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Course Criteria
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3.00 Credits
3 Y Partial derivatives, implicit functions, integration in several variables, line and surface integrals. Prereq: MAT 331, and 12 credits of calculus
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3.00 Credits
3 Y Real-number system, set theory and elementary topological properties of the real line, continuity and differentiability, sequences and series, uniform convergence, Riemann integration, and improper integrals. Prereq: MAT 412 or permission of instructor
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3.00 Credits
3 Y Complex number system and its arithmetic, geometric representation. Linear transformations. Analytic functions and the Cauchy-Riemann equations. Integration and Cauchy's theorem, Taylor and Laurent series, singularities, poles, and residues. Applications. Prereq: MAT 412 or MAT 511 or permission of instructor
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3.00 Credits
3 S First order differential equations. Second order linear differential equations. Power series solutions. Bessel's equations, Laplace transforms. Systems of first order differential equations. Applications. Credit will not be given for both MAT 514 and MAT 485. Prereq: 12 credits of calculus or equivalent
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3.00 Credits
3 Y Partial differential equations, boundary-value problems, Fourier series and orthogonal expansions, Bessel functions, and Legendre polynomials. Prereq: Either MAT 514 or MAT 485
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3.00 Credits
3 Y Topics may vary but may include partial differential equations, introduction to calculus of variations and Hamilton's principle, difference equations, complex variables, or integral equations. Prereq: MAT 514
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3.00 Credits
3 S Algebra of sets. Probability in finite samples spaces. Binomial and multinomial coefficients. Random variables. Expected value and standard deviation. Density functions. Statistical applications. Prereq: 12 credits of calculus
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3.00 Credits
3 Y Estimation and confidence intervals. Normal distribution and central limit theorem. Testing hypotheses, chi-square, t, and F distributions. Least squares, regression, and correlation. Prereq: MAT 521
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3.00 Credits
3 Y Topics chosen from: Markov chains, game theory, queuing theory, information theory Prereq: MAT 521
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3.00 Credits
3 Y Abstract vector spaces and inner product spaces, linear transformations and linear operators, eigenvalues and diagonalization. Primarily for mathematics majors. Prereq: MAT 275 or CIS 275, and MAT 331
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