# Department of Mathematics and Statistics

## Course Descriptions

#### Undergraduate

Students are expected to possess and be able to operate a basic scientific calculator if they enroll in mathematics courses.

**MAT 9 Developmental Mathematics**A review of fundamental topics of arithmetic needed for a study of algebra. This course will cover the following topics: addition, subtraction, multiplication, and division of fractions; use of decimals and percent; estimation; addition, subtraction, multiplication and division of real numbers; exponents; order of arithmetic operations; distributive property; combining like terms; substitution to evaluate expressions and formulas; grouping symbols; addition and multiplication principle; equations with fractions; formulas; sets; writing and graphing inequalities; solving inequalities and problem solving. Successful completion of an exit exam at a C level or higher is required.

**Credit earned in MAT 9 does not apply or accumulate toward any degree program at the University of Southern Maine. It does carry "institutional" credit, which means the credits count toward financial aid, athletic, or residential requirements, but not toward graduation.**

**MAT 100 Mathematics Bridge**A course covering foundational math concepts. Topics include study skills, numeracy, ratio and proportion, basic algebra and graphing, rational and radical expressions, and an introduction to probability. Students will engage in active learning in the classroom. A grade of C or better is necessary to take subsequent math courses. Cr 3.

**MAT 101 Algebraic Bridge**

This course reviews and reinforces the basic arithmetic and algebra skills and concepts needed for entry into the University's general education pathways. The course is based on student learning outcomes and uses mastery learning pedagogy. Prerequisite: grade of C or higher in MAT 9 or MAT 100, or appropriate placement test score. Cr 4.

**MAT 105 Mathematics for Quantitative Decision Making**

This is an introductory course in quantitative literacy that, through lecture and lab, emphasizes critical thinking, mathematical reasoning, and technological tools. Topics are selected to develop an awareness of the utility of mathematics in life and to instill an appreciation of the scope and nature of its decision-making potential. Prerequisite: grade of C or higher in MAT 100 or MAT 101, or appropriate placement test score. Cr 4.

**MAT 108 College Algebra**

A survey of the mathematics needed for Pre-Calculus and related analytical coursework. The topics include linear, quadratic, and absolute value equations and inequalities; graphs; and functions (linear, quadratic, polynomial, rational, exponential, and logarithmic). Prerequisite: grade of C or higher in MAT 101, or appropriate placement test score. Cr 4.

**MAT 120 Introduction to Statistics**

An introduction to probability and statistics through lecture and lab. Particular topics include random variables and their distributions, methods of descriptive statistics, estimation and hypothesis testing, regression, and correlation. Prerequisite: grade of C or higher in MAT 100 or MAT 101, or appropriate placement test score. Cr 4.

**MAT 131 Number Systems for Elementary Teachers**

This is the first course in a three-course sequence in mathematics recommended by the Committee on the Undergraduate Mathematics Program of the Mathematical Association of America for prospective primary and elementary teachers. Major emphasis is placed on an intuitive approach to the real number system and its subsystems. Prerequisite: grade of C or higher in MAT 101, or appropriate placement test score. Cr 3.

**MAT 132 Quantitative Reasoning for Elementary School Teachers**

This course focuses on probability and statistical content for elementary school teachers. It is designed to help future teachers see the relevance of mathematics and statistics to their and their future students' world and in becoming critical, questioning citizens in an increasingly quantitative world. Prerequisite: MAT 131. Cr 4.

**MAT 140 Pre-Calculus Mathematics**

A brief review of elementary algebra followed by a study of the algebraic, exponential, logarithmic, and trigonometric functions. Prerequisite: MAT 108 or appropriate score on the College Level Math exam. Cr 3.

**MAT 145 Discrete Mathematics I**

This course is an introduction to discrete mathematics necessary for a study of computer science. Topics will include a study of functions, sets, basic logic systems, and combinatorics. Prerequisite: MAT 108 or MAT 140 or MAT 152, or permission of instructor. Cr 3.

**MAT 148 Applied Calculus**

An introduction to limits and differential and integral calculus of algebraic and transcendental functions of one variable. Applications of derivatives and definite integrals with an emphasis on problems from the fields of technology will be introduced. Graphing calculators and computer technology will be used when appropriate. Prerequisite: MAT 140. Cr 3.

