Courses
Listed below are frequently given graduate-level courses in Mathematics and Statistics. Please consult the department’s website: https://www.umass.edu/mathematics-statistics/, which contains an updated list of regularly scheduled and special topics courses.
Graduate students in other departments should consult the Undergraduate Catalog for mathematics courses which may carry graduate credit in their own departments or which in any event may be of interest, especially those in applied mathematics, probability, and statistics.
All courses carry 3 credits unless otherwise specified.
Mathematics
513 Combinatorics
Cross-listed with CMPSCI 575. A basic introduction to combinatorics and graph theory for advanced students in computer science, mathematics, and related fields. Topics include elements of graph theory, Euler and Hamiltonian circuits, graph coloring, matching, basic counting methods, generating functions, recurrences, inclusion-exclusion, Polya’s theory of counting. Prerequisites: mathematical maturity, calculus, linear algebra, discrete mathematics course such as CMPSCI 250 or MATH 455. MATH 411 recommended but not required.
522 Fourier Methods
The course introduces and uses Fourier series and Fourier transform as a tool to understand varies important problems in applied mathematics: linear ODE & PDE, time series, signal processing, etc. We'll treat convergence issues in a non-rigorous way, discussing the different types of convergence without technical proofs. Topics: complex numbers, sin & cosine series, orthogonality, Gibbs phenomenon, FFT, applications, including say linear PDE, signal processing, time series, etc; maybe ending with (continuous) Fourier transform.
523H Introduction to Modern Analysis I
Construction of the real number system; sequences, series, functions of one real variable, limits, continuity, differentiability, Riemann integral; sequences and series of functions. Prerequisites: MATH 233, 235 and 300 or equivalent.
524 Introduction to Modern Analysis II
Topology of Euclidean space and functions of several variables (implicit function theorem), introduction to Fourier analysis, metric spaces and normed spaces. Applications to differential equations, calculus of variations, and others.
532H Topics in Ordinary Differential Equations
Topics chosen from: Sturm-Liouville theory, series solutions, stability theory and singular points, numerical methods, transform methods. Prerequisite: MATH 235 and 431.
534H Introduction to Partial Differential Equations
Classification of second-order partial differential equations, wave equation, Laplace’s equation, heat equation, separation of variables. Prerequisites: MATH 233, 235, and 431.
538 Introduction to Nonlinear Waves
The aim of this course will be to give an overview of the mathematical background, physical applications and numerical computations associated with a number of prototypical wave systems both at the continuum and at the lattice level.
545 Linear Algebra for Applied Mathematics
Basic concepts (over real or complex numbers): vector spaces, basis, dimension, linear transformations and matrices, change of basis, similarity. Study of a single linear operator: minimal and characteristic polynomial, eigenvalues, invariant subspaces, triangular form, Cayley-Hamilton theorem. Inner product spaces and special types of linear operators (over real or complex fields): orthogonal, unitary, self-adjoint, hermitian. Diagonalization of symmetric matrices, applications. Prerequisite: MATH 235 or equivalent.
548 Stochastic Processes and Simulation
Introduction to some fundamental stochastic processes such as discrete state Markov chains, Poisson processes, and Brownian motion, as well as an array of important stochastic models. Analysis of random walks, convergence of discrete and continuous-time Markov processes to stationarity, Poisson processes and other point processes, Brownian motion and Martingale processes. Introduction to Monte Carlo methods and computer modeling of stochastic systems, including random variable generation, expectation estimation with confidence interval formation, importance sampling, stochastic optimization, MCMC algorithms and sampling of Brownian motion.
551 Introduction to Scientific Computing
Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis. Prerequisites: MATH 233, and either MATH 235 or consent of instructor; knowledge of a high level programming language.
552 Applications of Scientific Computing
Introduction to the application of computational methods to models arising in science and engineering, focusing mainly on the solution of partial differential equations. Topics include finite differences, finite elements, boundary value problems, fast Fourier transforms. Prerequisite: MATH 551 or consent of instructor.
