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Mathematics |
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MA-GY 6873 Nonparametric Methods in Statistics 3 Credits This course covers statistical methods not bound by assumption of known parametric form of the distribution of observations. Applications to engineering and scientific research in which observations are not ordered on a numerical scale. Order statistics, tolerance regions, permutation tests, goodness of fit tests, limiting distributions and largesample properties of tests.
Prerequisite(s): MA-GY 6813 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 6913 Time Series Analysis I 3 Credits In this course, students carefully study tractable models for statistical analysis of scalar time series. Models treated: (l) “error plus trend” models, (2) stationary stochastic process models with special emphasis on autoregressive models. Estimation, tests of hypotheses and multiple-decision procedures for these models. Spectral representation and filtering, estimation of spectral density.
Prerequisite(s): MA-GY 6813 and MA-GY 6843 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 6923 Time Series Analysis II 3 Credits In this course, students carefully study tractable models for statistical analysis of scalar time series. Models treated: (l) “error plus trend” models, (2) stationary stochastic process models with special emphasis on autoregressive models. Estimation, tests of hypotheses and multiple-decision procedures for these models. Spectral representation and filtering, estimation of spectral density and in continuation of MA-GY 6913 .
Prerequisite(s): MA-GY 6913 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7013 Abstract Algebra 3 Credits This course covers basic algebraic structures, groups, rings, fields, integral domains and modules. Field extensions and Galois theory.
Prerequisite(s): MA-GY 6013 or equivalent. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7033 Linear Algebra I 3 Credits This course covers basic ideas of linear algebra: fields, vector spaces, basis, dependence, independence, dimension. Relation to solving systems of linear equations and matrices. Homomorphisms, duality, inner products, adjoints and similarity.
Prerequisite(s): MA-UY 2012 and MA-UY 2122 or equivalent. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7043 Linear Algebra II 3 Credits This course continues MA-GY 7033 . Topics covered are basic concepts of linear algebra continuing with: range, nullity, determinants and eigenvalues of matrices and linear homomorphisms, the polar decomposition and spectral properties of linear maps, orthogonality, adjointness and its applications.
Prerequisite(s): MA-GY 7033 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7213 Real and Complex Analysis I 3 Credits This course provides rigorous and comprehensive treatment of real analysis. Topics covered: outer measure, Lebesgue measure, Lebesgue integral, convergence theorems, functions of bounded variation, integration in measure spaces, the Radon-Nikodyn Theorem and Fubini’s Theorem.
Prerequisite(s): MA-GY 6213 and MA-GY 6223 or equivalent. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7223 Real and Complex Analysis II 3 Credits This course continues MA-GY 7213 and provides a rigorous and comprehensive treatment of complex analysis. Topics covered: analytic and meromorphic functions, differentiation and integration, Cauchy’s theorem, Morera’s theorem, Power and Laurent series, residue theory, Rouche’s theorem, conformal mappings, the Riemann mapping theorem and Riemann surfaces.
Prerequisite(s): MA-GY 7213 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7313 Functional Analysis I 3 Credits This course, together with its sequel MA-GY 7323 , introduces the language and methods of functional analysis. It covers normed spaces, Hilbert spaces, bounded linear functionals, Hahn-Banach theorem, the dual space, bounded operators, Fredholm theory of compact operators, self-adjoint operators and applications to classical analysis.
Prerequisite(s): MA-GY 6013 and MA-GY 7213 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7323 Functional Analysis II 3 Credits This course, together with its prequel MA-GY 7313 , introduces the language and methods of functional analysis. It covers normed spaces, Hilbert spaces, bounded linear functionals, Hahn-Banach theorem, the dual space, bounded operators, Fredholm theory of compact operators, self-adjoint operators and applications to classical analysis.
