52 courses with the subject MATH, each shown exactly as we captured it from the college's catalog, with every element we hold. Where the wording looks broken, that is our reading of the catalog, not the college's text.
MATH 504Linear Algebra & Matrix Analysis3.0
Course topics include the QR decomposition, Schur's triangularization theorem, the spectral decomposition for normal matrices, the Jordan canonical form, the Courant-Fisher theorem, singular value and polar decompositions, the Gersgorin disc theorem, the Perron-Frobenius theorem, and other current matrix analysis topics. Applications of the material are outlined as well.
A continuation of MATH 505. Uniform convergence, Fourier series, Lebesque integral in Euclidean spaces, differential calculus in Euclidean spaces, inverse and implicit functions theorems, change of variables in multiple integrals.
Covers basic concepts in applied probability; random variables, distribution functions, expectations, and moment generating functions; specific continuous and discrete distributions and their properties; joint and conditional distributions; discrete time Markov chains; distributions of functions of random variables; probability integral transform; and central limit theorem.
Covers probability plots and graphical techniques for determining distribution of data, including sampling and sampling distributions, law of large numbers, parametric point estimation, maximum likelihood estimation, Bayes estimation, properties of estimators, sufficient statistics, minimum variance unbiased estimators, and parametric interval estimation. Introduces hypothesis testing.
Covers polynomial interpolation, numerical solutions of nonlinear equations, numerical integration (Newton-Cotes, Gauss quadrature), error estimates of various numerical methods, and function approximation (polynomial, Fourier, Pade).
Covers numerical linear algebra and matrix computation, direct and iterative methods for solving linear systems and eigenvalue problems, least square problems, various matrix factorizations (QR, singular value decomposition, LU and Cholesky), and Krylov subspace methods.
Covers graphs and networks, with an emphasis on algorithms. Includes minimum spanning trees, shortest path problems, connectivity, network flows, matching theory, Eulerian and Hamiltonian tours, graph coloring, and random graphs.
Covers mathematical tools for the analysis of algorithms, including combinatorics, recurrence relations and generating functions, elementary asymptotics, and probabilistic methods.
This third course in the Abstract Algebra sequence covers a selection of topics in advanced modern algebra such as symmetries, representation theory, algebraic geometry, homological algebra, Galois Theory and coding theory.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credits
Type
course
Repeatable
Can be repeated 3 times for 9 credits Prerequisites: MATH 533 [Min Grade: C] and MATH 534 [Min Grade: C]
Covers general topological spaces, metric spaces, and function spaces; open sets, limit points, limits of sequences, convergence, separation axioms, compactness, connectedness, continuity, homeomorphisms, and product of N-spaces; and specialized applications to the real line, Euclidean N-space, and well-known function spaces.
Topics will be selected from the following: Differential structures, immersion theorems, tangent bundles, vector fields and distributions, integral manifolds, integration on manifolds, differential forms, general Stokes Theorem, applications to physics and engineering.
Intended to introduce students to contemporary computing environments and the associated tools. Uses contemporary software tools and specific applications from science and engineering to illustrate numerical and visualization methods.
MATH 572Financial Mathematics: Fixed Income Securities3.0
The course is a mathematical introduction to interest rates and interest rates related instruments including loans, bonds, mortgages and swaps. The course emphasizes the mathematical aspects of the subject and computational implementation.
Advanced matrix analysis, including topics such as inequalities involving eigenvalues and/or singular values, norms and their duals, operator monotone and convex functions, spectral variation and spectral perturbation, matrix inequalities, numerical range and its variations.
Covers basics of modern probability theory: properties of probability measures, independence, Borel-Cantelli lemma, zero-one law, random variables, distribution theory, and expectations.
Covers further development of modern probability theory, including modes of convergence of random variables, series of random variables, weak and strong laws of large numbers, characteristics functions, inversion formula and continuity theorem, and central limit theorem.
This third course in the probability sequence covers a selection of topics in modern probability theory. Topics may include: theory of sums of independent random variables, inequalities, martingale theory, combinatorial probability.