557 Linear Optimization & Polytopes
This proof-based course covers the fundamentals of linear optimization and polytopes and the relationship between them. The course will give a rigorous treatment of the algorithms used in linear optimization. The topics covered in linear optimization are graphical methods to find optimal solutions in two and three dimensions, the simplex algorithm, duality and Farkas' lemma, variation of cost functions, an introduction to integer programming and Chvatal-Gomory cuts. The topics covered simultaneously in polytopes are two- and three-dimensional polytopes, f-vectors, equivalence of the vertex and hyperplane descriptions of polytopes, the Hirsch conjecture, the secondary polytope, and an introduction to counting lattice points of polytopes.
563H Differential Geometry
Differential geometry of curves and surfaces in Euclidean 3-space using vector methods. Prerequisites: MATH 233 and 235.
571 Introduction to Mathematical Cryptography
The main focus of this course is on the study of cryptographical algorithms and their mathematical background, including elliptic curve cryptography and the Advanced Encryption Standard. Lectures will emphasize both theoretical analysis and practical applications. To help master these materials, students will be assigned Computational projects using computer algebra software.
605 Probability Theory I
A modern treatment of probability theory based on abstract measure and integration. Random variables, expectations, independence, laws of large numbers, central limit theorem, and general conditioning using the Radon-Nikodym theorem.
606 Stochastic Processes
An introduction to stochastic processes, covering Monte Carlo methods, Markov chains in discrete and continuous time, martingales, and Brownian motion. Theory and applications will each play a major role in the course. Applications will range widely and may include problems from population genetics, statistical physics, chemical reaction networks, and queueing systems, for example.
611 Algebra I
Introduction to groups, rings, and fields. Direct sums and products of groups, cosets, Lagrange’s theorem, normal subgroups, quotient groups. Polynomial rings, UFDs and PIDs, division rings. Fields of fractions, GCD and LCM, irreducibility criteria for polynomials. Prime field, characteristic, field extension, finite fields.
612 Algebra II
A continuation of MATH 611. Topics in group theory (e.g., Sylow theorems, solvable and simple groups, Jordan-Holder and Schreier theorems, finitely generated Abelian groups). Topics in ring theory (matrix rings, prime and maximal ideals, Noetherian rings, Hilbert basis theorems). Modules, including cyclic, torsion, and free modules, direct sums, tensor products. Algebraic closure of fields, normal, algebraic, and transcendental field extensions, basic Galois theory. Prerequisite: MATH 611 or equivalent.
621 Complex Analysis
Complex number field, elementary functions, holomorphic functions, integration, power and Laurent series, harmonic functions, conformal mappings, applications.
623 Real Analysis I
General theory of measure and integration and its specialization to Euclidean spaces and Lebesgue measure; modes of convergence, Lp spaces, product spaces, differentiation of measures and functions, signed measures, Radon-Nikodym theorem.
624 Real Analysis II
Continuation of MATH 623. Introduction to functional analysis; elementary theory of Hilbert and Banach spaces; functional analytic properties of Lp-spaces, applications to Fourier series and integrals; interplay between topology, and measure, Stone-Weierstrass theorem, Riesz representation theorem. Further topics depending on instructor.
645 Differential Equations and Dynamical Systems I
Classical theory of ordinary differential equations and some of its modern developments in dynamical systems theory. Linear systems and exponential matrix solutions. Well-posedness for nonlinear systems. Qualitative theory: limit sets, invariant set and manifolds. Stability theory: linearization about an equilibrium, Lyapunov functions. Autonomous two-dimensional systems and other special systems. Prerequisites: advanced calculus, linear algebra and basic ODE.
646 Applied Math and Math Modeling
Classical methods in applied mathematics and math modeling, including dimensional analysis, asymptotics, regular and singular perturbation theory for ordinary differential equations, random walks and the diffusion limit, and classical solution techniques for PDE. The techniques will be applied to models arising throughout the natural sciences.
651 Numerical Analysis I
The analysis and application of the fundamental numerical methods used to solve a common body of problems in science. Linear system solving: direct and iterative methods. Interpolation of data by function. Solution of nonlinear equations and systems of equations. Numerical integration techniques. Solution methods for ordinary differential equations. Emphasis on computer representation of numbers and its consequent effect on error propagation. Prerequisites: advanced calculus, knowledge of a scientific programming language.