Prerequisite(s): MA-GY 7313 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7333 Measure Theory I 3 Credits This course presents a unified treatment of the part of measure theory that is most useful for its application in modern analysis. Topics covered: sets and classes, measures and outer measures, measurable functions, integration, general set functions, product spaces, transformations, probability. The dominated convergence theorem, Riesz Representation Theorem, Vitali-Caratheodory theorem, etc., are covered in conjunction with many examples.
Prerequisite(s): Graduate status. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7343 Measure Theory II 3 Credits This course continues MA-GY 7333 and presents a unified treatment of the part of measure theory that is most useful for applications in modern analysis. Topics covered: Fubini’s theorem along with convolutions and distributions are applied to explicit examples. In this part, Baire’s theorem, the Banach-Steinhaus theorem, the Open Mapping theorem, the Hahn-Banach Theorem are derived with the properties of the Radon-Nikodym derivatives to naturally generalize calculus both differential and integral.
Prerequisite(s): MA-GY 7333 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7353 Fourier and Laplace Transforms 3 Credits This course presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. Topics covered: application of transform methods to partial differential equations of mathematical physics. Includes introduction to the Wiener-Hopf technique.
Prerequisite(s): Graduate status or permission of adviser. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7403 Topology 3 Credits This course covers topological spaces. Compactness, connectedness, continua, extension theorems and metrization theorems. Simplexes, simplicial topology and applications. Fixed point theorems. Graphs and networks. Homology and cohomology theory. Introduction to Morse theory.
Prerequisite(s): MA-GY 6213 and MA-GY 6223 or equivalent. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7503 Manifolds and Lie Groups 3 Credits This course covers elementary theory of manifolds. Tangent space, mappings, submanifolds, fields, fiber bundles, Lie groups, homogeneous spaces. Elements of the theory of connections, Riemannian geometry. Imbedded manifolds. Calculus of variations. Harmonic forms, complex manifolds and Morse theory.
Prerequisite(s): MA-GY 6213 and MA-GY 6223 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7543 Topological Methods in Analysis 3 Credits This course covers aspects of topological methods and applications to existence theorems in analysis. Use of fixed-point theorems and topological degree to study properties of solutions to ordinary and partial differential equations. No previous courses in topology are required.
Prerequisite(s): MA-UY 4623 or MA-GY 6223 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7603 Topics in Algebra I 3 Credits Course content varies. In spring of the year before the course offering, a detailed description is posted and mailed to all graduate mathematics students.
Prerequisite(s): MA-GY 7013 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7613 Topics in Algebra II 3 Credits Course content varies. In spring of the year before the course offering, a detailed description is posted and mailed to all graduate mathematics students.
Prerequisite(s): MA-GY 7603 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7623 Topics in Linear Algebra I 3 Credits Course content varies.
Prerequisite(s): MA-GY 7033 and MA-GY 7043 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7633 Topics in Linear Algebra II 3 Credits Course content varies.
Prerequisite(s): MA-GY 7623 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7643 Topics in Real Analysis I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6213 and MA-GY 6223 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7653 Topics in Real Analysis II 3 Credits Course content varies.
Prerequisite(s): MA-GY 7643 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7663 Topics in Complex Analysis I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6303 and MA-GY 6313 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7673 Topics in Complex Analysis II 3 Credits Course content varies.
Prerequisite(s): MA-GY 7663 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7683 Topics in Geometry I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6403 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7693 Topics in Geometry II 3 Credits Course content varies.
Prerequisite(s): MA-GY 7683 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7703 Topics in Topology I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6403 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7713 Topics in Topology II 3 Credits Course content varies.
Prerequisite(s): MA-GY 7703 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7723 Topics in Applied Mathematics I 3 Credits Course content varies.
Prerequisite(s): Graduate status or permission of adviser. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7733 Topics in Applied Mathematics II 3 Credits Course content varies.
Prerequisite(s): MA-GY 7723 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7743 Topics in Probability I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6813 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7753 Topics in Probability II 3 Credits Course content varies.
