Applied & Computational Mathematics
Concentration

Advanced Numerical Methods for PDEs

Development, analysis, and implementation of numerical methods to approximate solutions of partial differential equations. An advanced study of numerical methods for approximating the solution of partial differential equations. Topics may include: numerical methods for hyperbolic PDEs; finite element methods; discontinuous Galerkin methods; spectral methods; pseudo spectral (collocation) methods; radial basis function methods; numerical methods for time-stepping of PDEs

• Course type: Lecture

Analy Geom & Calc III

An introduction to multivariable and vector calculus. This is the third and the final semester of the Calculus sequence. Topics cover 3-D analytical geometry, partial derivatives, directional derivatives, gradient, applications, multiple integrals, parameterized curves, and surfaces, vector fields, line and surface integrals, Green¿s theorem, flux and divergence, Stokes¿ and the divergence theorems.

Applied Statistical Consulting

Engagement of students with communities having statistical analysis needs. Academic faculty, graduate and undergraduate students, external businesses. Focus on problems of statistical analysis of data or design of experiments. Skills include multiple regression, analysis of variance, design of experiments, nonlinear estimation, spatial and time series analysis, contingency table analyses. Topics covered include: research process, questionnaire design, experimental design, sampling methods, data collection and preparation, data analysis, statistical report writing

Applied Statistical Investigation

Investigation in applied statistics. Topics for investigation chosen in 

Calculus I

An intensive study of differential calculus and its applications, and an introduction to integrals, Topics include: limits, continuity, indeterminate forms, differentiation and integration of algebraic and transcendental functions, implicit and logarithmic differentiation, and applications to science and engineering. This is the first semester of the standard calculus sequence designed for students interested in Mathematics, Physics, Chemistry, Engineering and Mathematical/Computational Biology. This course fulfills the general education core requirements for Mathematics, Physics, Chemistry, Engineering and Mathematical/Computational Biology majors who matriculated prior to Fall 2012 and has been approved by University Studies Curriculum for students matriculating in Fall 2012 or later.

• Course type: Lecture
• Course hours: 4 hours per week

Calculus II

An intensive study of the techniques and applications of integration and infinite series. Topics include: techniques of integration and its application, improper integrals, infinite series (including convergence tests, the interval of convergence for power series, and Taylor series), and parametric equations and polar coordinates. This is the second semester of the standard calculus sequence designed for students interested in Mathematics, Physics, Chemistry, Engineering and Mathematical/Computational Biology. This course fulfills the general education core requirements for Mathematics, Physics, Chemistry, Engineering and Mathematical/Computational Biology majors who matriculated prior to Fall 2012 and has been approved by University Studies Curriculum for students matriculating in Fall 2012 or later.

• Course type: Lecture
• Course hours: 4 hours per week

Complex Analysis

Analytic functions, differentiation, integration, conformal mapping, calculus of residues and infinite series.

• Course type: Lecture
• Course hours: 3 hours per week

Differential Equation

An introduction to ordinary differential equations and their analysis. Topics cover first order linear and nonlinear ordinary differential equations, second order and higher order homogeneous and nonhomogeneous linear differential equations, the linear system of ordinary differential equations, qualitative analysis, numerical solutions, series solutions.

Discrete Mathematics I

An introduction to mathematical reasoning, mathematical logic, and methods of proof. Topics include: properties of numbers, elementary counting methods, discrete structures, Boolean algebra, introduction to directed and undirected graphs, methods of proof, and applications in mathematics and computer science. This is the first semester of a discrete mathematics sequence designed for Mathematics, Computer and Information Sciences majors. This course fulfills the general education core requirements for Mathematics, Computer and Information Sciences majors who matriculated prior to Fall 2012 and has been approved by University Studies Curriculum for students matriculating in Fall 2012 or later.

• Course type: Lecture
• Course hours: 3 hours per week

Discrete Mathematics II

A study of mathematical foundations for advanced mathematics and theoretical computer science. Topics include: mathematical reasoning including mathematical induction, combinatorial analysis including simple probability, discrete structures (such as sets, recursions, relations, and trees), algorithmic thinking, applications, and modeling (such as combinatorial circuits). This is the second semester of a discrete mathematics sequence designed for Mathematics and Computer Information Sciences majors. This course fulfills the general education core requirements for Mathematics, Computer and Information Sciences majors who matriculated prior to Fall 2012 and has been approved by University Studies Curriculum for students matriculating in Fall 2012 or later.

• Course type: Lecture
• Course hours: 3 hours per week

Elementary Topology

An introduction to basic ideas of modern topology. Topics chosen from: topological spaces, continuous functions, topological equivalence, identification spaces, surfaces, homotopy, fundamental groups, knots and links.

• Course type: Lecture
• Course hours: 3 hours per week

High Performance Scientific Computing

Topics in high performance computing (HPC). Topics will be selected from the following: parallel processing, computer arithmetic, processes and operating systems, memory hierarchies, compilers, run time environment, memory allocation, preprocessors, multi-cores, clusters, and message passing. Introduction to the design, analysis, and implementation, of high-performance computational science and engineering applications.

