Mathematics & Statistics

• CAS MA 542: Modern Algebra II
  Undergraduate Prerequisites: (CASMA541) or consent of instructor. - Vector spaces and modules, Galois theory, linear transformations and matrices, canonical forms, bilinear and quadratic forms.
• CAS MA 555: Numerical Analysis I
  Undergraduate Prerequisites: (CASMA225 OR CASMA230) - Graduate Prerequisites: (CASMA225 OR CASMA230) - Numerical solutions of equations, iterative methods, analysis of sequences. Theory of interpolation and functional approximation, divided differences. Numerical differentiation and integration. Polynomial theory. Ordinary differential equations.
• CAS MA 556: Numerical Analysis II
  Undergraduate Prerequisites: (CASMA555 & (CASMA242 OR CASMA442)) or consent of instructor. - Graduate Prerequisites: (CASMA555 & (CASMA242 OR CASMA442)) or consent of instructor. - Numerical linear algebra; norms, elimination methods, error analysis, conditioning, eigenvalues, iterative methods, least squares and nonlinear functional minimization. Partial differentiation equation boundary value and initial value problems. Finite element methods. Legendre and Chebyshev polynomials. Treatment in greater depth of selected topics from CAS MA 555.
• CAS MA 561: Methods of Applied Mathematics 1
  Undergraduate Prerequisites: CASMA 226 or CASMA 230 and CASMA 226 or CASMA231; or consent of instructor - Graduate Prerequisites: graduate standing. - Derivation and analysis of the classical equations of mathematical physics; heat equation, wave equation, and potential equation. Initial boundary value problems, method of separation of variables, eigenvalue problems, eigenfunction expansions. Fourier analysis. Existence and uniqueness of solution.
• CAS MA 562: Methods of Applied Mathematics 2
  Undergraduate Prerequisites: (CASMA 225 or CASMA 230) and (CASMA 226 or CASMA 231) and (CASMA 242 or CASMA 442) or consent of instructor - Calculus of variations, first-order non-linear partial differential equations, Hamilton-Jacobi theory, Rayleigh-Ritz procedure, perturbation methods.
• CAS MA 563: Introduction to Differential Geometry
  Undergraduate Prerequisites: (CASMA225 OR CASMA230) and (CASMA226 OR CASMA231) and (CASMA242 or CASMA442); or consent of i nstructor. - Study of local properties of curves and surfaces in the three-dimensional Euclidean space; curvature, torsion, Frenet equations, tangent and normal planes; first and second fundamental form; developable surfaces, principal, mean and Gaussian curvature; vector fields, covariant differentiation, geodesics, surfaces of constant curvature.
• CAS MA 564: Introduction to Topology
  Undergraduate Prerequisites: (CASMA225 OR CASMA230) and (CASMA411 or CASMA511); or consent of instructor. - Introduction to point set and algebraic topology. Topological spaces and continuity. Compactness and connectedness. Metrizable topological spaces. Product topology and Tychonoff's theorem. The fundamental group and van Kampen's theorem. Covering spaces and the universal cover.
• CAS MA 565: Mathematical Models in the Life Sciences
  Undergraduate Prerequisites: (CASMA226 OR CASMA231) - Graduate Prerequisites: (CASMA226 OR CASMA231) - An introduction to mathematical modeling, using applications in the biological sciences. Mathematics includes linear difference and differential equations, and an introduction to nonlinear phenomena and qualitative methods. An elementary knowledge of differential equations and linear algebra is assumed.
• CAS MA 568: Statistical Analysis of Point Process Data
  Undergraduate Prerequisites: CASMA 213 and CASMA 214 or consent of instructor. Graduate Prerequisites: graduate standing. - Introduces the theory of point processes and develops practical problem-solving skills to construct models, assess goodness-of-fit, and perform estimation from point process data. Applications to neural data, earthquake analysis, financial modeling, and queuing theory.
• CAS MA 569: Optimization Methods of Operations Research
  Undergraduate Prerequisites: (CASMA 225 or CASMA 230 or CDSDS 122) AND (CASMA 242 or CASMA 442 or ENGEK 103 or CDSCS 132) or consent of instructor. - Graduate Prerequisites: graduate standing. - Optimization of linear functions: linear programming, simplex method; transportation, assignment, and network problems. Optimization of non-linear functions: unconstrained optima, constrained optima and Lagrange multipliers, Kuhn-Tucker conditions, calculus of variations, and Euler's equation.
