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MS in Data Science Courses. Required Courses DS-GA Introduction to Data Science Introduces students to basic software algorithms and software tools, teaches how to deal with data, representing data, and methodology. Course aims and objectives: After taking this class, students should: Approach business problems data-analytically.

Understand fundamental principles of data science, such as using data to get information about an unknown quantity of interest, calculating and using data similarity, fitting models to data, supervised and unsupervised modeling, overfitting and its avoidance, evaluation and model analytics, visualization, predictive modeling, causal inference, the data mining process, problem decomposition, data science strategy, solution deployment, and more.

Course Descriptions

Be able to apply the most important data science methods, using open-source tools. Prerequisites: Calculus and linear algebra at the undergraduate level DS-GA Machine Learning and Computational Statistics The course covers a wide variety of topics in machine learning, pattern recognition, statistical modeling, and neural computation.

Course aims and objectives: Teach intermediate topics in machine learning Provide hands-on experience in designing and programming data science algorithms Prerequisites: DS-GA Introduction to Data Science, or undergraduate course in Machine Learning. Course aims and objectives: Teach exact and approximate inference methods in graphical models. Teach learning techniques for graphical models and structured prediction.

Teach methods for causal inference. Course aims and objectives: Students will demonstrate an ability to handle a problem in data science from the point of problem definition through delivery of a solution. In doing so, they will demonstrate proficiency in collecting and processing real-world data, in designing the best methods to solve the problem, and in implementing a solution.

Students will demonstrate competence in presenting material by delivering two presentations: a proposal on how to approach the problem and their final solution. Students will learn how to work in small teams by working with at least one other student on their project. MAS Combinatorics This course treats various concepts in combinatorics in detail. It covers enumeration, sieve methods, graphs, partially ordered sets, generating functions, and extreme problems.

MAS Topics in Mathematics I This course introduces mathematics trends or subjects that are not covered in any of the regular courses. MAS Topics in Mathematics II This course introduces mathematics trends or subjects that are not covered in any of the regular courses. MAS Topics in Mathematics This course introduces mathematics trends or subjects that are not covered in any of the regular courses. Topics include curves, surfaces, varieties, sheaves, and divisors.

MAS Lie Algebra This course introduces the theory of semisimple Lie algebras over an algebraically closed field of characteristic zero, with an emphasis on representations. Topics include Lie algebras, root systems and simple roots, the Weyl group, Cartan subalgebras, simple algebras, weight vector, the Weyl-Kostant-Steinberg formula, and admissible lattices. Topics include the basic concepts of Lie groups, differentiable manifolds, homogeneous space, Lie algebras, representations of Lie groups and Lie algebras, and structures of Lie groups.

Topics include the definition of Riemannian manifolds, geodesics and curvature, the first and second variational formulas, Jacobi fields and conjugate points, comparison theorems, volume, and the Bishop-Gromov theorem. MAS Symplectic Geometry This course covers the basic concepts of linear symplectic geometry, symplectic manifold, and complex structure. Symplectic group action and various symplectic invariants are treated. It also covers Hodge decomposition theorem, Lefchetz decomposition theorem, and Kodaira embedding theorem.

MAS Homotopy Theory This course covers advanced topics in algebraic topology such as fibration and cofibration, H-spaces and co-H-spaces, the suspension theorem, the Hurwicz theorem, obstruction theory, homotopy operations, and spectral sequences.

Topics include characters of locally compact abelian groups, Hardy space method, conjugate functions, maximal functions, the Hilbert transform method, and wavelet transform methods. MAS Functional Analysis Topics include Banach space, Hilbert space, linear operators defined on a vector space of functions, Hahn-Banach theorem, the Banach-Steinhaus theorem, Banach fixed point theorem, the open mapping theorem, Schauder theorem, solutions of differential and integral equations, differential calculus of operators and applications, spectral theory and applications, and variational methods.

MAS Generalized Functions This course introduces basic properties of distributions and other generalized functions. Topics include locally convex vector spaces, distribution theory, generalized differentiation, integral transforms, Sobolev spaces, and applications to partial differential equations. MAS Partial Differential Equations This course introduces the modern theory of linear partial differential equations based on distribution theory.

Topics include the classification of partial differential operators, hyper-ellipticity and local solvability of operators, the Cauchy problem for hyperbolic equations, boundary value problems for elliptic equations, Laplace, heat, and wave equations, and an introduction to the theory of pseudo differential operators. MAS Nonlinear Differential Equations This course introduces various nonlinear differential equations, their solutions and related theories, and their applications to engineering and sciences. MAS Ordinary Differential Equations This course introduces the basic theory of ordinary differential equations, including the existence and uniqueness of the solution of ordinary differential equations, the properties of autonomous system, the stability of solutions, the Lyapunov function, the properties of periodic solutions, and applications.

