prerequisites:
none
This course is a continuation of Artificial Intelligence (IT 530). Emphasis is placed on advanced topics and the major areas of current research within the field. Theoretical and practical issues involved with developing large-scale systems are covered. Same as CS 630. Pre-req: IT 530
Prerequisites:
CIS 518
The design of large-scale, knowledge¿based data mining. Emphasis on concepts and application of machine learning using big data. Examination of knowledge representation techniques and problem¿solving methods used to design knowledge¿based systems. Pre-req: instructor permission required
Prerequisites:
CIS 518
Preparation of a master's degree thesis under the direction of the student's graduate advisor. Pre-req: consent
Prerequisites:
none
Second Year
Fall - 7 Credits
This course combines theory with hands-on projects in modern computer vision techniques. It covers both foundational and advanced topics, including deep learning, image processing, feature detection and matching, object detection, segmentation, and recognition. The focus is on the practical application of Convolutional Neural Networks and Generative Adversarial Networks in computer vision, while also exploring image generators and addressing the ethical and legal challenges related to synthetic images.
Prerequisites:
CIS 631
This course prepares students to tackle the ethical, legal, and technical challenges of AI technologies, focusing on issues such as bias, privacy, accuracy, security, and misinformation. Students will explore methods to identify and mitigate bias in AI models, alongside techniques for ensuring data privacy. The course also covers the application of interpretable machine learning and explainable AI techniques and provides a critical examination of data governance frameworks and regulatory guidelines for responsible AI deployment and audits.
Prerequisites:
CIS 518
Preparation of a master's degree thesis under the direction of the student's graduate advisor. Pre-req: consent
Prerequisites:
none
Spring - 7 Credits
This course explores both the theoretical foundations and practical applications of Natural Language Processing (NLP). Key topics include text processing, language models, sequence-to-sequence models, sentiment analysis, named entity recognition, and machine translation. The course also covers advanced techniques for building and fine-tuning large language models, such as recurrent neural networks, transformers, reinforcement learning, and retrieval-augmented generation. Through hands-on projects and case studies, students will apply their knowledge to build, optimize, and deploy NLP applications, while assessing their ethical implications.
Prerequisites:
CIS 631
Preparation of a master's degree thesis under the direction of the student's graduate advisor. Pre-req: consent
Prerequisites:
none
Elective Course in Major *3 credits
Policies
Admission: Preference will be given to applicants with minimum grade point average of 3.0 and a demonstrated ability to consistently perform at a B or better level in upper division mathematics and/or statistics courses. An applicant must also meet the general admission requirements of the College of Graduate Studies and Research.
Financial Assistance: Approximately 30 graduate assistantships are available in the department each year. Graduate assistant duties include teaching or research.
General Program Requirements: All programs require an alternate plan paper or thesis, a comprehensive exam, and an oral defense of the alternate plan paper or thesis. At least 50% of the course work of each program must be at the 600 level. Alternate plan paper and thesis credit are not counted as course work. After completing 16 credits, the student must select an examining committee composed of a minimum of three graduate faculty members. The comprehensive exam may be attempted twice. Under certain circumstances, the third attempt may be granted by appealing to the Graduate Faculty.
Course Application Policy: No course can be used to satisfy more than one program requirement.
Degree Master of Science
Major Credits 34
Total Credits 34
Locations Mankato
Career Cluster Science, Technology, Engineering, Mathematics
