• MATH 5405: Meth Appl Math II

  3.00 Credits

  University of Wyoming

  
  A continuation of MATH 5400. Prerequisite: MATH 5400.
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• MATH 5430: Ord Diff Equat II

  3.00 Credits

  University of Wyoming

  
  Differential equations constitute the mathematical language for problems of continuous change. ODEs deal with evolutionary processes involving one independent variable. This course revisits solution techniques but emphasizes the theoretical framework. Topics include: existence and uniqueness, linear and nonlinear differential systems, asymptotics and perturbations, and stability. Prerequisite: MATH 4200, 4430.
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• MATH 5440: Par Diff Equat II

  3.00 Credits

  University of Wyoming

  
  The theory of PDEs is important for abstract mathematics, applied science, and mathematical modeling. This course covers solution techniques but emphasizes the theoretical framework. Topics include: first order systems; characteristics; hyperbolic, elliptic and parabolic equations; separations of variables; series and transforms; integral relations; Green's functions, maximum principles; variational methods. Prerequisite: MATH 4200 and 4440.
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• MATH 5490: Tpcs: Applied Math

  1.00 - 6.00 Credits

  University of Wyoming

  
  Prerequisite: consent of instructor.
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• MATH 5500: Adv Linear Algebra

  3.00 Credits

  University of Wyoming

  
  An introduction to the theory of abstract vector spaces and linear transformations from an axiomatic point of view, with applications to matrix theory. Topics include vector spaces, dimension, linear transformations, dual spaces and functionals, inner product spaces, and structure theorems. Prerequisite: MATH 3500 and MATH 4500.
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• MATH 5510: Combinatorial Theory

  3.00 Credits

  University of Wyoming

  
  An introduction to combinatorics covering both classical and contemporary topics. Includes some of the following: generating functions, recursion formulas, partially ordered sets, inclusion- exclusion, partitions, graph theory, Ramsey theory, combinational optimization, Latin squares, finite geometries, and design theory.
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• MATH 5530: Theory of Groups

  3.00 Credits

  University of Wyoming

  
  An in-depth study of various aspects of group theory, building on MATH 5550. Topics include some of the following: classical theory of finite groups (both Abelian and non-Abelian), infinite Abelian groups, free groups, permutation groups, group representations, endomorphism, extensions, and cohomology. Prerequisite: MATH 5550.
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• MATH 5550: Abstract Algebra I

  3.00 Credits

  University of Wyoming

  
  Studies the structure of groups, rings, and fields. For each, concepts of substructures, quotient structures, extensions, homomorphism, and isomorphism are discussed. Prerequisite: MATH 3500 or MATH 5500.
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• MATH 5555: Abstract Alg II

  3.00 Credits

  University of Wyoming

  
  A continuation of MATH 5550, examining in depth selected topics from the theory of rings, fields, and algebras, including Galois theory. Prerequisite: MATH 5550.
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• MATH 5570: Matrix Thry & Comb

  3.00 Credits

  University of Wyoming

  
  An overview of matrix theory and its applications to combinatorics. Topics include Smith normal form, the Perron-Frobenius theory of non-negative matrices, location and perturbation of eigenvalues, and interlacing of eigenvalues. Applications include structure theorums for (0,1)-matrices, network flows, spectra of graphs, and the permanent. Prerequisite: MATH 5500.
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