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MATH 4540: Classical Differential Geometry I
3.00 Credits
University of Toledo
Smooth curves in Euclidean space including the Frenet formulae. Immersed surfaces with the Gauss map, principal curvatures and the fundamental forms. Special surfaces including ruled surfaces and minimal surfaces. Intrinsic Geometry including the Gauss Theorem Egregium.
Prerequisite:
MATH 2860 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4540 - Classical Differential Geometry I
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MATH 4550: Classical Differential Geometry II
3.00 Credits
University of Toledo
Tensors, vector fields, and the Cartan approach to surface theory, Bonnet's Theorem and the construction of surfaces via solutions of the Gauss Equation. Geodesics parallel transport, and Jacobi Fields. Theorems of a global nature such as Hilbert's Theorem or the Theorem of Hopf-Rinow.
Prerequisite:
MATH 4540 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4550 - Classical Differential Geometry II
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MATH 4600: Advanced Statistical Methods I
3.00 Credits
University of Toledo
Basics of descriptive statistics, study designs and statistical inference. Properties of, and assumptions required for, inference for means, variances, and proportions from one and two-sample paired and unpaired studies. Introduction to ANOVA with multiple comparisons. Model assessment and diagnostics. Statistical software will be employed. Opportunities to apply procedures to real data. Emphasis placed on the foundations to approaches in introductory statistics.
Prerequisite:
MATH 2600 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 2640 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 3610 FOR LEVEL UG WITH MIN. GRADE OF D- OR MATH 4690 FOR LEVEL UG WITH MIN. GRADE OF D-
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MATH 4600 - Advanced Statistical Methods I
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MATH 4610: Applications Of Statistics II
3.00 Credits
University of Toledo
Continuation of Applications of Statistics I.
Prerequisite:
MATH 4600 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4610 - Applications Of Statistics II
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MATH 4620: Theory Of Interest
3.00 Credits
University of Toledo
This course covers the measurement of interest, certain annuities, yield rates, amortization and sinking funds, bonds and other securities and application of interest theory.
Prerequisite:
MATH 1840 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 1860 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4620 - Theory Of Interest
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MATH 4640: Statistical Computing
3.00 Credits
University of Toledo
Modern statistical computing, including programming tools, modern programming methodologies, design of data structures and algorithms, numerical computing and graphics. Additional topics selected from simulation studies, rejection sampling, importance sampling, Monte Carlo integration, and bootstrapping.
Prerequisite:
MATH 3610 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 4600 FOR LEVEL UG WITH MIN. GRADE OF C- OR MATH 4690 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4640 - Statistical Computing
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MATH 4680: Introduction To Theory Of Probability
3.00 Credits
University of Toledo
Probability spaces, random variables, probability distributions, moments and moment generating functions, limit theorems, transformations and sampling distributions.
Prerequisite:
MATH 2850 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4680 - Introduction To Theory Of Probability
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MATH 4690: Introduction To Mathematical Statistics
3.00 Credits
University of Toledo
Sampling distributions, point and interval estimation, hypothesis testing, regression and analysis of variance.
Prerequisite:
MATH 4680 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4690 - Introduction To Mathematical Statistics
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MATH 4710: Methods Of Numerical Analysis I
3.00 Credits
University of Toledo
Floating point arithmetic; polynomial interpolation; numerical solution of nonlinear equations; Newton's method. Likely topics include: numerical differentiation and integration; solving systems of linear equations; Gaussian elimination; LU decomposition; Gauss-Seidel method.
Prerequisite:
MATH 2860 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4710 - Methods Of Numerical Analysis I
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MATH 4720: Methods Of Numerical Analysis II
3.00 Credits
University of Toledo
Likely topics include: Computation of eigenvalues and eigenvectors; solving systems of nonlinear equations; least squares approximations; rational approximations; cubic splines; fast Fourier transforms; numerical solutions to initial value problems; ordinary and partial differential equations.
Prerequisite:
MATH 4710 FOR LEVEL UG WITH MIN. GRADE OF C-
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MATH 4720 - Methods Of Numerical Analysis II
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