652 Numerical Analysis II
Presentation of the classical finite difference methods for the solution of the prototype linear partial differential equations of elliptic, hyperbolic, and parabolic type in one and two dimensions. Finite element methods developed for two dimensional elliptic equations. Major topics include consistency, convergence and stability, error bounds, and efficiency of algorithm. Prerequisites: Math 651, familiarity with partial differential equations.
655 Biomedical and Health Data Analysis
In this course, we will review, develop, and evaluate some computational biology methods. We will implement most of these methods in Python. Although programming skills, machine learning, or computational biology background are preferred, they are not required for this course. Importantly, this is a research-based course; it is an introduction on how to do research in computational biology. We all work as a team to learn novel methods in computational biology and hopefully find ways to improve them. We will read some recently published papers, which include four cutting-edge papers on computational oncology, implement the methods that have been introduced in these papers, and reproduce their results.
657 Mathematical Theory of Machine Learning
Introduction to the theoretical foundation of machine learning with an emphasis on the statistical learning theory. Topics include the framework of statistical learning, PAC learning theory, VC dimensions, (stochastic) gradient descent, support vector machines, kernel methods, Rademacher complexity, covering and packing numbers, and introduction to neural networks. Provides a mathematical foundation for the study of neural networks in a subsequent advanced course on mathematical theory of deep learning.
652 Numerical Analysis II
Presentation of the classical finite difference methods for the solution of the prototype linear partial differential equations of elliptic, hyperbolic, and parabolic type in one and two dimensions. Finite element methods developed for two dimensional elliptic equations. Major topics include consistency, convergence and stability, error bounds, and efficiency of algorithm. Prerequisites: MATH 651, familiarity with partial differential equations.
662 Convex Polytopes
Introduction to the theory of convex polytopes and their applications to algebraic combinatorics. Covers basic facts and properties of polytopes including faces of polytopes, valuation theory, Ehrhart theory, and triangulations. We will also cover the following families of polytopes with interest in other fields: root polytopes, flow polytopes, polytopes from partially ordered sets, associahedra, and generalized permutahedra.
663 Sums of Squares: Theory and Applications
The theory of sums of squares (SOS) blends exciting ideas from optimization, real algebraic geometry and convex geometry. Over the last two decades, interest in the theory and application of SOS polynomials has exploded because of the work of Shor, Nesterov, Lasserre and Parrilo that connects SOS polynomials to modern optimization via semidefinite programming. Since then, there has been many thrilling applications in combinatorics, theoretical computer science, and engineering. This course will cover both the theory and some applications.
664 Combinatorial Optimization
A rigorous mathematical introduction to combinatorial optimization with proofs. Maximization and minimization problems in graphs and networks; matchings in bipartite graphs and in general graphs, assignment problem, polyhedral combinatorics, total unimodularity, matroids, matroid intersection, min arborescence, max flow;min cut, max cut, traveling salesman problem, stable sets and perfect graphs. One of our main tools will be integer programming, and we will also sometimes rely on semidefinite programming. Many of these problems come from real-world applications, so we will also sometimes discuss the algorithms necessary to solve them.
671 Topology
Topological spaces. Metric spaces. Compactness, local compactness. Product and quotient topology. Separation axioms. Connectedness. Function spaces. Fundamental group and covering spaces.
672 Algebraic Topology
Introduction to the basic tools of algebraic topology. Emphasis will be placed on being able to compute these invariants, not just on their definitions and associated theorems. Topics include: Simplical and cell complexes, singular and simplicial homology, long exact sequences and excision, cohomology, Künneth formulas, Poincaré duality.
679 Numerical Algorithms & Practices
This course covers various topics in Scientific Computing including: basic numerical techniques of linear algebra and their applications, data formats and practices, matrix computations with an emphasis on solving sparse linear systems of equations and eigenvalue problems. Students will learn about the state-of-the-art programming practices in numerical linear algebra, and will be introduced to numerical parallel algorithms and parallel programming with OpenMP, MPI and hybrid. For students to be successful in this course they should know Linear Algebra basics, and have interests in math and programing.
691T Seminar - Teaching in University Curricula
1 Credit. A seminar course dedigned to support graduate students as they teach their first discussion/recitation section at UMass. The seminar will focus on four components of teaching: who the students are, teaching calculus concepts, instruction techniques, and assessment.