**MAT 152 Calculus A**

The first course in a three-semester sequence covering basic calculus of real variables, Calculus A introduces the concept of limit and applies it to the definition of derivative and integral of a function of one variable. The rules of differentiation and properties of the integral are emphasized, as well as applications of the derivative and integral. This course also includes an introduction to the transcendental functions. Prerequisite: MAT 140 or appropriate score on the College Level Math exam. Cr 4.

**MAT 153 Calculus B**

The second course in a three-semester sequence covering basic calculus of real variables, Calculus B includes techniques of integration, indeterminate forms and L'Hopital's Rule, improper integrals, infinite series, conic sections, parametric equations, and polar coordinates. Prerequisite: MAT 152. Cr 4.

**MAT 210 Business Statistics**

This course investigates graphical and numerical methods of descriptive statistics; basic probability; discrete and continuous random variables and their distributions (binomial, hypergeometric, Poisson, uniform, exponential, and normal); sampling distributions; estimation; tests of hypotheses; and other selected topics. Applications will be chosen primarily from business. Prerequisite: MAT 108 (or concurrent). Cr 4.

**MAT 220 Statistics for the Biological Sciences**

This course treats basic statistical methods as applied to the biological sciences. The topics emphasized are descriptive statistics, discrete and continuous distributions, statistical estimation, hypothesis testing procedures, chi-square methods (goodness of fit and two-way tables), analysis of variance, and simple and multiple regression. Students will use at least one computer-based statistical package. Prerequisite: MAT 152. Cr 4.

**MAT 231 Algebra for Elementary Teachers**

The second course in a three-course sequence in mathematics recommended by the Committee on the Undergraduate Mathematics Program of the Mathematical Association of America for prospective primary and elementary teachers. Emphasis is upon the properties of operations in several different algebraic systems. Equations are studied in finite systems as well as in conventional algebra. Prerequisite: MAT 131. Cr 3.

**MAT 232 Geometry for Elementary Teachers**

The third course in a three-course sequence in mathematics recommended by the Committee on the Undergraduate Mathematics Program of the Mathematical Association of America for prospective primary and elementary teachers. Emphasis is upon constructions, congruence, parallelism, and similarity. Direct and indirect methods of proof are studied, but the main approach is intuitive. Prerequisite: MAT 131. Cr 3.

**MAT 242 Applied Problem Solving**

This course is designed to examine mathematical concepts and apply them to solving modeling problems in various contexts. The focus will be on the Common Core State Standards mathematical concepts and practices, in particular, mathematical modeling. Students will formulate essential questions, gather and organize data, discover patterns, and interpret and communicate information verbally and in writing. Prerequisite: MAT 108. Cr 3.

**MAT 252 Calculus C**

The third course in a three-semester sequence covering basic calculus of real variables, Calculus C includes vectors, curves and surfaces in space, multivariate calculus, and vector analysis. Prerequisite: MAT 153. Cr 4.

**MAT 264 Statistical Software Packages**

The overall objective of the course is to enable students to develop the ability to use SAS and R for basic statistical analyses, and to prepare for more advanced uses of SAS and R. A number of topics concerning computing and statistics will be covered in both SAS and R. Topics include data acquisition, cleaning, and management using SAS; reading data into SAS from various sources, recoding variables, subsetting and merging data, exporting results in other formats. Graphical procedures, basic descriptive and inferential statistics. Introduction to SAS macros. Data acquisition, cleaning, and management in R; use of regular expressions; functional and object-oriented programming; graphical, descriptive, and inferential statistical methods; random number generation; Monte Carlo methods including resampling, randomization, and simulation. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**MAT 281 Introduction to Probability**

This course will cover basic concepts of probability, including discrete and continuous random variables and their distributions, moment generating functions, and bivariate random variables and their distributions. Some basic sampling distributions will also be discussed. Prerequisite: MAT 153. Cr 3.

**MAT 282 Statistical Inference**

This course will examine various statistical methods and applications such as point and interval estimation; methods of estimation including methods of moments, maximum likelihood and least-squares method; hypothesis testing; simple and multiple linear regression; and one-factor and two-factor ANOVA. Some statistical packages may be used throughout the course. Prerequisite: MAT 281 or permission of instructor. Cr 3.