Prerequisite(s): MA-GY 7743 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7763 Topics in Statistics I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6833 and MA-GY 6843 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7773 Topics in Statistics II 3 Credits Course content varies.
Prerequisite(s): MA-GY 7763 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7813 Probability 3 Credits This course covers measure-theoretic foundations of probability. Expectations, distribution functions, characteristic functions. Modes of convergence of random variables and distribution functions. Laws of large numbers. The multidimensional central-limit theorems and related asymptotic expansions. Infinitely divisible distributions.
Prerequisite(s): MA-GY 7213 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7833 Stochastic Processes I 3 Credits This course covers foundations of stochastic processes. Kolmogorov’s extension theorem. Properties of sample paths. Conditional expectation. Martingales. Classes of stochastic processes. Gaussian processes, Markov processes and others. Second order properties. Stationary processes. Applications.
Prerequisite(s): MA-GY 7813 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 7843 Stochastic Processes II 3 Credits This course covers: foundations of stochastic processes. Kolmogorov’s extension theorem. Properties of sample paths. Conditional expectation. Martingales. Classes of stochastic processes. Gaussian processes, Markov processes and others. Second order properties. Stationary processes. Applications. This course runs in continuation of it’s prequel MA-GY 7833 .
Prerequisite(s): MA-GY 7833 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8003 Advanced Topics in Discrete Mathematics I 3 Credits Course content varies. In spring of the year before course offering, a detailed description is posted and mailed to all graduate mathematics students.
Prerequisite(s): MA-GY 6003 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8013 Advanced Topics in Discrete Mathematics II 3 Credits Course content varies. In spring of the year before course offering, a detailed description is posted and mailed to all graduate mathematics students.
Prerequisite(s): MA-GY 8003 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8023 Advanced Topics in Algebra I 3 Credits Course content varies.
Prerequisite(s): MA-GY 7033 and MA-GY 7043 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8033 Advanced Topics in Algebra II 3 Credits Course content varies.
Prerequisite(s): MA-GY 8023 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8043 Advanced Topics in Real Analysis I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6213 and MA-GY 6223 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8053 Advanced Topics in Real Analysis II 3 Credits Course content varies.
Prerequisite(s): MA-GY 8043 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8063 Advanced Topics in Linear Algebra I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6303 and MA-GY 6313 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8073 Advanced Topics in Linear Algebra II 3 Credits Course content varies.
Prerequisite(s): MA-GY 8063 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8103 Advanced Topics in Complex Analysis I 3 Credits Course content varies.
Prerequisite(s): MA-GY 7213 and MA-GY 7223 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8113 Advanced Topics in Complex Analysis II 3 Credits Course content varies.
Prerequisite(s): MA-GY 7213 and MA-GY 7223 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8123 Advanced Topics in Geometry I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6403 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8133 Advanced Topics in Geometry II 3 Credits Course content varies.
Prerequisite(s): MA-GY 6403 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8143 Advanced Topics in Topology I 3 Credits Course content varies.
Prerequisite(s): MA-GY 7403 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8153 Advanced Topics in Topology II 3 Credits Course content varies.
Prerequisite(s): MA-GY 7403 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8163 Advanced Topics in Applied Mathematics I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6003 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8173 Advanced Topics in Applied Mathematics II 3 Credits Course content varies.
Prerequisite(s): MA-GY 6003 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8183 Advanced Topics in Probability I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6813 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8193 Advanced Topics in Probability II 3 Credits Course content varies.
Prerequisite(s): MA-GY 6813 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8203 Advanced Topics in Statistics I 3 Credits Course content varies.
Prerequisite(s): MA-GY 6833 and MA-GY 6843 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8213 Advanced Topics in Statistics II 3 Credits Course content varies.
Prerequisite(s): MA-GY 6833 and MA-GY 6843 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8383 Advanced Topics in Differential Equations 3 Credits Course content varies.