Statistics - A Full University Course on Data Science Basics

MAS Stochastic Differential Equations Markov processes, Poisson processes, Brownian motions, Ito integrals, solutions of linear stochastic differential equations, and their asymptotic analysis, boundary value problems, filtering theory and applications to optimal control theory are treated. This course covers Markov chains and processes, Gauss processes, diffusion processes, stationary processes, ergodic theory, spectral theory, and prediction theory.

MAS Graphic Models in Statistics A statistical model from which we can represent the stochastic relationship among variables via a graph is called a graphical model. This model is easy to analyze with and draws much attention for its availability to the research fields of expert systems and artificial intelligence. Major topics include stochastic independence, independence graphs, information theory, the inverse of the variance-covariance matrix, the graphical Gauss model, the graphical log-linear model, the graph chain model, the mixed-variable model, and decomposition.

MAS Multivariate Statistical Analysis This course covers statistical analysis methods for data with multiple random variables.

  • Calculus Sequences.
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  • MS in Data Science Courses?

Major topics of the course include multivariate normal distribution, properties of variance-covariance matrices of random vectors, distributions of sample variance- covariance matrices, T-square statistics, statistical classification, multivariate analysis of variance, independence of random vectors, testing hypotheses on variance-covariance matrices, principal component analysis, canonical correlation analysis, and factor analysis.

MAS Computational Models of Neural Networks This course covers the models of biological and artificial neural networks in variety of perspectives. We cover topics such as models of neurons, neural coding, dynamics of neural networks, feed-forward neural networks, sample complexity, generalization bounds, optimization, and application to engineering problems. Numerical algorithms using the method of finite elements, and convergence tests and stability will be treated.

Especially we study the steady state theory for Stokes equations.

Course Descriptions

MAS Numerical Partial Differential Equations This course provides a basic foundation in numerical methods for partial differential equations. The course introduces the methods for some model partial differential equations, then goes into more depth for each method as it applies to other types of equations. Topics include the concentrate finite difference method for initial-boundary value problems, the finite difference method for elliptic problems, the finite difference method for parabolic problems, the finite difference method for hyperbolic problems, stability, convergence, and applications.

MAS High Speed Computation Parallel processing, multi-grid, domain decomposition for large scale computations are treated. We introduce parallel processing algorithms for super-computing.

Table of contents

MAS Computational Methods in Financial Mathematics This course is an introduction to computational methods for the numerical simulations of financial market models. It emphasizes Monte Carlo and quasi-Monte Carlo methods, including pseudorandom numbers generations, reduction of variance, computational methods for option pricing, and data analysis of financial market. MAS Cryptology and Coding Theory This course introduces second year graduate students to cry, coding, and data compression.

MAS Knot Theory This course studies knotting and linking phenomena of circles in a 3-dimensional space. More general embeddings of codimension 2 are also studied. The theories of knots, links, and braids are not only interesting enough by their own right, but they also are important to the understanding of low-dimensional manifolds, DNA folding, quantum physics, and related concepts. Various approaches are developed, typically including algebraic, geometric, and combinatorial methods.

Topics covered by this course may vary depending on the offering. MAS Transformation Group Theory This course treats fundamental properties of topology of transformation groups, such as fixed point set and tube-slice, differential transformation groups and isotropy representations, bundle theory and G-vector bundle theory, G-simplicity complexes, and Smith theory. MAS Ergodic Theory This is a study of the basic structures of dynamical systems and families of systems, with applications to number theory, physics, geometry, and information theory.

Topics include the Birkhoff ergodic theorem, mixing transformations, spectral properties, classification of measure-theoretic entropy, topological dynamics, invariant measures, topological entropy, and applications to number theory, physics, geometry and information theory. Frechet derivative, equilibrium point, Cauchy stress principle hyperelasticity, 3-dimensional elasticity and existence theory are introduced. MAS Finite Element Method This course studies the variation formula, the Ritz method, the Galerkin method, the finite element methods of elliptic equations, parabolic equations, and hyperbolic equations, analysis of the impact of the curvilinear boundary, analysis of error and convergence, and applications to engineering.

MAS Statistical Methods in Financial Mathematics This course covers statistical methodologies that are useful for financial markets. Topics include volatility estimation, regression analysis, asset valuation model, estimation of yield curve, financial time series, risk management, term structure. Statistical softwares are treated as well. Selected topics in current trends in mathematics will be treated MAS Topics in Mathematics I This course introduces mathematics trends or subjects that are not covered in any of the regular courses.

Research MAS M. Students choose topics and carry out research individually under the supervision of a chosen advisor. Greater statistics is everything related to learning from data, from the first planning or collection, to the last presentation or report. Lesser statistics is the body of statistical methodology. This is a Greater Statistics course.

There are basically two kinds of "statistics" courses. The real kind shows you how to make sense out of data. These courses would include all the recent developments and all share a deep respect for data and truth. The imitation kind involves plugging numbers into statistics formulas. The emphasis is on doing the arithmetic correctly. These courses generally have no interest in data or truth, and the problems are generally arithmetic exercises.

If a certain assumption is needed to justify a procedure, they will simply tell you to "assume the It seems like you all are suffering from an overdose of the latter.