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Course Criteria
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3.00 Credits
Intended to develop widely-applicable mathematical skills. Basic principles such as induction, the pigeonhole principle, symmetry, parity, and generating functions.
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3.00 Credits
Algebra of matrices, real and complex vector spaces, linear transformations, and systems of linear equations. Eigenvalues, eigenvectors, Cayley-Hamilton theorem, inner product spaces, and orthonormal bases. Hermitian matrices. Designed primarily for mathematics College of Arts and Science / Courses 187 A&S majors. Pre- or corequisite: 175. Credit is not given for both 204 and 194 or 205a-205b.
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4.00 Credits
Vector algebra and geometry; linear transformations and matrix algebra. Real and complex vector spaces, systems of linear equations, inner product spaces. Functions of several variables and vector-valued functions: limits, continuity, the derivative. Extremum and nonlinear problems, manifolds. Multiple integrals, line and surface integrals, differential forms, integration on manifolds, theorems of Green, Gauss, and Stokes. Eigenvectors and eigenvalues. Emphasis on rigorous proofs. Enrollment limited to first-year students with test scores of 5 on the Calculus BC advanced placement examination or the approval of the director of undergraduate studies. Credit is not given for both 205a-205b and 175, 194, or 204.
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4.00 Credits
Continuation of 205a. Vector algebra and geometry; linear transformations and matrix algebra. Real and complex vector spaces, systems of linear equations, inner product spaces. Functions of several variables and vector-valued functions: limits, continuity, the derivative. Extremum and nonlinear problems, manifolds. Multiple integrals, line and surface integrals, differential forms, integration on manifolds, theorems of Green, Gauss, and Stokes. Eigenvectors and eigenvalues. Emphasis on rigorous proofs. Enrollment limited to first-year students with test scores of 5 on the Calculus BC advanced placement examination or the approval of the director of undergraduate studies. Credit is not given for both 205a-205b and 175, 194, or 204.
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3.00 Credits
First- and second-order differential equations, applications, linear differential equations, series solutions, boundary-value problems, existence and uniqueness theorems. Intended for mathematics and advanced science majors. Prerequisite: multivariable calculus and linear algebra. Credit is not given for both 208 and 196 or 198.
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3.00 Credits
Elementary combinatorics including permutations and combinations, the principle of inclusion and exclusion, and recurrence relations. Graph theory including Eulerian and Hamiltonian graphs, trees, planarity, coloring, connectivity, network flows, some algorithms and their complexity. Selected topics from computer science and operations research. Prerequisite: linear algebra.
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3.00 Credits
Discrete and continuous probability functions, cumulative distributions. Normal distribution. Poisson distribution and Poisson process. Conditional probability and Bayes’ formula. Point estimation and interval estimation. Hypothesis testing. Covariance and correlation. Linear regression theory and the principle of least squares. Monte Carlo methods. Intended for students in Electrical Engineering and Computer Engineering. Prerequisite: multivariable calculus. No credit for students who have completed 218.
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3.00 Credits
Discrete and continuous probability models, mathematical expectation, joint densities. Laws of large numbers, point estimation, confidence intervals. Hypothesis testing, nonparametric techniques, applications. Students taking 218 are encouraged to take 218L concurrently. Prerequisite: multivariable calculus. No credit for students who have completed 216.
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1.00 Credits
Applications of the theory developed in 218. Emphasis on data analysis and interpretation. Topics include the one- and two-sample problems, paired data, correlation and regression, chi-square, and model building. Pre- or corequisite: 216 or 218.
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3.00 Credits
A brief review of basic applied statistics followed by a development of the analysis of variance as a technique for interpreting experimental data. The generalized likelihood ratio principle, completely randomized designs, nested designs, orthogonal contrasts, multiple comparisons, randomized block designs, Latin squares, factorial designs, 2n designs, fractional factorials, confounding, introduction to response surface methodology. Applications will be emphasized. Prerequisite: 218 or equivalent.
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