Mathematical Sciences

All courses, arranged by program, are listed in the catalog. Courses designated as “active” have been offered in the past three years. Courses designated as “inactive” have not been offered in the past three years and indicate the semester in which the course was last offered. If you cannot locate a specific course, try our advanced search link. Current class schedules, with posted days and times, may be found on the Registrar's Office website or by logging directly into iSiS.

92.500 Discrete Structures Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8402
Status Active

An introduction to discrete mathematics, including combinatorics and graph theory. The necessary background tools in set theory, logic, recursion, relations, and functions are also included. Masters degree credit for Teacher Option Only.

Pre/Co-Requisites: Pre-Req: MS Teacher Option only.

92.501 Real Analysis Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8403
Status Active

The class is aimed to give rigorous foundations to the basic concepts of Calculus such as limits of sequences and functions, continuity, Riemann integration. The main focus is given to rigorous proofs rather than computations. Tentative topics are: Real numbers (algebraic, order and distance structures); Archimedean property; Sequences and their limits. Bolzano-Weierstrass theorem; Cauchy sequences and completeness; Limit of a function; Continuity of a function at a point and on a set; Uniform continuity; Open and closed sets, idea of compactness, compactness of a closed interval; Sequences of functions, uniform convergence; Riemann integration. Prerequisites: Calculus I-III or equivalent, Discrete Structures or equivalent.

92.503 Mathematical Analysis Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8405
Status Active

Development of number systems, including axiomatic and constructive treatment of the integers and the reals; sequences and series; functions of a real variable and their properties, including continuity, derivatives and integrals; functions of several real variables, including partial derivatives and multiple integration; differential equations and applications; metric spaces. Masters degree credit for the Teacher Option only.

Pre/Co-Requisites: Pre-Req: MS Teacher Option only.

92.507 Applied Functional Analysis I Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8408
Status Active

Vector, metric, normed, Banach and Hilbert spaces. Spectral theory of linear, compact, and unbounded linear operators. Integral and differential equations, approximation theory, and quantum mechanics.

92.509 Probability and Mathematical Statistics Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8409
Status Active

This course provides a solid basis for further study in statistics and data analysis or in pattern recognition and operations research. It is especially appropriate for students with an undergraduate science or engineering major who have not had a rigorous calculus-based probability and statistics course. The course covers the topics in probability models, random variables, expected values, important discrete and continuous distributions, limit theorems, and basic problems of statistical inference: estimation and testing.

92.510 Computers and Calculators in Classroom Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8410
Status Active

Explores the roles of computers and calculators in instruction, examines some of the available software, and considers their use in a variety of areas of school mathematics, such as algebra, geometry (Euclidean and analytic) probability and statistics, and introductory calculus. Mathematics Masters degree credit for Teacher Option Only.

92.511 Complex Variables I Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 1227
Status Active

Discusses complex numbers, functions of a complex variable, mappings, derivatives, analytic functions, elementary functions. Laurent series, residues and poles, contour integration.

92.513 Number Theory Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8412
Status Active

Study of primes, congruences, number-theoretic functions, Diophantine approximation, quadratic forms and quadratic number fields. Additional topics as time permits.

92.519 Introduction to Probability and Statistics II Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 30831
Status Active

The course combines theory with applications and covers both fundamental topics in statistical inference and their applications in data analysis. Discussions of the theoretical topics of statistical estimation and hypotheses testing will be complemented by analyzing simulated and real data sets. The course is taught at the computer lab equipped with MINITAB, SAS and other packages. Students will learn how statistical theory helps using statistical software, how to choose the right tool for the problem at hand and how to interpret the output. Topics to be covered include point and interval estimation, hypotheses testing, maximum likelihood estimation, likelihood ratio and related tests, applications of statistical inference to commonly used statistical models, such as one-sample, two-sample and many-sample (ANOVA) models, linear regression models, goodness-of-fit tests and contingency tables, and elements of statistical quality control and experimental design. Time permitting, topics in nonparametric and robust statistics will also be covered. Pre-requisite; 92.386, 92.509 or equivalent.

92.520 Mathematical Problem Solving Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 1226
Status Active

Focuses on: mathematical resources, ability to use heuristics, the student's beliefs about the use of mathematics to solve problems, and the student's self-confidence as a problem solver. Effective strategies for incorporating problem solving in the curriculum will also be discussed.

92.521 Abstract Algebra I Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 1225
Status Active

Elementary group theory, groups, cosets, normal subgroups, quotient groups, isomorphisms, homomorphisms, applications.

