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Course Criteria
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0.00 - 3.00 Credits
Cr. 3. Alt. F., offered 2008. Prereq : 504. Combinatorial designs and Latin squares. Construction methods including fi nite fi elds. Errorcorrecting codes. Adjacency matrices and algebraic combinatorics.
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0.00 - 3.00 Credits
Cr. 3. Alt. S., offered 2009. Prereq : 504 or permission of instructor. Ordered sets and lattices. Generating functions. Moebius inversion and other enumeration methods.
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0.00 - 3.00 Credits
Cr. 3. Alt. F., offered 2007. Prereq : 504 or permission of instructor. Structural and extremal theory of graphs. Topics include basic structures (trees, paths and cycles), networks, colorings, connectivity, topological graph theory, Ramsey theory, forbidden graphs and minors, introduction to random graphs, applications.
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0.00 - 3.00 Credits
Cr. 3. Alt. F., offered 2007. Prereq : 504. First semester of full-year course. Subalgebras, homomorphisms, congruence relations, and direct products. Lattices and closure operators. Varieties and quasivarieties of algebras, free algebras, Birkhoff's theorems, clones, Mal'cev conditions. Advanced topics.
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0.00 - 3.00 Credits
Cr. 3. Alt. S., offered 2008. Prereq : 615. Continuation of Math 615.
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0.00 - 3.00 Credits
Cr. 3. Alt. F., offered 2008. Prereq : 504. Categories and functors and their applications.
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0.00 - 3.00 Credits
Cr. 3. Alt. S., offered 2009. Prereq : 504. Structure of Boolean algebras and their representations. Stone spaces and duality. Atomicity, completeness, distributivity, operators, extensions of homomorphisms. Examples and applications from mathematical logic and topology.
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0.00 - 3.00 Credits
Cr. 3. Alt. F., offered 2008. Prereq : Permission of instructor. Introduction to general topology. Topological spaces, continuous functions, connectedness, compactness. Topics selected from countability and separation axioms, metrization, and complete metric spaces.
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0.00 - 3.00 Credits
Cr. 3. Alt. S., offered 2009. Prereq : 504. Foundations of algebraic topology. The fundamental group, simplicial homology groups, and singular homology groups.
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