• Course type: Lecture
• Course hours: 3 hours per week

Introduction to Scientific Computation

A calculus-based introduction to scientific computation, modeling, simulation and visualization using a variety of mathematics programming tools, scripting languages, and other software tools widely used by mathematicians. This course is project-driven and requires a strong background in mathematics. It is intended for students planning to take upper-level courses in applied or computational mathematics.

• Course type: Lecture

Introductory Real Analysis I

This course is a rigorous analysis of the concept of limits, continuity, the derivative and other selected areas.

• Course type: Lecture
• Course hours: 3 hours per week

Introductory Real Analysis II

Continuation of MTH 311 with emphasis on uniform convergence and related topics.

• Course type: Lecture
• Course hours: 3 hours per week

Linear Algebra

A study of solving systems of linear equations and their related matrices. Topics cover systems of linear equations, matrix theory including matrix factorizations, vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalizations, Gram-Schmidt process, the least-squares problems, the Spectral theorem of a real symmetric matrix, Triangle inequality and Cauchy-Schwarz inequality, possibly Singular Value Decomposition (SVD).

Math Modeling

Selected topics from the areas of linear programming, dynamic programming, Markov chains and game theory. Mathematical model building will be developed through the use of numerous case studies from the natural and social sciences, e.g., ecological models, network models, scheduling models, urban structure, traffic flow, growth, etc.

• Course type: Lecture
• Course hours: 3 hours per week

Mathematical & Computational Consulting

An intensive introduction to real-world mathematics using an assortment of mathematical challenges presented by industrial-problems. This course aims to prepare students to integrate and apply their mathematical knowledge to novel problems presented in industrial or research settings. Topics will be selected from the following: multidisciplinary projects solicited from various research groups at UMass Dartmouth, from local and national industries/universities/labs, and from crowdsourcing websites.

• Course type: Lecture

Mathematical Statistics

Continuation of MTH 331. Classical estimation methods and hypothesis testing are studied. This course also covers Chi square tests for goodness-of-fit and independence, regression and correlation analysis, and one-way and two-way analysis of variance including factorial designs and tests for the separation of means.

• Course type: Lecture
• Course hours: 3 hours per week

Numerical Analysis I

Theory and computer-oriented practice in obtaining numerical solutions of various problems. Topics include stability and conditioning, nonlinear equations, systems of linear equations, interpolation and approximation theory.

• Course type: Lecture
• Course hours: 3 hours per week

Numerical Analysis II

Numerical methods for solving initial value problems. Topics include: numerical differentiation and integration, Euler method and Taylor's series method, Runge-Kutta methods, multi-step methods, and stiff equations

• Course type: Lecture
• Course hours: 3 hours per week

Numerical Linear Algebra

An introduction to numerical linear algebra. Numerical linear algebra is fundamental to all areas of computational mathematics. This course will cover direct numerical methods for solving linear systems and linear least squares problems, stability and conditioning, computational methods for finding eigenvalues and eigenvectors, and iterative methods for both linear systems and eigenvalue problems.

• Course type: Lecture
• Course hours: 3 hours per week

Numerical Methods for Partial Differential Equations

Numerical methods for solving parabolic, hyperbolic, and elliptic partial differential equations. The course will emphasize the concepts of consistency, convergence and stability. Topics include: implicit and explicit methods, truncation error, Von Newmann stability analysis, and the Lax equivalence theorem.

• Course type: Lecture
• Course hours: 3 hours per week

Numerical Optimization

An introduction to constrained and unconstrained optimization. Numerical optimization is an essential tool in a wide variety of applications. The course covers fundamental topics in unconstrained optimization and also methods for solving linear and nonlinear constrained optimization problems.

• Course type: Lecture
• Course hours: 3 hours per week

Partial Differential Equation

Introduction to partial differential equations. Topics include: the classification of partial differential equations, the heat equation, the potential equation, separation of variables, Fourier series, the wave equation, and Sturm-Liouville eigenvalue problems.

• Course type: Lecture

Probability

A calculus-based introduction to statistics. This course covers probability and combinatorial problems, discrete and continuous random variables and various distributions including the binomial, Poisson, hypergeometric normal, gamma and chi-square. Moment generating functions, transformation and sampling distributions are studied.

• Course type: Lecture
• Course hours: 3 hours per week

Selected Topics In Math

A special course to meet the needs of students for material not encountered in other courses. Topics dealt with require the approval of the departmental chairperson.

• Course type: Lecture
• Course hours: 3 hours per week

Small World Networks

Modeling small-world networks. This experiential-learning course focuses on the simulation and analysis of small ­world networks, including social networks, food chains and the world-wide web. Models will include regular lattices, random graphs, Strogatz-Watts networks, an random accretion models of Barabasi and Albert and of Aeillo, Chung and Lu.

• Course type: Lecture

Statistical Computing

Introduction to statistical computing with the R programming language. Topics chosen from: numerical and graphical statistical analyses: algorithms in statistical computing; random number generation: generating distributions: random sampling and permutations; bootstrapping: matrix computations in linear models; non-linear optimization; R constructs: functions: objects; data structures; flow control; input and output; debugging; logical design; tidyverse and other R packages.

• Course type: Lecture