696 Independent Study
Credit, 1-6.
703 Topics in Geometry I
Inverse and implicit function theorems, rank of a map. Regular and critical values. Sard’s theorem. Differentiable manifolds, submanifolds, embeddings, immersions and diffeomorphisms. Tangent space and bundle, differential of a map. Partitions of unity, orientation, transversality embeddings in Rn. Vector fields, local flows. Lie bracket, Frobenius theorem. Lie groups, matrix Lie groups, left invariant vector fields. Prerequisite: MATH 671 or consent of instructor.
704 Topics in Geometry II
Tensor calculus, differential forms, integration, closed and exact forms. DeRham cohomology. Vector bundles. Introduction to Riemannian Geometry: Gaussian curvature, curvature tensor. Connections, curvature, Chern classes. Prerequisite: MATH 703.
705 Symplectic Topology
Introduction to symplectic topology along with its connections to differential, algebraic, complex and contact geometry and topology.
706 Stochastic Calculus
Introduction to the theory of stochastic differential equations oriented towards topics useful in applications (Brownian motion, stochastic integrals, and diffusion as solutions of stochastic differential equations), and the study of diffusion in general (forward and backward Kolmogorov equations, stochastic differential equations and the Ito calculus, as well as Girsanov's theorem, Feynman-Kac formula, Martingale representation theorem). Applications to mathematical finance will be included as time permits.
707 Algebraic Geometry
A fast-paced introduction to algebraic geometry with a strong emphasis on examples. Topics will include projective varieties and schemes, singularities, differential forms, line bundles and sheaves, and sheaf cohomology, including the Riemann--Roch theorem and Serre duality for algebraic curves.
708 Complex Algebraic Geometry
An introductory course in complex algebraic geometry. The basic techniques of Kahler geometry, Hodge theory, line and vector bundles which are needed for the study of the geometry and topology of complex projective algebraic varieties will be introduced and illustrated in basic examples.
711 Homological Algebra
Homological algebra can be seen as a generalization and extension of linear algebra, and so it plays an essential role in many areas of contemporary mathematics. Like linear algebra, it is important to understand both algorithms but also powerful structural results, and we will give due attention to both aspects. This course will lay foundations in a way guided by modern views (e.g., we will introduce model categories) but will also explore classic applications, like group cohomology and Lie algebra cohomology, so that computational facility is developed. By the end of the course, you will know what a derived category is and how to run a spectral sequence.
713 Introduction to Algebraic Number Theory
Valuations, rings of integral elements, ideal theory in algebraic number fields of algebraic functions of one variable, Dirichlet-Hasse unit theorem and Riemann-Roch theorem for curves. Prerequisites: MATH 611 and 612 or equivalent.
714 Arithmetic of Elliptic Curves
Elliptic curves, as the only smooth projective algebraic curves equipped with a group law, play a central role in modern arithmetic geometry. The goal of this course is to learn the tools and techniques required to study these groups over the rational numbers by first studying them over finite fields, p-adic fields and archimedean fields.
717 Representation Theory
Representation theory studies the way groups, rings and other algebraic structures can act by linear symmetries. We will consider representations of finite groups, the general linear group, the symmetric group, and quiver algebras. If time permits, more advanced topics such as Soergel bimodules and applications to knot homology may be introduced.
718 Lie Algebras
Lie algebras are linear algebraic structures of great utility in mathematics and physics as an efficient tool for the study of symmetries of objects. This course will cover the fundamentals of the subject, including nilpotent and solvable Lie algebras, as well as semisimple Lie algebras and their representations.
721 Riemann Surfaces
This course introduces Riemann surfaces from the points of view of 1-dimensional complex manifolds and also 2-dimensional real oriented conformal manifolds. Topics covered included the structure of holomorphic maps between Riemann Surfaces (Riemann-Hurwitz Theorem), holomorphic line;vector bundles, Chern classes, the Picard group of holomorphic line bundles, the Abel-Jacobi map, and the basic theorems of Riemann Surface theory: Mittag-Leffler, Riemann-Roch, Serre duality, Kodaira embedding and Serre's GAGA principle.
725 Introduction to Functional Analysis I
Banach and Hilbert spaces, continuous linear operators, spectral theory, Banach algebras. Prerequisite: Math 623 or 705.