Prerequisite(s): MA-GY 6233 and MA-GY 6243 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 8583 Advanced Topics in Differential Geometry 3 Credits Course content varies.
Prerequisite(s): MA-GY 6403 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 9413 Reading in Mathematics I 3 Credits In this course, reading is guided by faculty members and devoted mainly to scholarly papers.
Prerequisite(s): Department’s permission. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 9423 Reading in Mathematics II 3 Credits In this course, reading is guided by faculty members and devoted mainly to scholarly papers.
Prerequisite(s): Department’s permission. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 9433 Reading in Mathematics III 3 Credits In this course, reading is guided by faculty members and devoted mainly to scholarly papers.
Prerequisite(s): Department’s permission. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 9443 Reading in Mathematics IV 3 Credits In this course, reading is guided by faculty members and devoted mainly to scholarly papers.
Prerequisite(s): Department’s permission. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 9453 Reading in Mathematics V 3 Credits In this course, reading is guided by faculty members and devoted mainly to scholarly papers.
Prerequisite(s): Department’s permission. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 9463 Reading in Mathematics VI 3 Credits In this course, reading is guided by faculty members and devoted mainly to scholarly papers.
Prerequisite(s): Department’s permission. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 9583 Selected Topics in Advanced Mathematics I 3 Credits This course reviews current mathematics research. Specific topics vary, depending on instructor.
Prerequisite(s): Department’s permission. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-GY 9593 Selected Topics in Advanced Mathematics II 3 Credits This course reviews current mathematics research. Specific topics vary, depending on instructor.
Prerequisite(s): Department’s permission. Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 902 Introduction to Precalculus 2 Credits This course covers foundations of Algebra: exponents, multiplication of algebraic expressions, factoring algebraic expressions, working with algebraic fractions, proportionality, rates of change, equation of a line, completing squares, the quadratic formula, solving equations, system of linear equations, inequalities, domain and range of functions.
Prerequisite(s): Placement exam. Note: Credit for this course may not be used to satisfy the minimum credit requirement for graduation.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 912 Precalculus A 2 Credits This course covers exponential and logarithmic functions, transformations of functions; trigonometric functions.
Prerequisite(s): MA-UY 902 . Note: Credit for this course may not be used to satisfy the minimum credit requirement for graduation.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 914 Precalculus 4 Credits This course covers foundations of Algebra: exponents, multiplication of algebraic expressions, factoring algebraic expressions, working with algebraic fractions, proportionality, rates of change, equation of a line, completing squares, the quadratic formula, solving equations, systems of linear equations, inequalities, domain and range of functions, exponential and logarithmic functions, compositions, transformations of functions, right triangles, trigonometry of triangles.
Prerequisite(s): Placement exam. Corequisite(s): Note: Credit for this course may not be used to satisfy the minimum credit requirement for graduation.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 922 Precalculus B 2 Credits Continuation of Precalculus: trigonometric functions, compositions, inverses and combinations of functions, polynomial and rational functions.
Prerequisite(s): MA-UY 912 . Note: Credit for this course may not be used to satisfy the minimum credit requirement for graduation.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 954 Precalculus B 4 Credits This course covers the fundamentals of algebra with a focus on Management and the Life Sciences. The topics include: foundations of Algebra, solving equations, exponents, working with algebraic expressions, working with algebraic fractions, proportionality, rates of change, lines in the plane, completing squares, the quadratic formula, systems of linear equations, inequalities, graphs, exponentials, logarithms, inverses, compositions, transformations of functions and right angle trigonometry.
Prerequisite(s): Placement exam. Corequisite(s): Note: Course required only for specific Majors in place of MA 914. Credit for this course may not be used to satisfy the minimum credit requirement for graduation.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 1002 The Art of Mathematics 2 Credits This is an introductory course about Mathematics. Areas of Mathematics. History of Mathematics. Mathematical Methods. Great Mathematicians. Famous open and solved mathematical problems. The study of Mathematics. Mathematical Software.