92.523 Linear Algebra Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8418
Status Active

Sets and maps; vector spaces and linear maps, matrix of linear maps, solving systems of equations, scalar products and orthogonality, eigenvalues and applications. Masters degree credit for Teachers Option Only.

Pre/Co-Requisites: Pre-Req: MS Teacher Option only.

92.526 Topology Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 33480
Status Active

Metric spaces, topological spaces, connectedness, compactness, the fundamental group, classifications of surfaces, Brouwer's fixed point theorem.

Pre/Co-Requisites: Pre-req: 92.403 Mathematical Analysis or 92.501 Real Analysis

92.527 Geometry Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 1224
Status Active

This course is designed for current and prospective geometry teachers. In addition to the development of Euclidean geometry, students will become familiar with geometry applications in Geometer�s Sketchpad software, and to a lesser degree with other geometry software applications including Geogebra, Cabri, Maple and/or Mathematica. There will be an introduction to spherical and hyperbolic geometry and triangle measurements will be computed for each. Calculus based derivations of area and volume for surfaces and solids will be generated and related to Euclidean geometry topics.

Pre/Co-Requisites: Pre-Req: MS Teacher Option only.

92.529 Differential Geometry Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8421
Status Active

Differential geometry involving curves and surfaces in 3-space. Curvature, torsion, Frenet equations, intrinsic equations, involutes and evolutes.

92.530 Applied Mathematics I Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8422
Status Active

Ordinary and partial differential equations; Fourier series and Fourier integrals; Laplace transform; matrix theory.

92.531 Applied Mathematics II Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8423
Status Active

Vector analysis and vector calculus; Gauss, Green, and Stokes theorems; complex analysis; calculus of variations; special functions; orthogonal functions.

92.532 Advanced Geometry Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 38483
Status Active

Historical perspectives: Euclid's synthetic geometry, Descartes' analytic geometry, attempts to prove parallel postulate,emergence of non-Euclidean geometry's, axiomatic development of geometry, Klein's Erlanger Programm; projective,affine,and metric geometries;non-Euclidean geometry's; foundations of geometry; algebraic geometry; finite geometry. Requires knowledge of linear algebra,abstract algebra for groups and fields including Galois fields, some familiarity with propositions and set-theoretic topology as covered in a course on Discrete Mathematics.

92.535 History of Mathematics Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 1223
Status Active

Examines ancient numeral systems, Babylonian and Egyptian mathematics, Pythagorean mathematics, duplication, trisection, and quadrature, Euclid's elements and Greek mathematics after Euclid, Hindu and Arabian mathematics, European mathematics from 500 to 1600, origins of modern mathematics, analytic geometry, the history of calculus. Also covers the transition to the twentieth century and contemporary perspectives.

Pre/Co-Requisites: Pre-Req: MS Teacher Option only.

92.548 Mathematics Of Signal Processing Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8430
Status Active

Representation of signals: Fourier analysis, fast Fourier transforms, orthogonal expansions. Transformation of signals: linear filters, modulation; band-limited signals; sampling; uncertainty principle; Windows and extrapolation.

92.550 Mathematical Modeling Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8431
Status Active

Applications of mathematics to real life problems. Topics include dimensional analysis, population dynamics wave and heat propagation, traffic flow. Pre-requisite: 92.132 Calculus II.

92.551 Calculus of Variations Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8432
Status Active

The first variational problem, necessary conditions. Euler's equation. Generalization to dependent and independent variables. Constraints and Lagrange multipliers. Application to dynamics and elasticity. Direct methods.

92.552 Wavelet Analysis Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8433
Status Active

Introduction to time-frequency localization of signals; frames; windowed Fourier transforms; continuous and discrete wavelet transforms; time frequency sampling theorems; othonormal bases of wavelets; algebraic wavelet theory; applications to electrodynamics and optics.

92.555 Applied Math for Life Scientists Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8436
Status Active

The objective of this course is to give students an opportunity to learn how to use a computer algebra system in the context of reviewing some of the key mathematical topics that are used in the life sciences. The first half of the course includes a review of mathematical topics ranging from trigonometry through differential equations. A parallel introduction to a computer algebra system is also included in the first half. In the second half, students will study a mathematical topic such as pattern recognition or models for growth and complete a project using the computer algebra system. (UMassOnline).

92.563 Computational Mathematics Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8439
Status Active

Introduction and review of Taylor series. Finding roots of F(x)=0. Numerical interpolation and extrapolation. Curve fitting and nonlinear best fits. Numerical differentiation and integration. Differential equations, initial and boundary value problems.