Subject
MATH
Credits (min)
3
Credits (max)
3
Credit unit
Credits
Type
course
Repeatable
Can be repeated 2 times for 6 credits Prerequisites: MATH 611 [Min Grade: C]
Covers conditional probabilities, expectations, Markov chains, classification of states, recurrence and absorption probabilities, asymptotic behavior, random walk, birth and death processes, and ruin problems.
Covers derivation and classification of partial differential equations; elementary methods of solution, including Fourier series and transform techniques; linear and equilinear equations of the first order; hyperbolic, elliptic, and parabolic type equations; maximum principles; existence, uniqueness, and continuous dependence theorems; Riemann's method; method of characteristics; Green's functions; and variational and numerical methods.
Covers existence and uniqueness theorems, properties of solutions, adjoint equations, canonical forms, asymptotic behavior, phase space, method of isocline, classification of singular points, linear two-dimensional autonomous systems, non-linear systems, stability theory, Lyapunov's methods, quadratic forms, construction of Lyapunov's function, boundedness, limit sets, applications to controls, linear equations with periodic coefficients, Floquet theory, characteristic multipliers and exponents, existence of periodic solutions to weakly non-linear systems, jump phenomena, subharmonic resonance, and stability of periodic solutions.
Dynamical systems, including topics on phase portraits, invariant sets, one-dimensional and higher-dimensional flows, the study of equilibrium and other dynamical phenomena such as periodic orbits, homoclinic orbits and heteroclinic orbits, linear and structural stabilities of equilibrium, Poincaré maps of dynamical systems, bifurcations of equilibrium and periodic orbits, the normal forms of bifurcations, the existence of invariant manifolds, the persistence and differentiability of invariant manifolds under perturbation.
Covers algebra of sets, topology of metric spaces, compactness, completeness, function spaces, general theory of measure, measurable functions, integration, convergence theorems, and applications to classical analysis and integration.
An introduction to abstract linear spaces, including normed linear spaces, Hilbert spaces, Banach spaces, and their duals. Fundamental theorems such as the Hahn-Banach theorem, open mapping and closed graph theorems will be covered, along with possible applications to differential and integral equations and fundamentals of distribution theory.
Covers matrix groups, topological groups, locally isomorphic groups, universal covering groups, analytic manifolds, Lie groups; the Lie algebra of a Lie group, differential forms, and Lie's three theorems; analytic subgroups of a Lie group and compact Lie groups; and semisimple Lie algebras, general structure of Lie algebras, Cartan subalgebras, modules and representation, and computational techniques in representation theory.
Provides a rigorous treatment of theory and computational techniques in linear programming and its extensions, including formulation, duality theory, simplex and dual-simplex methods, and sensitivity analysis; network flow problems and algorithms; systems of inequalities, including exploiting special structure in the simplex method and use of matrix decompositions; and applications in game theory and integer programming.
Covers necessary and sufficient conditions for unconstrained and constrained optimization. Includes computational methods including quasi-Newtonian and successive quadratic programming, and penalty and interior methods.
Covers advanced topics in mathematical programming, including interior point methods in linear programming; stochastic optimization; multi-objective optimization; and global minimax, functional, and non-linear least squares optimization methods.
Introduction to calculus of variations. Covers applications to geometry, classical mechanics and control theory, Euler-Lagrange equations, problems with constraints, canonical equations, Hamiltonian mechanics, symmetries and Noether's theorem, Hamilton-Jacobi theory, introduction to optimal control, maximum principle, and Hamilton-Jacobi-Bellman equations.
This course covers methods of Abstract Algebra that can be applied to various combinatorial problems and conversely, combinatorial methods to approach problems in representation theory, algebraic geometry, and homological algebra.
This is an introduction to mathematical and computational techniques for analyzing neuronal models. Topics include conductance based models, neuronal excitability, bursting, neural networks, and compartmental models, as well as phase plane analysis, slow-fast systems, elements of applied bifurcation theory, and simulating differential equation models using MATLAB.