Weekly Lecture Hours: 2 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 1024 Calculus I 4 Credits This course covers: Library of functions, functions of one variable. Limits, derivatives of functions defined by graphs, tables and formulas, differentiation rules for power, polynomial, exponential and logarithmic functions, derivatives of trigonometric functions, the product and quotient rule, the chain rule, applications of the chain rule, maxima and minima, optimization. MA-UY 1324 is for students who wish to take MA 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA 1024 but with more contact hours a week, incorporating a full discussion of the required precalculus topics.
Prerequisite(s): Placement exam or MA-UY 912 or MA-UY 914 . Corequisite(s): Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 1054 Calculus I with Precalculus 4 Credits This course covers limits, definition of the derivative, differentiation rules for polynomial and trigonometric functions, applications of the chain rule and introduction to optimization. This Calculus I course provides an indepth review of precalculus.
Prerequisite(s): Diagnostic exam, MA-UY 954 , or MA-UY 912 or equivalent. Corequisite(s): Note: course required only for specific majors in place of MA 1024/1324.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 1124 Calculus II 4 Credits This course covers definite integrals, theorems about integrals, anti-derivatives, second fundamental theorem of calculus, techniques of integration, introduction to ordinary differential equations, improper integrals, numerical methods of integration, applications of integration, sequences, series, power series, approximations of functions via Taylor polynomials, Taylor series. MA-UY 1424 is for students who wish to take MA 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA 1124 but with more contact hours a week, incorporating a full discussion of the required precalculus topics.
Prerequisite(s): MA-UY 1024 or MA-UY 1324 . Corequisite(s): Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 1154 Calculus II with Precalculus 4 Credits This course covers the first and second derivative, optimization problems, antiderivatives, Fundamental Theorem of Calculus, techniques of integration, logarithmic and exponential functions, numerical methods of integration, applications of integration, introduction to differential equations, introduction to series. This Calculus II course provides an in-depth review of precalculus.
Prerequisite(s): MA-UY 1054 . Corequisite(s): Note: course required only for specific majors in place of MA 1124/1424.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 1324 Integrated Calculus I 4 Credits This course covers: Library of Functions, functions of one variable. Limits, derivatives of functions defined by graphs, tables and formulas, differentiation rules for power, polynomial, exponential and logarithmic functions, derivatives of trigonometric functions, the product and quotient rule, the chain rule, applications of the chain rule, maxima and minima, optimization. MA 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA 1324 covers the same material as MA-UY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics.
Prerequisite(s): Disgnostic exam or MA-UY 912 or MA-UY 914 . Corequisite(s): Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 1424 Integrated Calculus II 4 Credits This course covers definite integrals, theorems about integrals, anti-derivatives, second fundamental theorem of calculus, techniques of integration, introduction to ordinary differential equations, improper integrals, numerical methods of integration, applications of integration, sequences, series, power series, approximations of functions via Taylor polynomials, Taylor series. MA 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA 1424 covers the same material as MA-UY 1124 but with more contact hours a week, incorporating a full discussion of the required precalculus topics.
Prerequisite(s): MA-UY 1024 or MA-UY 1324 . Corequisite(s): Note: credit for this course may be used to satisfy the minimum credit requirement for graduation.
Weekly Lecture Hours: 6 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2012 Elements of Linear Algebra I 2 Credits This course introduces vector concepts. Linear transformations. Matrices and Determinants. Characteristic roots and eigenfunctions.
Prerequisite(s): MA-UY 1124 or equivalent. Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2034 Linear Algebra and Differential Equations 4 Credits MA-UY 2034 is an introduction to ordinary differential equations and linear algebra. The course develops the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that are widely used in modern engineering and science. Linear algebra is used as a tool for solving systems of linear equations as well as for understanding the structure of solutions to linear (systems) of differential equations. Topics covered include the fundamental concepts of linear algebra such as Gaussian elimination, Matrix Theory, linear transformations, vector spaces, subspaces, basis, eigenvectors, eigenvalues and the diagonalization of matrices, as well as the techniques for the analytic and numeric solutions of ordinary differential equations (and systems) that commonly appear in modern engineering and science.
