# Department of Mathematics and Statistics

## Course Descriptions

#### Undergraduate

It is expected that students will possess and be able to operate a basic scientific calculator if they enroll in mathematics courses.

**MAT 101 College Readiness Mathematics**

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. A grade of C- or better is needed to meet the University's mathematics readiness requirement. Prerequisites: MAT 009 or appropriate University 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: successful completion of the University's college readiness requirement in mathematics. Cr 4.

**MAT 108 College Algebra**

A more in-depth study of the topics introduced in MAT 101. The emphasis will be on the study of functions (polynomial, rational, logarithmic, exponential) and their graphs. Additional topics may include matrices, sequences, counting techniques, and probability. Through the activity-based lab component, applications and modeling will be stressed. Prerequisite: Successful completion of the University's college readiness requirement in mathematics. 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: successful completion of the University's college readiness requirement in mathematics. 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: successful completion of the University's college readiness requirement in mathematics. Cr 3.

**MAT 140 Pre-Calculus Mathematics**

A brief review of elementary algebra followed by a study of the algebraic, exponential, logarithmic, and trigonometric functions. Prerequisites: successful completion of the University's college readiness requirement in mathematics and two years of high school algebra or MAT 108. 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, MAT 140, 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 will usually include an introduction to the transcendental functions and some use of a computer algebra system. Prerequisite: successful completion of the University's college readiness requirement in mathematics and two years of high school algebra plus geometry and trigonometry or MAT 140. Cr 4.

**MAT 153 Calculus B**

The second course in a three-semester sequence covering basic calculus of real variables, Calculus B usually 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 180/EGN 180 Programming with Mathematica**

This course offers an introduction to programming with Mathematica. This course is designed to introduce students to Mathematica's traditional and unique programming features to help them solve typical computational problems encountered in sciences and engineering effectively and efficiently. This course includes many practical examples and hands-on exercises. Prerequisite: None. Cr 1.

**MAT 181/EGN 181 Computing with Mathematica**

This course offers an introduction to computing with Mathematica. This course is designed to introduce mathematics, science, and engineering students to the basic features of Mathematica, to help them solve typical computational problems encountered in their disciplines effectively and efficiently. This course includes many practical examples and hands-on exercises. Prerequisite: None. Cr 1.

**MAT 201 Teaching Seminar**

A seminar intended to expose students to teaching introductory college mathematics courses. Students will be expected to participate in discussions concerning issues of pedagogy and classroom management. Some classes will be student-led. Cr 1.

**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 (may be taken concurrently). 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 introduce mathematical concepts and apply them to solving problems in various contexts. The focus will be on mathematical ideas required by Maine's Learning Results. Topics include sets, functions, logic, numeration systems, and number theory. Students will formulate key questions, gather and organize data, discover patterns and similarities, and interpret and communicate information. Offered only at Lewiston-Auburn College. 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 260 Technological Tools for the Mathematical Sciences**

MAT 260 is designed for students in mathematics and disciplines which utilize mathematics. Specific topics will include the computer algebra system Mathematica and the technical word-processing system TEX. Prerequisite: MAT 152. Cr 2.

**MAT 264 Statistical Software Packages**

This course will use statistical packages such as SAS and MINITAB to introduce commonly used statistical methods in a non-theoretical manner. Particular topics might include summary measures, calculation of probabilities associated with various discrete and continuous distributions, confidence intervals and hypothesis testing, analysis of variance, regression, and various non-parametric methods. Some of these methods will be used to analyze real data collected during previous faculty consulting projects. Prerequisite: MAT 212 or consent of Department chair. Cr 2.

**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 such as SAS or MINITAB will be used extensively 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 the 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. Students will use a computer algebra system for projects. Prerequisite: MAT 153 or permission of the 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 the 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. Prerequisite: MAT 252 and MAT 290 or permission of the instructor. Cr 3.

**MAT 364 Numerical Analysis**

A study of the theory and application of computational algorithms for interpolation, equation solving, matrix methods, integration; 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 non-linear 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 370 Non-Euclidean Geometry**

A development of one or more of the non-Euclidean geometries. Prerequisite: MAT 290 or permission of the instructor. Cr 3.

**MAT 371 College Geometry**

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

**MAT 386 Sampling Techniques**

Sample 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 MAT 380. Cr 3.

**MAT 387 Introduction to Applied / Biostatical 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: permission of instructor. Cr 3.

**MAT 388 Statistical Quality Control**

Some aspects of quality specifications and tolerances, control charts for attributes and variables, certain inspection plans, plans by attributes and by variables, simple, double, and sequential sampling plans. Prerequisite: MAT 282 or MAT 380. 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 the instructor. Cr 3.

**MAT 395 Abstract Algebra**

Algebraic structures, such as groups, rings, integral domains, and fields. Prerequisite: MAT 290 or permission of the 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 nondeterministic models as queueing 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 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. Prerequisites: MAT 295 and either MAT 282 or MAT 380, 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. Cr 3.

**MAT 487 Introduction to Categorical Data Analysis**

This is an introductory course in analyzing categorical data arising from a variety of fields such as biological, biomedical and health sciences, social science, engineering, etc. The topics include contingency table analysis, logistic regression and Poisson regression modeling and model diagnostics. Writing formal statistical reports of projects based on real life data is a key component of the course. Prerequisite: 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 the 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 the 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 the 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 445 Teaching 7-12 Mathematics in Maine: Curriculum and Capstone Course**

Critical study of programs and techniques for teaching and learning mathematics in grades 7-12 for the slow, average, and advanced pupil, with the use of instructional media. Prerequisites: EDU 210, HRD/SBS 200, and 30 credit hours toward a mathematics major, or permission of the instructor. Cr 3.

#### Graduate (Back to top)

**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.

**OPR/STA 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.

**OPR/STA 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.

**OPR/STA 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.

**OPR/STA 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/or STATA. 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) for non-standard statistical methods, etc. Prerequisite: MAT 212 or 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 581 Statistical Quality Control**

Methods and philosophy of statistical process control, control charts for variables, control charts for attributes, CUSUM and EWMA control charts, some other statistical process control techniques, process capability analysis, and certain process design and improvements with experimental design. Prerequisite: MAT 282. Cr 3.

**STA 582 Introduction to Longitudinal Data Analysis**

This is an introductory course on how to use statistical techniques to analyze longitudinal (repeated measures) data and interpret the results from such analysis. The course will focus primarily on application of the various statistical models covered, with direct application illustrated using standard statistical software. Topics include random or mixed-effects models (also called HLM or multilevel models), covariance pattern models, generalized estimating equations (GEE) models, and missing data in longitudinal studies. 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 587 Categorical Data Analysis**

Topics to be examined include: two-way tables, generalized linear models, logistic and conditional logistic models, loglinear models, fitting strategies, model selection, and residual analysis. Prerequisite: MAT 282. Cr 3.

**STA 589 Survival Analysis**

Survival and reliability concepts, mathematics of survival models, parametric and non-parametric estimates from complete and censored data, Kaplan-Meier estimators, regression models including Poisson regression and Cox's proportional hazards model, time-dependent covariates, and analysis of rates. Prerequisite: MAT 282. Cr 3.

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

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

**STA 591 Topics in Biostatistics**

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/OPR 599 Independent Study**

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