731 Introduction to Partial Differential Equations I
Introduction to the modern methods in partial differential equations. Calculus of distributions: weak derivatives, mollifiers, convolutions and Fourier transform. Prototype linear equations of hyperbolic, parabolic and elliptic type, and their fundamental solutions. Initial value problems: Cauchy problem for wave and diffusion equations; well-posedness in the Hilbert-Sobolev setting. Boundary value problems: Dirichlet and Neumann problems for Laplace and Poisson equations; variational formulation and weak solutions; basic regularity theory; Green functions and operators; eigenvalue problems and spectral theorem. Prerequisites: advanced calculus and MATH 623-624.
732 Introduction to Partial Differential Equations II
A continuation of MATH 731. General class of equations and systems, modeled on the prototypes studied in 731. Linear hyperbolic systems. Parabolic evolution equations, and semigroups of operators. Linear elliptic equations of second order. Topics in nonlinear equations. Possible topics include: hyperbolic conservation laws; nonlinear parabolic systems—reaction-diffusion equations, Navier-Stokes equations; mean curvature equations; free-boundary problems. Prerequisite: MATH 731.
773 Low Dimensional Topology
The goal of this course is to study knots, surfaces, 3- and 4-dimensional spaces. Topics include: Morse theory, handlebodies and Kirby calculus, classification of surfaces, Heegaard splittings of 3-manifolds and Dehn surgeries, h-cobordism theory in higher dimensions, Wall and Freedman theorems, constructions of smooth, symplectic and complex manifolds, Gauge theory, exotic 4-manifolds.
774 Mapping Class Groups
The study of mapping class groups of surfaces connects to different fields of mathematics, such as geometry, topology, algebra and combinatorics. The rich algebraic structure and the intrinsic geometric nature of mapping class groups have led to an immense mathematical activity in the past several decades, yet with many unanswered questions up to date. The purpose of this course is to go over the fundamentals of the theory, discuss its various facets and applications, and introduce the students to open research problems on related topics.
796, 896 Independent Study
Maximum credit, 6.
899 Doctoral Dissertation
Credit, 18.
Statistics
501 Methods of Applied Statistics
For graduate and upper-level undergraduate students, with focus on practical aspects of statistical methods. Topics include: data description and display, probability, random variables, random sampling, estimation and hypothesis testing, one and two sample problems, analysis of variance, simple and multiple linear regression, contingency tables. Includes data analysis using a computer package. Prerequisites: high school algebra; junior standing or higher.
515 Introduction to Statistics I
First semester of a two-semester sequence. Emphasis on those parts of probability theory necessary for statistical inference. Probability models, sample spaces, conditional probability, independence, random variables, expectation, variance, discrete and continuous probability distributions, joint distributions, sampling distributions, the central limit theorem. Prerequisites: MATH 131, 132.
516 Introduction to Statistics II
Basic ideas of point and interval estimation and hypothesis testing; one and two sample problems, simple linear regression, topics from among one-way analysis of variance, discrete data analysis and nonparametric methods. Prerequisite: STATISTC 515 or equivalent.
525 Regression Analysis
Simple and multiple linear regression; correlation; the use of dummy variables; residuals and diagnostics; model building/variable selection, regression models and methods in matrix form; an introduction to weighted least squares, regression with correlated errors and nonlinear (including binary) regression. Prerequisite: STATISTC 516 or equivalent.
526 Design of Experiments
Planning, statistical analysis and interpretation of experiments. Designs considered include factorial designs, randomized blocks, latin squares, incomplete balanced blocks, nested and crossover designs, mixed models. Has a strong applied component involving the use of a statistical package for data analysis. Prerequisite: previous coursework in statistics.
530 Analysis of Discrete Data
Discrete/Categorical data are prevalent in many applied fields, including biological and medical sciences, social and behavioral sciences, and economics and business. This course provides an applied treatment of modern methods for visualizing and analyzing broad patterns of association in discrete/categorical data. Topics include forms of discrete data, visualization/exploratory methods for discrete data, discrete data distributions, correspondence analysis, logistic regression models, models for polytomous responses, loglinear and logit Models for contingency tables, and generalized linear models. This course is primarily an applied statistics course. While models and methods are written out carefully with some basic mathematical derivations, the primary focus of the course is on the understanding of the visualization and modeling techniques for discrete data, presentation of associated models/methods, data analysis, interpretation of results, statistical computation and model building.
