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Course Criteria
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3.00 Credits
Sequences and Series of functions, Differentiability, Integrability, Inverse and Implicit function theorems, Fundamental Theorems of Multivariable Calculus (Green¿s Theorem, Stokes Theorem, Divergence Theorem). Prerequisite: MATH 421.
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3.00 Credits
Simple properties of groups, groups of transformations,subgroups, homomorphisms and isomorphisms, theorems of Schreier and Jordan-Hoelder, mappings into a group, rings, integral domains, fields, polynomials, direct sums and modules. Offered every Fall semester.
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3.00 Credits
Rings, fields, bases and degrees of extension fields, transcendental elements, normal fields and their structures. Galois theory, finite fields; solutions of equations by radicals, general equations of degree n. Offered every Spring semester.
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3.00 Credits
The topology of the reals, Lebesque and Borel measurable functions, properties of the Lebesque integral, differential of the integral. Offered every Fall semester.
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3.00 Credits
Holomorphic and Harmonic functions and power series expansions. Complex integration. Cauchy's theorem and applications. Laurent series, singularities, Runge's theorem, and the calculus of residues. Additional topics may include Analytic continuation, Riemann surfaces, and conformal mapping. Prerequisites: MATH 521 and MATH 531. Recommended: MATH 451. Offered occasionally.
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3.00 Credits
Banach and Hilbert spaces. Linear functionals and linear operators. Dual spaces, weak and weak topologies. Hahn-Banach, Closed Graph and Open Mapping Theorems. Topological Vector spaces. Prerequisites: MATH 521 and MATH 531. Offered occasionally.
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3.00 Credits
Topological spaces, convergence, nets, product spaces, metrization, compact spaces, connected spaces. Offered every Fall semester.
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3.00 Credits
Compact surfaces, fundamental groups, force groups and free products, Seifert-van Kampean theorem, covering spaces. Offered every Spring semester.
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1.00 - 3.00 Credits
No course description available.
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0.00 Credits
No course description available.
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