Prerequisite(s): MA-UY 1124 or equivalent including AP/AB with score of 4 or 5. Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 |
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MA-UY 2054 Applied Business Data Analysis I 4 Credits This course covers applications of theories of random phenomena to problems in business management. Topics include probability theory, discrete and continuous probability distributions, sampling, measures of central value and dispersion, sampling distributions, statistical estimation and introduction to hypothesis testing. Use of statistical software is integrated with the previous topics; examples are drawn from problems in business decision-making. Applications to advanced statistical applications in business management. Emphasis is on application of concepts. Use of statistical software integrated with the previous topics.
Prerequisite(s): MA-UY 1054 or equivalent. Note: Course required only for Management Majors. Credit for this course may not be used to satisfy the requirements for other majors.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2112 Multivariable Calculus A 2 Credits This course introduces Multivariable Calculus. Analysis of functions of several variables, vector valued functions, partial derivatives, optimization techniques.
Prerequisite(s): MA-UY 2012 . Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2114 Calculus III: Multi-Dimensional Calculus 4 Credits Functions of several variables. Vectors in the plane and space. Partial derivatives with applications, especially Lagrange multipliers. Double and triple integrals. Spherical and cylindrical coordinates. Surface and line integrals. Divergence, gradient, and curl. Theorems of Gauss and Stokes.
Prerequisite(s): MA-UY 1124 or MA-UY 1424 Weekly Lecture Hours: 4 |
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MA-UY 2122 Multivariable Calculus B 2 Credits This course continues Multivariable Calculus. Multiple integrals, parametric equations, vector fields, line integrals, surface integrals and major theorems concerning their applications.
Prerequisite(s): MA-UY 2112 . Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2132 Ordinary Differential Equations 2 Credits This course covers first order differential equations: modeling and solving. Stability of autonomous equations. Higher order linear ordinary differential equations: Solution bases, Wronskian and initial value problems. Linear systems of first-order differential equations with constant coefficients: Elimination and eigenvalue method of solution. Elementary concepts of numerical analysis. Numerical solution of initial value problems for ordinary differential equations.
Prerequisite(s): MA-UY 2012 . Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2212 Data Analysis I 2 Credits This course covers basic theory of probability. Random variables. Distributions. Expectation. Functions of a random variable. Descriptive statistics. Data description. Sampling distributions. Use of statistical software is integrated with previous topics.
Prerequisite(s): MA-UY 1124 or equivalent. Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2222 Data Analysis II 2 Credits This course covers point and interval estimation. Hypothesis testing. Linear regression. One-way analysis of variance. Use of statistical software is integrated with the previous topics.
Prerequisite(s): MA-UY 2212 . Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2224 Data Analysis 4 Credits An introductory course to probability and statistics. It affords the student some acquaintance with both probability and statistics in a single term. Topics in Probability include mathematical treatment of chance; combinatorics; binomial, Poisson, and Gaussian distributions; the Central Limit Theorem and the normal approximation. Topics in Statistics include sampling distribution of sample mean and sample variance; normal, t-, and Chi-square distributions; confidence intervals; testing of hypotheses; least square regression model. Applications to scientific, industrial, and financial data are integrated into the course. NOTE: Cannot be taken if student is also taking or has already taken MA-UY 3012 or MA-UY 3022.
Prerequisite(s): MA-UY 1124 , MA-UY 1424 , or MA-UY 1132 Weekly Lecture Hours: 4 |
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MA-UY 2233 Introduction to Probability 3 Credits Standard first course in probability, recommended for those planning further work in probability or statistics. Probability of events, random variables and expectations, discrete and continuous distribution, joint and conditional distribution, moment generating functions, central limit theorem.
