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MATH 504: Multivariable Analysis
3.00 Credits
Saint Louis University-Main Campus
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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MATH 504 - Multivariable Analysis
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MATH 511: Algebra
3.00 Credits
Saint Louis University-Main Campus
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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MATH 511 - Algebra
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MATH 512: Algebra II
3.00 Credits
Saint Louis University-Main Campus
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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MATH 512 - Algebra II
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MATH 521: Real Analysis I
3.00 Credits
Saint Louis University-Main Campus
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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MATH 521 - Real Analysis I
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MATH 522: Complex Analysis
3.00 Credits
Saint Louis University-Main Campus
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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MATH 522 - Complex Analysis
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MATH 523: Functional Analysis
3.00 Credits
Saint Louis University-Main Campus
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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MATH 523 - Functional Analysis
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MATH 531: General Topology I
3.00 Credits
Saint Louis University-Main Campus
Topological spaces, convergence, nets, product spaces, metrization, compact spaces, connected spaces. Offered every Fall semester.
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MATH 531 - General Topology I
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MATH 532: General Topology II
3.00 Credits
Saint Louis University-Main Campus
Compact surfaces, fundamental groups, force groups and free products, Seifert-van Kampean theorem, covering spaces. Offered every Spring semester.
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MATH 532 - General Topology II
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MATH 593: Special Topics in Mathematics
1.00 - 3.00 Credits
Saint Louis University-Main Campus
No course description available.
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MATH 593 - Special Topics in Mathematics
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MATH 595: Special Study for Examinations
0.00 Credits
Saint Louis University-Main Campus
No course description available.
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MATH 595 - Special Study for Examinations
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