535 Statistical Computing
Introduces computing tools needed for statistical analysis including data acquisition from database, data exploration and analysis, numerical analysis and result presentation. Advanced topics include parallel computing, simulation and optimization, and package creation. The class will be taught in a modern statistical computing language.
540 Introduction to Statistical Learning
Introduction to some modern statistical regression and classification techniques including logistic regression, nearest neighbor methods, discriminant analysis, kernel smoothing, smoothing spline, local regression, generalized additive models, decision trees, random forests, support vector machines and deep learning. Clustering methods such as K-means and hierarchical clustering will be introduced. Finally, there will also topics on resampling-based model evaluation methods and regularization-based model selection methods. The course emphasizes the mathematics behinds these methods sufficient to understand the differences among the methods as well as the practical implementation of them.
550 Intro to Survey Sampling
This course is about how to write and use a modern programming language to explore and solve problems in pure and applied mathematics. We will use Python, and the first part of the course will review core language features and apply them to problems in mathematics. We will introduce specialized mathematical packages such as numpy. The remainder of the course---and its goal---is to help students develop the skills to translate mathematical problems and solution techniques into algorithms and code. Students will use code to solve and explore mathematical questions in several project areas. Students will work on projects both individually and in small groups.
596 Independent Study
Maximum credit, 6.
598C Statistical Consulting
Provides a forum for training in statistical consulting. Application of statistical methods to real problems, as well as interpersonal and communication aspects of consulting are explored in the consulting environment. Students enrolled in this class will become eligible to conduct consulting projects as consultants in the Statistical Consulting and Collaboration Services group in the Department of Mathematics and Statistics. Consulting projects arising during the semester will be matched to students enrolled in the course according to student background, interests, and availability.
605 Probability Theory
A modern treatment of probability theory based on abstract measure and integration. Random variables, expectations, independence, laws of large numbers, central limit theorem, and general conditioning using the Radon-Nikodym theorem. Introduction to stochastic processes: martingales, Brownian motion. Prerequisite: MATH 623.
607 Mathematical Statistics I
Probability theory, including random variables, independence, laws of large numbers, central limit theorem; statistical models; introduction to point estimation, confidence intervals, and hypothesis testing. Prerequisite: advanced calculus and linear algebra, or consent of instructor.
608 Mathematical Statistics II
Point and interval estimation, hypothesis testing, large sample results in estimation and testing; decision theory; Bayesian methods; analysis of discrete data. Also, topics from nonparametric methods, sequential methods, regression, analysis of variance. Prerequisite: STATISTC 607 or equivalent.
610 Bayesian Statistics
Introduction to Bayesian data analysis, including modeling and computation. We will begin with a description of the components of a Bayesian model and analysis (including the likelihood, prior, posterior, conjugacy and credible intervals). We will then develop Bayesian approaches to models such as regression models, hierarchical models and ANOVA. Computing topics include Markov chain Monte Carlo methods.
625 Regression Modeling
Regression is the most widely used statistical technique. In addition to learning about regression methods this course will also reinforce basic statistical concepts and expose students (for many for the first time) to "statistical thinking" in a broader context. This is primarily an applied statistics course. While models and methods are written out carefully with some basic derivations, the primary focus of the course is on the understanding and presentation of regression models and associated methods, data analysis, interpretation of results, statistical computation and model building. Topics covered include simple and multiple linear regression; correlation; the use of dummy variables; residuals and diagnostics; model building/variable selection, regression models and methods in matrix form; an introduction to weighted least squares, regression with correlated errors and nonlinear including binary) regression.
630 Statistical Methods for Data Science
This course provides an introduction to the statistical techniques that are most applicable to data science. Topics include regression, classification, resampling, linear model selection and regularization, tree-based methods, support vector machines and unsupervised learning. The course includes a computing component using statistical software.
631 Categorical Data Analysis
Distribution and inference for binomial and multinomial variables with contingency tables, generalized linear models, logistic regression for binary responses, logit models for multiple response categories, loglinear models, inference for matched-pairs and correlated clustered data.