Prerequisite(s): MA-UY 109, MA-UY 2112 , OR MA-UY 2114 . Note: Not open to students who have taken MA-UY 3012 or MA-UY 3022 . Also listed under: EE-UY 2233 |
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MA-UY 2312 Discrete Mathematics I 2 Credits This course covers logic and induction. Sets and functions. Recursive definitions. Counting techniques. Inclusion-exclusion principle.
Prerequisite(s): MA-UY 1124 or equivalent. Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2314 Discrete Mathematics 4 Credits Logic, proofs, set theory, functions, relations, asymptotic notation, recurrences, modeling computation, graph theory.
Prerequisite(s): Math Diagnostic Exam or MA-UY 912 or MA-UY 914 .
Note: This course and CS-GY 6003 cannot both be taken for credit.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2322 Discrete Mathematics II 2 Credits This course covers recurrence relations and generating functions. Equivalence relations and partial orderings. Graphs and connectivity of graphs. Trees and sorting. Boolean algebra, languages and finite state machines.
Prerequisite(s): MA-UY 2312 . Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 2414 Basic Practice of Statistics 4 Credits We are inundated by data, but data alone does not translate into useful information. Statistics provide the means for organizing, summarizing, and therefore better analyzing data so that we can understand what data tells us about critical questions. If one collects data then understanding how to use statistical methods is critical, but it is also necessary to understand and interpret all the information we consume on a daily basis. This course provides these basic statistical approaches and techniques. This course may not be acceptable as a substitute for any other Probability or Statistics course. See your advisor.
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MA-UY 3012 Introduction to Probability I 2 Credits This course covers probability of events. Random variables. Discrete and continuous distributions. Joint distributions. Expectation. Functions of a random variable.
Prerequisite(s): MA-UY 2112 or equivalent. Note: Not open to students who have taken MA 2212.
Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 3022 Probability Theory II 2 Credits This course covers multivariate random variables, moment generating functions, properties of expectation, limit theorems and gives an introduction to random processes and their applications.
Prerequisite(s): MA-UY 2212 or MA-UY 3012 . Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 3103 Problem Solving and Proofs 3 Credits This course covers mathematical problem solving, proofs and innovative reasoning. Discussion of independent challenging problems from Analysis, Complex Analysis, Probability, Combinatorics, Linear Algebra, Number Theory and Graph Theory.
Prerequisite(s): MA-UY 2312 and MA-UY 2012 or MA-UY 2034 and MA-UY 2314 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 3112 Complex Variables I 2 Credits This course covers functions of a complex variable. Derivatives and Cauchy-Riemann equations. Integrals and Cauchy integral theorem. Power and Laurent Series. Residue theory.
Prerequisite(s): MA-UY 2122 or equivalent. Weekly Lecture Hours: 4 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 3113 Advanced Linear Algebra and Complex Variables 3 Credits This course provides a deeper understanding of topics introduced in MA-UY 2012 and MA-UY 2034 and continues the development of those topics,while also covering functions of a Complex Variable. Topics covered include: The Gram-Schmidt Process,inner product spaces and applications , Singular value decomposition,LU decomposition. Derivatives and Cauchy-Riemann equations, Integrals and Cauchy integral theorem. Power and Laurent Series, Residue theory.
Prerequisite(s): MA-UY 2122 or MA-UY 2114 AND MA-UY 2012 or MA-UY 2034 . Note: Course not open to students who have taken MA-UY 3112.
Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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MA-UY 3203 Linear Optimization 3 Credits This course examines linear optimization problems with constraints; optimality conditions and duality theory, the simplex method, complexity of the simplex method, interior point methods, selected applications, network flow problems and the network simplex method.
Prerequisite(s): MA-UY 2312 and MA-UY 2112 . Weekly Lecture Hours: 3 | Weekly Lab Hours: 0 | Weekly Recitation Hours: 0 |
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