**MAT 290 Foundations of Mathematics**

Selected topics in set theory, symbolic logic, and methods of proofs needed in more advanced mathematics courses. Prerequisite: MAT 153 or permission of instructor. Cr 4.

**MAT 295 Linear Algebra**

An introduction to the theory of vector spaces and linear transformations. Particular topics will include the study of systems of linear equations, matrices, determinants, Euclidean vector spaces, inner product spaces, and theory of diagonalization. Prerequisite: MAT 153 or permission of instructor. Cr 4.

**MAT 350 Differential Equations**

A study of various methods for solving ordinary differential equations, including series methods and Laplace transforms. The course also introduces systems of linear differential equations, Fourier series, and boundary value problems. Prerequisite: MAT 252. Cr 4.

**MAT 352 Real Analysis**

Limits, continuity, differentiation, and integration of functions of one or more real variables, infinite series, uniform convergence, and other selected topics. Prerequisites: MAT 252 and MAT 290 or permission of instructor. Cr 3.

**MAT 355 Complex Analysis**

A study of the complex number system and its applications: differentiation and integration of complex-valued functions, the Cauchy integral theorem and formula, Taylor and Laurent series, singularities and residues, conformal mappings. Prerequisites: MAT 252 and MAT 290 or permission of instructor. Cr 3.

**MAT 364 Numerical Analysis**

A study of the theory and application of computational algorithms for interpolation, equation solving, matrix methods, integration, and error analysis. Prerequisites: MAT 252, MAT 295, and COS 160; or permission of instructor. Cr 3.

**MAT 366 Deterministic Models in Operations Research**

Formulation and analysis of mathematical models for the optimal solution of decision-making problems under certainty. Linear programming; the simplex method, duality and sensitivity analysis. Network analysis: shortest paths, minimal spanning tree, network flows. Introduction to nonlinear optimization: convex programming, Kuhn-Tucker conditions. Applications to pricing, allocation, production planning, transportation, and scheduling problems. Prerequisites: MAT 153 and MAT 295. Cr 3.

**MAT 371 College Geometry**

Selected topics from Euclidean geometry. Prerequisite: MAT 290 or permission of instructor. Cr 3.

**MAT 380 Probability and Statistics**

This course explores concepts and techniques of collecting and analyzing statistical data, examines some discrete and continuous probability models, and introduces statistical inference, specifically, hypothesis testing, and confidence interval construction. Not for mathematics major credit. Prerequisite: MAT 153. Cr 3.

**MAT 383 System Modeling and Simulation**

This course is designed to introduce the fundamental elements of successful system modeling using simulation. Applications to computer, communications, and inventory systems, as well as to traditional engineering problems, will be discussed. Topics include model validation and verification, input/output analysis, and the generation of various types of random data. Students are required to conduct a simulation project in their area of interest using a simulation language. Prerequisite: MAT 281 or MAT 380 or permission of instructor. Cr 3.

**MAT 386 Sampling Techniques**

Simple random sampling, stratified random sampling, sampling for proportions, estimation of sample size, systematic sampling, multistage sampling, regression and ratio estimates, non-sampling error. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**MAT 387 Introduction to Applied/Biostatistical Methods**

This is an introductory statistical methodology course with emphases on applications in biological and health sciences. Topics include distributional theory, estimation and testing hypotheses, rank-based and related distribution-free tests, large sample chi-squared tests, analysis of rates and proportions, paired sample methods, permutation and re-sampling methods. Writing formal statistical reports of projects based on real-life data is a key component of the course. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**MAT 392 Theory of Numbers**

Basic course in number theory, including such topics as divisibility properties of integers, prime numbers, congruences, multiplicative number-theoretic functions, and continued fractions. Prerequisite: MAT 290 or permission of instructor. Cr 3.

**MAT 395 Abstract Algebra**

Algebraic structures, such as groups, rings, integral domains, and fields. Prerequisite: MAT 290 or permission of instructor. Cr 3.

