Mathematics & Statistics

• CAS MA 505: History of Mathematics
  Undergraduate Prerequisites: (CASMA225 OR CASMA230) and (CASMA242 or CASMA442); or consent of instructor. - The development of mathematics from Antiquity through the 18th Century. Assuming background in modern mathematics, its roots are systematically pursued in terms of modern techniques, structures, and results. Providing the emergence of mathematical concepts and procedures, a coherent, unifying view of number, geometry, algebra, calculus, and mathematical analysis is presented. Effective Fall 2018, this course fulfills a single unit in the following BU Hub area: Historical Consciousness.
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  • Historical Consciousness
• CAS MA 511: Introduction to Analysis I
  Undergraduate Prerequisites: (CASMA225 OR CASMA230) - Graduate Prerequisites: (CASMA225 OR CASMA230) - Fundamental concepts of mathematical reasoning. Properties of the real-number system, elementary point-set theory, metric spaces. Limits, sequences, series, convergence, uniform convergence, continuity. Differentiability for functions of a single variable, Riemann-Stieltjes integration.
• CAS MA 512: Introduction to Analysis II
  Undergraduate Prerequisites: (CASMA511) - Graduate Prerequisites: (CASMA511) - Background of CAS MA 511 used to develop further topics of calculus. Exponential and logarithmic functions, Taylor series, power series, real analytic functions. Differential and integral calculus for functions of several variables. Line and surface integrals, divergence theorem, Stokes's theorem, inverse and implicit function theorems, change of variables. Fourier analysis.
• CAS MA 531: Mathematical Logic
  Undergraduate Prerequisites: (CASMA293) or consent of instructor. - Graduate Prerequisites: (CASMA293) or consent of instructor. - The investigation of logical reasoning with mathematical methods. The syntax and semantics of sentential logic and quantificational logic. The unifying Godel Completeness Theorem, and models of theories. A look at the Godel Incompleteness Theorem and its ramifications. Effective Fall 2018, this course fulfills a single unit in the following BU Hub area: Philosophical Inquiry and Life's Meanings.
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  • Philosophical Inquiry and Life's Meanings
• CAS MA 532: Foundations of Mathematics
  Undergraduate Prerequisites: (CASMA531) - Axiomatic set theory as a foundation for mathematics and as a field of mathematics: Axiom of Choice, the Continuum Hypothesis, and consistency results. Also offered as CAS PH 461.
• CAS MA 539: Methods of Scientific Computing
  Undergraduate Prerequisites: (CASMA 225 or CASMA 230) & (CASMA 242 or CASMA 442) and programming experience or consent of instructor. - An introduction to topics including computational linear algebra, solutions of linear equations, numerical integration and solution of differential equations, finite element methods, and methods of stochastic simulation (i.e., Monte Carlo methods).
• CAS MA 541: Modern Algebra 1
  Undergraduate Prerequisites: (CASMA242 OR CASMA442) - Basic properties of groups, Sylow theorems, basic properties of rings and ideals, Euclidean rings, polynomial rings.
• 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