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Course Criteria
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3.00 Credits
Introduces groups, rings and fields.
Prerequisite:
MATH A253 UA C AND MATH A265 UA C
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3.00 Credits
Introduces Euclidean and non-Euclidian plane geometry and topics selected from affine geometry and projective geometry.
Prerequisite:
MATH A253 UA C AND MATH A265 UA C
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3.00 Credits
Introduces enumeration and graph theory with some algorithms.
Prerequisite:
MATH A251 UA C (AND MATH A261 UA C OR MATH A265 UA C )
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3.00 Credits
Examines fundamental concepts of number theory including primes, divisibility, congruences, quadratic reciprocity, number theoretic functions, continued fractions and Diophantine equations.
Prerequisite:
MATH A265 UA C
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3.00 Credits
Studies linear equations, matrices, determinants, finite dimensional vector spaces, linear transformations, characteristic values and inner product spaces.
Prerequisite:
MATH A252 UA C
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3.00 Credits
Vector calculus, exterior calculus, optimization techniques, and integration with applications. Emphasizes the use of linear and multilinear algebra techniques to generalize the basic methods of calculus to several independent and dependent variables.
Prerequisite:
MATH A253 UA D AND MATH A314 UA D
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3.00 Credits
Investigates the limit concept with special reference to functions on the real line. Topics include continuous functions and their properties, sequences and series, and differentiation and integration of functions.
Prerequisite:
MATH A253 UA C AND MATH A265 UA C
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3.00 Credits
Theory and applications, including moment generating functions, conditional expectation, Poisson processes, Markov chains, and topics selected from branching processes, queuing theory, random walks, and reliability theory.
Prerequisite:
MATH A252 UA D AND STAT A307 UA D
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3.00 Credits
Topics include random variables, distribution functions, expectation and moment generating function, special parametric families of univariate distributions, joint and conditional distributions, stochastic independence, conditional expectation, distributions of functions of random variables, convergence concepts, and parametric estimation by maximum likelihood.
Prerequisite:
MATH A253 UA D AND STAT A307 UA D
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3.00 Credits
Explores analytic functions, Cauchy's theorem, sequences and series, integration, and residues.
Prerequisite:
MATH A253 UA C AND MATH A265 UA C
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