**MAT 460 Mathematical Modeling**

An introduction to the process of formulating problems in mathematical terms, solving the resulting mathematical model and interpreting the results and evaluating the solutions. Examples will be chosen from the behavioral, biological, and physical sciences. Prerequisites: junior or senior standing, some elementary calculus including differentiation and integration, elementary probability, and some computer programming experience. Cr 3.

**MAT 461 Stochastic Models in Operations Research**

This course applies probabilistic analysis to such non-deterministic models as queuing models, inventory control models, and reliability models. Additional topics include simulation, elements of dynamic programming, and Markov decision analysis. Prerequisite: MAT 281 or MAT 380 or permission of instructor. Cr 3.

**MAT 470 Non-Euclidean Geometry**

Development of one or more of the non-Euclidean geometries. Prerequisite: MAT 371 or permission of instructor. Cr 3.

**MAT 484 Design and Analysis of Experiments**

This course is intended to acquaint students with such standard designs as one-way, two-way, and higher-way layouts, Latin-square and orthogonal Latin-square designs, BIB designs, Youdeen square designs, random effects, and mixed-effect models, nested designs, and split-plot designs. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**MAT 485 Introduction to Applied Regression**

This is an introduction to linear regression and time series analysis. Topics include model building, model diagnostics using residual analysis, choice of models, model interpretation, linear time series models, stationary processes, moving average models, autoregressive models, and related models. Technical writing for project reports is required for this course. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**MAT 486 Introduction to Big Data Analytics**This is an introductory course of big data and predictive analytics covering foundational techniques and tools required for data science. The course focuses on concepts, principles, and techniques applicable to industry and establishes a baseline that can be enhanced by further formal training and additional real-world experience. Topics include basic database management systems, data pre-processing, association rules, decision trees, naive Bayes, clustering, and memory-based reasoning. The class follows a learning-by-doing approach in which the students will complete projects on real-world data sets. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**MAT 488 Introduction to Data Mining**This is an introductory course in statistical data mining. The course emphasizes the understanding and application of data mining methods and algorithms. Topics include data preparation, exploratory data analysis and visualization, cluster analysis, logistic regression, decision trees, association rules, model assessment, and other topics. Applications to real-world data will be illustrated using standard computer packages. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**MAT 490 Topology**

An introduction to fundamental concepts in topology, including topological spaces, mappings, convergence, separation and countability, compactness, connectedness, metrization, and other selected topics. Prerequisites: MAT 252 and MAT 290 or permission of instructor. Cr 3.

**MAT 492 Graph Theory and Combinatorics**

This course is designed to acquaint students with some fundamental concepts and results of graph theory and combinatorial mathematics. Applications will be made to the behavioral, managerial, computer, and social sciences. Prerequisite: MAT 290 or permission of instructor. Cr 3.

**MAT 496 Introduction to Data Science**This is an introductory course in data science. It will cover three major components in data science: database management, analytics, and communication and visualization. Topics include data manipulation at scale, machine learning and data mining algorithms, statistical modeling, and information visualization. After completing this course, students will be able to work with large datasets and perform predictive analytics using a range of tools. Course projects will cover all phases of producing data products from the raw data. Prerequisites: MAT 281 and MAT 282, or permission of instructor. Cr 3.

**MAT 497 Independent Study in Mathematics**

An opportunity for juniors and seniors who have demonstrated critical and analytical capability to pursue a project independently, charting a course and exploring an area of interest within their major field. Prerequisites: junior or senior standing, permission of instructor, and permission of the Department Chair. Cr 1-3.

**MAT 498 Topics**

Selected topics in advanced mathematics. Prerequisite: permission of instructor. Cr 3.

#### Mathematics Education

**MME 400 Elementary Mathematics Methods**

This course is designed for those preparing to be elementary and middle school mathematics teachers and provides experiences to develop and apply mathematical content and pedagogical knowledge and skills. The primary focus of this course is on how to create positive learning communities that support all students in developing a deep understanding of mathematical concepts and procedures. Major areas of focus include: creating problem-based learning experiences; creating effective, supportive learning environments; the appropriate and effective use of models and tools for promoting understanding of mathematical ideas, including the use of technology and manipulatives; understanding learning progressions of important mathematical ideas; promoting the National Council of Teachers’ Process Standards; supporting students’ understanding of the Common Core Standards and Practices; assessing and building on students’ mathematical understandings; creating adaptive learning materials to differentiate instruction for individuals and groups of learners. Prerequisite: permission of instructor. Cr 3.