92.564 Applied Linear Algebra Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8440
Status Active

Use of iterative algorithms to find exact or approximate constrained solutions to large, and often spares, systems of linear equations, and on applications, such as medical imaging, in which such problems arise. Maximization of likelihood and entropy. Emphasis on exploiting sparseness, accelerating convergence, and stabilizing calculations in the presence of noise. Block-iterative methods and bounds for singular values will be included. Basic results in matrix theory presented as needed.

92.568 Approximation Theory Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 31893
Status Active

92.570 Probability and Statistics Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8444
Status Active

Overview of descriptive statistics, data analysis, probability of events, discrete random variables, continuous random variables, normal, binomial and other probability distributions, central limittheorem, survey sampling, estimation, hypothesis testing, regression, experimental design, analysis of categorical data, nonparametric statistics. Masters degree credit for Teachers Option Only.

Pre/Co-Requisites: Pre-Req: MS Teacher Option only.

92.572 Optimization Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8446
Status Active

Optimization without calculus; geometric programming; convex sets and convex functions; review of linear algebra; linear programming and the simplex method; convex programming; iterative barrier-function methods; iterative penalty-function methods; iterative least-squares algorithms; iterative methods with positivity constraints; calculus of variations; applications to signal processing, medical imaging, game theory.

92.576 Statistical Programming using SAS Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8449
Status Active

An introduction to creation and manipulation of databases and statistical analysis using SAS software. SAS is widely used in the pharmaceutical industry, medical research and other areas.

92.578 Statistical Inference and Data Mining Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 31943
Status Active

Topics in nonasymptotic direct computational methods for statistical inference in data mining. Background in probability and statistics required.

92.582 Time Series Analysis Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8454
Status Active

Building models for discrete time series and dynamic systems and their use in forecasting and control. Stationary and non-stationary time series models. Box-Jenkins (ARMA) and other techniques.

92.584 Stochastic Process Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8456
Status Active

Markov chains and processes, random walks, stationary, independent increments, and Poisson processes. Ergodicity. Examples (e.g., diffusion, queuing theory, etc.).

92.587 Measure and Probability Theory Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8459
Status Active

This course presents the mathematical foundations of Probability Theory, including the concepts of Probability Space and random variable. Various types of convergence of sequences and measurable functions will be introduced, and precise statements and proofs of the probability limit theorems (Law of Large Numbers, Central Limit Theorems, etc.) will be given. Theory of measure and Lebesgue integration will be introduced. If time permits, conditional probabilities will be discussed.

92.588 Mathematical Statistics Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8460
Status Active

Random variables, densities, joint and conditional distributions, expectations, variance, estimation, sufficiency and completeness, hypothesis testing, limiting distributions.

92.590 Statistical Quality Control Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8462
Status Active

Overview of quality and managing quality, Define Measure Analyze Improve Control (DMAIC), the six sigma approach to quality, visual representation of data, Pareto charts, histograms, process capability vs specification (process) limits, t-tests, ANOVA, and other statistical hypothesis testing in quality, normal probability plots, control charts, measurement system analysis, application of regression analysis to manufacturing and/or design, Minitab.

92.591 Linear Statistics Modeling and Regression Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8463
Status Active

Model building via linear regression models. Method of least squares, theory and practice. Checking for adequacy of a model, examination of residuals, checking outliers. Practical hand on experience in linear model building on real data sets. Prerequisite: Probability, Biostatistics, or Statistics for Engineering and Science.

92.592 Multivariate Statistics Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8464
Status Active

Nonlinear model building via the method of least squares. Discriminant and factor analysis, principal components, profile analysis, canonical correlation, cluster analysis. Experience on real data sets.

92.593 Experimental Design Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8465
Status Active

How to design, carry out, and analyze experiments. Randomized block designs, randomization, blocking, matching, analysis of variance and covariance, control of extraneous variables.

92.651 Selected Topics in Mathematics Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8467
Status Active

Intended to satisfy individual student needs. Topics include various fields of mathematics.

92.653 Selected Topics Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8469
Status Active

Advanced topics in various fields of mathematics and related fields. Since topical coverage varies from term to term, a student may be allowed to receive credit more than once for this course.

92.742 Thesis Review Credits: 1

Course Details
Min Credits 1
Max Credits 1
Course ID 35257
Status Active

92.743 Graduate Research/Math Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 8489
Status Active

92.965 Introduction To Pascal Credits: 3

Course Details
Min Credits 3
Max Credits 3
Course ID 11633
Status Active