## MATHEMATICS APPLIED

- MAP 2302Ordinary Differential EquationsThis course covers differential equations of the first order, linear equations of the second, systems of first order equations, power series solutions, Laplace transforms, numerical methods. Not open to students having credit in MAP 3305.
- MAP 2480Biocalculus Computer LaboratoryThis computer laboratory applies calculus methods and mathematical programming software to assist students in solving problems from biology, medicine, and psychology.
- MAP 4103Mathematical ModelingThis course covers the application of mathematics to real life situations, construction of mathematical models, use of elementary and advanced mathematical methods, and case studies.
- MAP 4153Vector Calculus with Introduction to TensorsThis course covers vector calculus: gradient, divergence, curl; differential operators in orthogonal curvilinear coordinates; line, surface, and volume integrals; Stokes' and Green's theorems; subscript notation, Cartesian tensors; and applications.
- MAP 4170Introduction to Actuarial MathematicsThis course covers amount function, dollar-weighted and time-weighted rates, force of interest; special annuity types, bonds, capitalization and applications. Yield curves, spot rates, forward rates, duration, convexity and immunization and additional financial concepts.
- MAP 4175Actuarial ModelsThis course covers single- and multiple-life survival analysis; mortality laws, deterministic methods, and contingent payments and annuities; premium principles and reserves for continuous, discrete, and semi-continuous insurance products; as well as multiple decrement theory (competing risks) and applications.
- MAP 4176Actuarial Models, Credibility, and SimulationThis course covers claim frequency models, individual loss models, aggregate loss models, multiple-life and multiple-decrement survival models, multiple-state transition models, credibility theory, and simulation.
- MAP 4202OptimizationThis course covers linear programming, unconstrained optimization, searching strategies, equality and inequality constrained problems.
- MAP 4216Calculus of VariationsThis course covers fundamental problems, weak and strong extrema, necessary and sufficient conditions, Hamilton-Jacobi theory, dynamic programming, control theory and Pontryagins maximum principle.
- MAP 4341Elementary Partial Differential Equations IThis course covers separation of variables, Fourier Series, Sturm-Liouville problems, multidimensional initial boundary value problems, nonhomogeneous problems, Bessel functions, and Legendre polynomials.
- MAP 4342Elementary Partial Differential Equations IIThis course covers solution of first-order quasi-linear partial differential equations, classification and reduction to normal form of linear second-order equations, Green's function, infinite domain problems, the wave equation, radiation condition, spherical harmonics.
- MAP 4481Mathematical Modeling in BiologyThis course is an introduction to the use of mathematical models in biology. Linear and nonlinear difference and ordinary differential equations, linear stability analysis, phase plane analysis. Applications may include population biology, infectious diseases, chemical kinetics, and physiology.
- MAP 4934Topics in Applied MathematicsSpecial topics course. May be repeated to a maximum of twelve semester hours. May be repeated within the same semester.
- MAP 5107Mathematical ModelingThis course covers formulation and application of mathematical models for problems arising in the natural sciences, engineering, economics, and industry. Related mathematical topics, including dimensional analysis and scaling, role of dimensionless numbers, perturbation methods, self-similar solutions, traveling waves and solitons, symmetry and symmetry breaking, bifurcations, inverse problems and regularization techniques.
- MAP 5165Methods of Applied Mathematics IThis course covers continuous and discrete models from physics, chemistry, biology, and engineering are analyzed using perturbation methods, analytical and geometrical tools, and dynamical systems theory.
- MAP 5177Actuarial ModelsThis course covers survival models; life probabilities; tables, mortality laws; contingent payment models; life annuities; premium principles and net premium reserves for continuous, discrete and semi-continuous life insurances, multiple life models, multiple decrement theory (theory of competing risks) and applications to pension plans, pricing and nonforfeiture models.
- MAP 5178Advanced Actuarial Models, Credibility, and SimulationThis course examines claim frequency models, individual loss models, aggregate loss models, multiple-life and multiple-decrement survival models, multiple-state transition models, credibility theory, and simulation.