**MME 434 Secondary Mathematics Methods**

This course focuses on research-based, best practices in teaching mathematics in grades 7-12. It is designed for those preparing to be middle school and secondary mathematics teachers and provides experiences to develop and apply mathematical content and pedagogical knowledge and skills. A primary focus of this course is on how to create positive learning communities that support all students in developing a deep understanding of mathematical concepts and procedures. Major areas of emphasis include: creating problem-based learning experiences; implementing high-level mathematical tasks; creating effective, supportive learning environments; the appropriate and effective use of models and tools for promoting understanding of mathematical ideas, including the use of technology; promoting the National Council of Teachers’ Process Standards; supporting students’ understanding of the Common Core Standards and Practices; assessing and building on students’ mathematical understandings. Prerequisite: permission of instructor. Cr 3.

#### Graduate

**MME 554 Secondary Mathematics Methods**

This course focuses on research-based, best practices in teaching mathematics in grades 7-12. It is designed for those preparing to be middle school and secondary mathematics teachers and provides experiences to develop and apply mathematical content and pedagogical knowledge and skills. A primary focus of this course is on how to create positive learning communities that support all students in developing a deep understanding of mathematical concepts and procedures. Major areas of emphasis include: creating problem-based learning experiences; implementing high-level mathematical tasks; creating effective, supportive learning environments; the appropriate and effective use of models and tools for promoting understanding of mathematical ideas, including the use of technology; promoting the National Council of Teachers’ Process Standards; supporting students’ understanding of the Common Core Standards and Practices; assessing and building on students’ mathematical understandings. Prerequisite: permission of instructor. Cr 3.

**STA 501 Ethical Issues in Biostatistics**

This course examines a variety of ethical controversies in biotechnology, medicine, and the environment. It also examines the major ethical principles in conducting biomedical research including ethical aspects related to the production and use of biomedical statistical analyses. Cr 2.

**STA/OPR 561 Deterministic Models in Operations Research**

Formulation and analysis of deterministic models in operations research, linear programming, integer programming, project management, network flows, dynamic programming, non-linear programming, game theory, and group projects on practical problems from business and industry. Prerequisite: MAT 152 or MAT 295 or permission of instructor. Cr 3.

**STA/OPR 562 Stochastic Modeling in Operations Research**

Formulation and analysis of stochastic models in operations research, Markov chains, birth-death models, Markov decision models, reliability models, inventory models, applications to real-world problems, and group projects on practical problems from business and industry. Prerequisite: MAT 281 or MAT 380 or permission of instructor. Cr 3.

**STA/OPR 563 System Modeling and Simulation**

Basic simulation methodology, general principles of model building, model validation and verification, random number generation, input and output analysis, simulation languages, applications to computer and communication networks, manufacturing, business, and engineering will be considered, and group projects on practical problems from business and industry. Prerequisite: MAT 281 or MAT 380 or permission of instructor. Cr 3.

**STA/OPR 564 Queuing Networks**

Queuing and stochastic service systems, birth-death processes, Markovian queues, open and closed Jackson networks, priority queues, imbedded Markov chain models, optimal control and design, stochastic scheduling, applications to computer and communication networks, manufacturing, business, and engineering will be considered, and projects on practical problems from business and industry. Prerequisite: MAT 281 or MAT 380 or permission of instructor. Cr 3.

**STA 574 Statistical Programming**

This course focuses on statistical programming using software SAS and R. Emphasis will be placed on the data manipulation, including reading, processing, recoding, and reformatting of data. The approach will be to teach by example, with an emphasis on hands-on learning. Topics include, but are not limited to, data management, database programming, statistical graphics, generating statistical reports, Basic statistical procedures (routine), modifying and creating MACROs (Routines), and R functions for non-standard statistical methods. The course will also cover the basic SQL statements with SAS PROC SQL and use them to optimize SAS programs. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**STA/OPR 575 Graduate Internship and Writing**

The course is intended to give students work experience with statistical data analysis through paid or unpaid internship opportunities. The student is expected to spend a minimum of ten weeks working with area businesses on statistical problems approved by the Graduate Committee. The student will submit to the Graduate Committee a formal written report on the internship experience. The report format should adhere to all the elements of a formal project/ thesis. At least one oral presentation to the public is expected before the student receives a pass/fail grade. Students within the Biostatistics track are required to take three credits; two for the internship experience and one for the writing component. Cr var.

