Courses

The listing of a course description here does not guarantee a course’s being offered in a particular semester. Please refer to the published schedule of classes on the MyBU Student Portal for confirmation a class is actually being taught and for specific course meeting dates and times.

• GRS MA 679: Applied Statistical Machine Learning
  Continues topics of GRS MA 678 at a more advanced level. Application of supervised and unsupervised statistical machine learning techniques with extensive use of computation. Advanced topics such as analysis of network data, Bayesian nonparametric models are considered.
• GRS MA 681: Accelerated Introduction to Statistical Methods for Quantitative Research
  Introduction to statistical methods relevant to research in the computational sciences. Core topics include probability theory, estimation theory, hypothesis testing, linear models, GLMs, and experimental design. Emphasis on developing a firm conceptual understanding of the statistical paradigm through data analyses.
• GRS MA 684: Modern Regression Analysis in R
  Application of multivariate data analytic techniques. Multiple regression and correlation, confounding and interaction, variable selection, categorical predictors and outcomes, logistic regression, factor analysis, MANOVA, discriminant analysis, regression with longitudinal data, repeated measures, ANOVA.
• GRS MA 685: Advanced Topics in Applied Statistical Analysis
  Continues topics of GRS MA 684 at a more advanced level. Canonical correlation, multivariate analysis of variance, multivariate regressions. Categorical dependent variables techniques; discriminant analysis, logistic regression, log-linear analysis. Factor analysis; principal-axes, rotations, factor scores. Cluster analysis. Power analysis. Extensive use of statistical software.
• GRS MA 703: Statistical Analysis of Network Data
  Methods and models for the statistical analysis of network data, including network mapping and characterization, community detection, network sampling and measurement, and the modeling and inference of network and networked-indexed processes. Balance of theory and concepts, illustrated through various applications.
• GRS MA 711: Real Analysis
  Measure theory and integration on measure spaces, specialization to integration on locally compact spaces, and the Haar integral. Lp spaces, duality, and representation theorems. Introduction to Banach and Hilbert spaces, open mapping theorem, spectral theorem for Hermitian operators, and compact and Fredholm operators.
• GRS MA 713: Functions of a Complex Variable I
  The theory of analytic functions. Integral theorems, contour integration, conformal mapping, and analytic continuation.
• GRS MA 717: Functional Analysis I
  Theory of Banach and Hilbert spaces, and Hahn-Banach and separation theorems. Dual spaces. Banach contraction mapping theorem. Reflexivity and Krein-Milman theorem. Operator theory. Brouwer-Schauder fixed-point theorems. Applications to probability, dynamical systems, and applied mathematics.
• GRS MA 721: Differential Topology I
  Differential manifolds, tangent bundles, transversality, winding numbers, and vector bundles.
• GRS MA 722: Differential Topology II
  Intersection theory, Lefschetz fixed point theory, integration on manifolds, vector fields and flows, and Frobenius' theorem.
• GRS MA 725: Differential Geometry I
  Geometry of surfaces in Euclidean space; geodesics and curvature of Riemannian manifolds; topological restrictions on curvature.
• GRS MA 726: Differential Geometry II
  Topics include connections on vector bundles, moving frames, Hodge theory, spectral geometry, and characteristic classes.
• GRS MA 727: Algebraic Topology I
  Covers singular and simplical homology theory. Cohomology and cup products. Duality on manifolds. Lefschetz and fixed-point formula.
• GRS MA 731: Lie Groups and Lie Algebras
  Classical Lie groups, associated Lie algebras, exponential map, closed subgroups and homogeneous spaces, classification of simple Lie algebras, and elementary representation theory of Lie algebras. Selection of applications to analysis, geometry, or algebra.
• GRS MA 741: Algebra I
  Basic properties of groups, rings, fields, and modules. Specific topics include the Jordan-Holder and Sylow theorems, local rings, theory of localization, modules over PIDs, and Galois theory.
• GRS MA 742: Algebra II
  Advanced topics in algebra. Linear and multilinear algebra, commutative algebra, and an introduction to category theory and homological algebra. Further topics may include representation of groups, completions, real fields, and elementary algebraic number theory and algebraic geometry.
• GRS MA 743: Algebraic Number Theory I
  Algebraic integers, completions, ramification and the discriminant, cyclotomic and quadratic fields, ideal class groups, Dirichlet's unit theorem, ideles, and adeles. Further topics are chosen from analytic number theory, class field theory, and the theory of Diophantine equations.
• GRS MA 745: Algebraic Geometry I
  Affine and projective varieties, morphisms and rational maps, nonsingular varieties, Bezout's theorem, and an introduction to sheaves and schemes. Further topics are chosen from the advanced theory of schemes, algebraic curves, Riemann-Roch theorem, algebraic surfaces, and sheaf cohomology.
• GRS MA 746: Algebraic Geometry II
  Continuation of topics in algebraic geometry begun in GRS MA 745, including sheaves, schemes, sheaf cohomology, and further study of algebraic curves and surfaces.
• GRS MA 750: Nonparametric and Semiparametric Data Modeling
  Introduces theory and methods of non- and semiparametric data analysis. Topics include scatterplot smoothers, bias/variance trade-off, selection of smoothing parameter, generalized additive model, smoothing spline, and Bayesian nonparametric models. Applications in various fields are discussed.

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