632 Applied Multivariate Statistics
This course provides an introduction to the more commonly-used multivariate statistical methods. Topics include principal component analysis, factor analysis, clustering, discrimination and classification, multivariate analysis of variance (MANOVA), and repeated measures analysis. The course includes a computing component in R.
633 Data Visualization
The increasing production of descriptive data sets and corresponding software packages has created a need for data visualization methods for many application areas. Data visualization allows for informing results and presenting findings in a structured way. This course provides an introduction to graphical data analysis and data visualization. Topics covered include exploratory data analysis, data cleaning, examining features of data structures, detecting unusual data patterns, and determining trends. The course will also introduce methods to choose specific types of graphics tools and understanding information provided by graphs. The statistical programming language R is used for the course.
639 Time Series Analysis and Applications
Time series analysis is an effective statistical methodology for modelling time series data (a series of observations collected over time) and forecasting future observations in many areas, including economics, social sciences, physical and environmental sciences, medicine, and signal processing. This course presents the fundamental principles of time series analysis including mathematical modeling of time series data and methods for statistical inference. Topics covered will include modeling and inference in the following models: smoothing methods, decomposition methods, (nonseasonal/seasonal) autoregressive moving average (ARMA) models, unit root and differencing, (nonseasonal/seasonal) autoregressive integrated moving average (ARIMA) models, spectral analysis, (generalized) autoregressive conditionally heteroscedastic models, time regression models with autocorrelated error, lagged regression, and vector autoregressive (VAR) model.
660 Statistical Consulting
This class focuses on skills statisticians need to bring their classroom knowledge to practical problems. Half of the class will meet concurrently with the Statistical Consulting Practicum, and be focused around real consulting problems brought in by clients. The other half will explore in greater depths methods, techniques, and approaches useful in practical problems but not usually covered in the standard curriculum. Specific topics covered may vary slightly based on the mix of clients this semester, but typically include methods like power analysis, missing data, practical mixed models, and practical model selection and interpretation, as well as soft skills like maintaining professional relationships, asking questions, listening, and communicating with non-statisticians. Wherever possible, content will be motivated by specific current or past consulting projects.
661 Applied Statistics and Data Analysis
This course gives students a brief overview of several topics of practical importance to statisticians doing data analysis. It focuses on topics not typically covered in the required curriculum, but of use to students earning advanced degrees in statistics. The early part of the course focuses on R for data science, including data acquisition, data manipulation and visualization, modeling, programming, and result presentation. The second part presents overviews of many topics, each providing a foundation from which students may extend their understanding, should they need to use the method in practice, or wish to consider more detailed study or research. Each topic covered includes both a technical overview and an application, implemented in software. Specific topics include: Simulation studies, mixed effect models, and missing data, and may also include other topics that arise from consulting projects or student interests, potentially including randomization methods, Markov chain Monte Carlo, missing data, casual modeling, survival analysis, network analysis, exploratory data analysis, and cross-validation. One hour each week will meet concurrently with the Statistical Consulting Practicum, where students will engage with academic and non-academic clients and the statistical problems arising in their work.
691P Statistics Cross-Disciplinary Research
Students will work in teams to collaborate with researchers in other disciplines on research projects. Students in the course will learn new statistical methods, a discipline where statistics is applied, how to work collaboratively, how to use R, and how to present oral and written reports.
696 Independent Study
Maximum credit, 6.
705 Linear Models I
Basic results on the multivariate normal distribution; linear and quadratic forms; noncentral Chi-square and F distributions; inference in linear models, including point and interval estimation, hypothesis testing, etc. Prerequisites: STATISTC 607-608 or equivalent; linear algebra.
725 Estimation Theory and Hypothesis Testing
The advanced theory of statistics, including methods of estimation (unbiasedness, equivariance, maximum likelihood, Bayesian, minimax), optimality properties of estimators, hypothesis testing, uniformly most powerful tests, unbiased tests, invariant tests, relationship between confidence regions and tests, large sample properties of tests and estimators. Prerequisites: STATISTC 605 and 608.
796, 896 Independent Study
Maximum credit, 6.
899 Doctoral Dissertation
Credit, 18.