- MAP 5196Mathematics for Data ScienceThis course covers the core mathematics of data science: linear algebra, vector calculus and optimization, probability and graph theory. Applications of these topics will be presented and used as motivation.
- MAP 5207OptimizationThis course covers linear programming, unconstrained optimization, searching strategies, equality and inequality constrained problems.
- MAP 5217Calculus of VariationsThis course covers fundamental problems, weak and strong extrema, necessary and sufficient conditions, Hamilton-Jacobi theory, dynamic programming, control theory, and Pontryagins maximum principle.
- MAP 5345Elementary Partial Differential Equations IThis course covers the separation of variables; Fourier series; Sturm-Liouville problems; multidimensional initial boundary value problems; nonhomogeneous problems; Bessel functions and Legendre polynomials.
- MAP 5346Elementary Partial Differential Equations IIThis course covers the solution of first order quasi-linear partial differential equations; classification and reduction to normal form of linear second order equations; Greens function; infinite domain problems; the wave equation; radiation condition; spherical harmonics.
- MAP 5395Finite Element MethodsThis course covers the methods of weighted residuals, finite element analysis of one and two-dimensional problems, isoparametric elements, time dependent problems, algorithms for parabolic and hyperbolic problems, applications, advanced Galerkin techniques.
- MAP 5423Complex Variables, Asymptotic Expansions, and Integral TransformsThis course covers ordinary differential equations in the complex plane; special functions. Asymptotic methods: Laplaces method, steepest descent, stationary phase, WKB. Integral transforms: Fourier, Laplace, Hankel.
- MAP 5431Introduction to Fluid DynamicsThis course covers the physical properties of viscous fluids, hydrostatics, kinematics of flow fields, governing equations. Dynamics of viscous incompressible fluids: vorticity, boundary layer flow, potential flow.
- MAP 5486Computational Methods in BiologyThis course introduces biological topics where mathematical and computational methods are applicable, including discrete and continuous models of biological systems, numerical methods for differential equations, nonlinear differential equations, and stochastic models.
- MAP 5601Introduction to Financial MathematicsThis course covers partial differential equations, discussion of Brownian motion, Black-Scholes analysis, introduction to measure and probability: financial applications.
- MAP 5611Introduction to Computational FinanceThis course covers the computational methods for solving mathematical problems in finance; basic numerical methods, numerical solution of parabolic partial differential equations, including convergence and stability, solution of the Black-Scholes equation, boundary conditions for American options and binomial and random walk methods.
- MAP 5615Monte Carlo Methods in Financial MathematicsThis course examines how the theory of Monte Carlo Methods is developed in the context of topics selected from computational finance, such as pricing exotic derivatives, American option pricing, and estimating sensitivities. The theory includes pseudorandom numbers, generation of random variables, variance reduction techniques, low-discrepancy sequences, and randomized quasi-Monte Carlo methods.
- MAP 5932Topics in Applied MathematicsCourse Description not on file
- MAP 6356Advanced Partial Differential Equations IThis course introduces the general classical theory of ordinary differential equations, hyperbolic, parabolic, and elliptic partial differential equations. With each case, some fundamental analytical tools are utilized to probe the nature of the corresponding solutions. Main themes of the course include: the existence and uniqueness of solutions for various initial and boundary value problems, and the properties and solutions of the wave equation, the heat equation, and the Laplace and Poisson equations.
- MAP 6437Advanced Topics in Applied MathematicsCourse Description not on file
- MAP 6621Financial Engineering IThis course offers a quantitative treatment of core problems in the investment industry. Topics include techniques and analysis of active portfolio management including risk factor models and mean-variance optimization, the Martingale approach to derivative pricing for both discrete and continuous models, applied stochastic calculus, and stochastic interest rate models.
- MAP 6939Advanced Seminar in Applied MathematicsCourse Description not on file