**STA 580 Applied Statistical/Biostatistical Methods**

Basics in distribution theory (focus on CLT and sampling distributions); standard one-, two-sample problems (both parametric and nonparametric); one-, two-way ANOVA; estimation and testing theory (focus on normal theory and the principles of likelihood), various chi-square tests (Wald, Likelihood ratio, and Score tests); and analysis of contingency tables. Prerequisites: MAT 153 and MAT 282. Cr 3.

**STA 583 Sample Survey Design and Analysis**

In this course, students will develop an understanding of alternative probability sample designs and the statistical and practical factors that impact design choices. Develop the ability to select an estimator for a population parameter and an estimator of its variance, given a sample design and auxiliary information (covariates). Introduce statistical principles and methods used to study disease and its prevention or treatment in human populations in clinical trials, including phase I to IV clinical trials. Ways of treatment allocation that will ensure valid inference on treatment comparison will be discussed. Other topics include sample size calculation, early stopping of a clinical trial, and noncompliance. Prerequisite: MAT 282. Cr 3.

**STA 584 Advanced Design and Analysis of Experiments**

Topics covered include one-way and two-way layouts, factorial experiments, fractional replications in factorial experiments, BIB and PBIB designs, and repeated measure design. Prerequisite: MAT 282. Cr 3.

**STA 585 Linear Models and Forecasting**

This is an introductory regression and forecasting modeling course. Topics include basic concepts of linear models and forecasting, simple and multiple linear regression, model building and diagnostics, time series regression and smoothing, and forecasting time series with ARIMA (Autoregressive Integrated Moving Average) and Box-Jenkins models. Prerequisite: MAT 282. Cr 3.

**STA 586 Predictive Modeling with Big Data**This is an introductory course of big data and predictive analytics covering foundational techniques and tools required for data science. The course focuses on concepts, principles, and techniques applicable to industry and establishes a baseline that can be enhanced by further formal training and additional real-world experience. Topics include basic database management systems, data pre-processing, association rules, decision trees, naive Bayes, clustering, memory-based reasoning, support vector machine, and some ensemble learning algorithms. The class follows a learning-by-doing approach in which the students will complete projects on real-world data sets. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**STA 588 Introduction to Statistical Data Mining**This is an introductory course in statistical data mining and machine learning. The course emphasizes the understanding and application of data mining and machine learning methods and algorithms. Topics include both supervised and unsupervised learning algorithms for clustering and classification. Some advanced algorithms such as boosting, bootstrap aggregation, random forests, shrinkage regression, principal component, and factor analysis will also be covered. Applications to real-world data will be illustrated using standard computer packages. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**STA/OPR 590 Master's Project/Thesis**

The project must be approved by the Graduate Committee in advance. Offered only as a pass/fail course. Prerequisites: full graduate standing and faculty approval. Cr 6.

**STA 591 Topics in Biostatistics**

The course will be offered on demand. Based on students' interests, the course may cover one or more of the following topics: clinical trials, computer-intensive statistical methods, statistical methods in bioinformatics, environmental statistics, or a combination of these topics. Prerequisites: full graduate standing and faculty approval. Cr 3.

**STA 596 Practical Data Science**

This is an introductory course in data science. It will cover a full technical pipeline from database management to data analytics and the final data product. Topics include data manipulation at scale, machine learning and data mining algorithms, statistical modeling, information visualization, and special topics chosen from text mining and social network analysis. After completing this course, students will be able to work with large datasets and perform predictive analytics using a range of tools. Course projects will include cleaning, processing, and analyzing data at scale, along with formal technical writing with appropriate data visualizations. Prerequisite: MAT 282 or permission of instructor. Cr 3.

**STA/OPR 597 Independent Study**

An opportunity for graduate students to pursue areas not currently offered in the graduate curriculum. Cr 3.