• CAS MA 570: Stochastic Methods of Operations Research
  Undergraduate Prerequisites: (CASMA 225 or CASMA 230 or CDSDS 122) AND (CASMA 242 or CASMA4 42 or ENGEK 103 or CASCS 132) or consent of instructor) - Poisson processes, Markov chains, queuing theory. Matrix differential equations, differential-difference equations, probability-generating functions, single- and multiple-channel queues, steady-state and transient distributions.
• CAS MA 573: Qualitative Theory of Ordinary Differential Equations
  Undergraduate Prerequisites: (CASMA 225 or CASMA 230) and (CASMA 226 OR CASMA 231) and (CASMA 242 OR CASMA 442) or consent of instructor. - Eigenvalues, eigenvectors, Jordan normal forms. Linear systems of differential equations, Phase portrait, Hamiltonian systems, stability theory. Applications to systems arising in mechanics, economics, ecology, electrical circuit theory, etc.
• CAS MA 575: Linear Models
  Undergraduate Prerequisites: (CASMA 214 or CASMA 116) AND (CASMA 581 or ENGEK 381 or ENGEK 500 or CASCS 237) AND (CASMA 242 or ENGEK 103 or CDSDS 121 or CASMA 442 or CASCS 132) or consent of instructor. - Post-introductory course on linear models. Topics to be covered include simple and multiple linear regression, regression with polynomials or factors, analysis of variance, weighted and generalized least squares, transformations, regression diagnostics, variable selection, and extensions of linear models. Effective Fall 2019, this course fulfills a single unit in the following BU Hub area: Quantitative Reasoning II, Teamwork/Collaboration.
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  • Quantitative Reasoning II
  • Teamwork/Collaboration
• CAS MA 576: Generalized Linear Models
  Undergraduate Prerequisites: (CASMA575) or consent of instructor. - Covers topics in linear models beyond MA 575: generalized linear models, analysis of binary and polytomous data, log-linear models, multivariate response models, non-linear models, graphical models, and relevant model selection techniques. Additional topics in modern regression as time allows.
• CAS MA 577: Mathematics of Financial Derivatives
  Undergraduate Prerequisites: (CASMA 581 or ENGEK 381 or ENGEK 500); or consent of instructor. - Develops the probabilistic tools used in finance and presents the methodologies that are used in the pricing of financial derivatives. No previous knowledge of finance is required.
• CAS MA 578: Bayesian Statistics
  Undergraduate Prerequisites: CASMA 575 or consent of instructor. - The principles and methods of Bayesian statistics. Subjective probability, Bayes rule, posterior distributions, predictive distributions. Computationally based inference using Monte Carlo integration, Markov chain simulation. Hierarchical models, mixture models, model checking, and methods for Bayesian model selection.
• CAS MA 579: Numerical Methods for Biological Sciences
  Undergraduate Prerequisites: (CASMA226 OR CASMA231) or equivalent, and elementary knowledge of linear algebra. - Introduction to the use of numerical methods for studying mathematical models of biological systems. Emphasis on the development of these methods; understanding their accuracy, performance, and stability; and their application to the study of biological systems.
• CAS MA 581: Probability
  Undergraduate Prerequisites: (CASMA 225 OR CASMA 230 or CDSDS 122) or consent of instructor. - Graduate Prerequisites: (CASMA225 OR CASMA230) or consent of instructor. - Basic probability, conditional probability, independence. Discrete and continuous random variables, mean and variance, functions of random variables, moment generating function. Jointly distributed random variables, conditional distributions, independent random variables. Methods of transformations, law of large numbers, central limit theorem. Cannot be taken for credit in addition to CASMA 381.
• CAS MA 582: Mathematical Statistics
  Undergraduate Prerequisites: : (CASMA 581 or ENGEK 381 or ENGEK 500) or consent of instructor. - Point estimation including unbiasedness, efficiency, consistency, sufficiency, minimum variance unbiased estimator, Rao-Blackwell theorem, and Rao-Cramer inequality. Maximum likelihood and method of moment estimations; interval estimation; tests of hypothesis, uniformly most powerful tests, uniformly most powerful unbiased tests, likelihood ratio test, and chi-square test.
• CAS MA 583: Introduction to Stochastic Processes
  Undergraduate Prerequisites: CASMA 581 or ENGEK 381 or ENGEK 500) or consent of instructor. - Basic concepts and techniques of stochastic process as they are most often used to construct models for a variety of problems of practical interest. Topics include Markov chains, Poisson process, birth and death processes, queuing theory, renewal processes, and reliability.