Mathematics BA

This is a continuation of MATH 210 Calculus I and a working knowledge of that material is expected. Through a conceptual and theoretical framework this course covers the definite integral, the fundamental theorem of calculus, applications of integration, numerical methods for evaluating integrals, techniques of integration and series.

Full course description for Calculus II

This is an introductory course in real analysis. Starting with a rigorous look at the laws of logic and how these laws are used in structuring mathematical arguments, this course develops the topological structure of real numbers. Topics include limits, sequences, series and continuity. The main goal of the course is to teach students how to read and write mathematical proofs.

Full course description for Introduction to Analysis

This is a continuation of Math 211 Calculus II and covers calculus as it applies to functions of several variables. Topics include vectors and plane curves, partial differentiation, curves and vectors in space, multiple integrals, vector fields, line integrals, and Stokes Theorem.

Full course description for Calculus III: Multivariable Calculus

The need to solve systems of linear equations frequently arises in mathematics, the physical sciences, engineering and economics. In this course we study these systems from an algebraic and geometric viewpoint. Topics include systems of linear equations, matrix algebra, Euclidean vector spaces, linear transformations, linear independence, dimension, eigenvalues and eigenvectors.

Full course description for Linear Algebra and Applications

This is a calculus-based probability course. It covers the following topics. (1) General Probability: set notation and basic elements of probability, combinatorial probability, conditional probability and independent events, and Bayes Theorem. (2) Single-Variable Probability: binomial, geometric, hypergeometric, Poisson, uniform, exponential, gamma and normal distributions, cumulative distribution functions, mean, variance and standard deviation, moments and moment-generating functions, and Chebysheff Theorem. (3) Multi-Variable Probability: joint probability functions and joint density functions, joint cumulative distribution functions, central limit theorem, conditional and marginal probability, moments and moment-generating functions, variance, covariance and correlation, and transformations. (4) Application to problems in medical testing, insurance, political survey, social inequity, gaming, and other fields of interest.

Full course description for Probability

This course develops the more advanced mathematical tools necessary for an in-depth analysis of dynamic models. Topics include first order differential equations, first order systems, linear systems, nonlinear systems and numerical methods.

Full course description for Ordinary Differential Equations

By extending the familiar concepts of arithmetic, this course introduces abstract algebraic structures. Topics include an introduction to number theory; group theory, including the classification of all finite abelian groups; rings, integral domains, and fields.

Full course description for Abstract Algebra

This course integrates reading of the mathematical literature with presentation of student developed projects.

Full course description for Mathematics Capstone

An introduction to methods and techniques commonly used in data science. This course will use object-oriented computer programming related to the processing, summarization and visualization of data, which will prepare students to use data in their field of study and to effectively communicate quantitative findings. Topics will include basics in computer programming, data visualization, data wrangling, data reshaping, ethical issues with the use of data, and data analysis using an object-oriented programming language. Students will complete a data science project.

Full course description for Data Science and Visualization

This is the first course of a two semester sequence covering the fundamental concepts of physics. This course covers Newton's laws of motion, work, energy, linear momentum, rotational motion, gravity, equilibrium and elasticity, periodic motion, fluid mechanics, temperature, heat, and the laws of thermodynamics. Laboratories emphasize application of physics concepts and quantitative problem solving skills. Intended for science majors and general education students with strong mathematical background.

Full course description for Calculus Based Physics I

Mathematical modeling is the process of using mathematics and computational tools to gain insights into complex problems arising in the sciences, business, industry, and society. Mathematical modeling is an iterative process which involves a computational approach to the scientific method. Assumptions are established, a mathematical structure consistent with those assumptions is developed, hypotheses are produced and tested against empirical evidence, and then the model is refined accordingly. The quality of these models is examined as part of the verification process, and the entire cycle repeats as improvements and adjustments to the model are made. This course provides an introduction to both the mathematical modeling process as well as deterministic and stochastic methods that are commonly employed to investigate time-dependent phenomena.

Full course description for Introduction to Mathematical Modeling

Optimization covers a broad range of problems that share a common goal - determining the values for the decision variables in a problem that will maximize (or minimize) some objective function while satisfying various constraints. Using a mathematical modeling approach, this course introduces mathematical programming techniques and concepts such as linear programming, sensitivity analysis, network modeling, integer linear programming, goal programming, and multiple criteria optimization. Software is used to solve real-world problems with an emphasis on interpretability of results. Applications include determining product mix, routing and logistics, and financial planning.

Full course description for Optimization

Stochastic processes involve sequences of events governed by probabilistic laws. Many applications of stochastic processes occur in biology, medicine, psychology, finance, telecommunications, insurance, security, and other disciplines. This course introduces the basics of applied stochastic processes such as Markov chains (both discrete-time and continuous-time), queuing models, and renewal processes. Software is used to solve real-world problems with an emphasis on interpretation of results and the role of stochastic processes in management decision-making.

Full course description for Introduction to Stochastic Processes

This course goes beyond the Euclidean Geometry typically taught in high schools. This is a modern approach to geometry based on the systematic use of transformations. It includes a study of some advanced concepts from Euclidean Geometry and then proceeds to examine a wide variety of other geometries, including Non-Euclidean and Projective Geometry. A working knowledge of vectors, matrices, and multivariable calculus is assumed.

Full course description for Modern Geometry

Starting with an introduction to the complex plane, this course covers holomorphic functions and power series, Cauchy's Theorem, contour integration and its applications.

Full course description for Complex Variables

This course addresses the theory and practice of using algorithms and computer programming to solve mathematical problems. Possible topics include roundoff and truncation errors, solution of nonlinear equations, systems of linear and nonlinear equations, interpolation and approximation, numerical differentiation and integration, numerical solution of ordinary differential equations.

Full course description for Computational Mathematics

This course covers the theory of initial and boundary value problems for linear parabolic, elliptic, and hyperbolic partial differential equations. Topics may include first order equations, second order equations, separation of variables, the Sturm-Liouville problem, transform methods, Green's functions, Fourier series, numerical methods and modeling applications.

Full course description for Partial Differential Equations

This course provides students with significant problem-solving experience through investigating complex, open-ended problems arising in real-world settings. Working in teams, students apply mathematical modeling processes to translate problems presented to them into problems that can be investigated using the mathematical, statistical, and computational knowledge and thinking they have gained from previous coursework. Significant emphasis is placed on justifying approaches used to investigate problems, coordinating the work of team members, and communicating analyses and findings to technical and non-technical audiences.

Full course description for Advanced Mathematical Modeling