• MATH 6390: Advanced Algebra II

  3.00 Credits

  Utah State University

  
  This course focuses on topics in research-level algebra, including commutative and non-commutative algebra, homological algebra, and category theory. Prerequisite(s): MATH 5310 with a C- or better
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• MATH 6410: Existence and Uniqueness of Solutions to ODE

  1.00 Credits

  Utah State University

  
  This course introduces the traditional theory of ODE, including the existence and uniqueness of solutions via Picard iteration and the study of continuous dependence of solutions on initial conditions and parameters. Prerequisite/Restriction: MATH 5210
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• MATH 6420: Classical Methods in PDE

  2.00 Credits

  Utah State University

  
  This course emphasizes the theoretical underpinnings of solution techniques and equation behaviors. Topics include diffusion, wave, and Laplace equations from an advanced point of view, classification of second order equations, Green's functions, the adjoint problem, and fundamental solutions. Prerequisite/Restriction: MATH 5210
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• MATH 6440: ODE and Dynamics

  2.00 Credits

  Utah State University

  
  This course is an introduction to subjects in dynamical systems theory. Topics include two-D flows - Poincaré-Bendixson theorem, hamiltonian dynamics, Poincaré maps, and bifurcations and the center manifold theorem. Prerequisite/Restriction: MATH 5470 or equivalent experience
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• MATH 6450: Analysis of PDE

  2.00 Credits

  Utah State University

  
  Students prepare for research on the theoretical or numerical aspects of partial differential equations, including Sobolev spaces, embedding theorems, interpolation inequalities, weak solutions of linear and nonlinear partial differential equations, calculus of variations, and existence theory for nonlinear elliptic PDEs. Prerequisite/Restriction: MATH 5420 MATH 5210 or MATH 6420 or MATH 6210
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• MATH 6470: Advanced Asymptotic Methods

  2.00 Credits

  Utah State University

  
  This course introduces advanced theory of asymptotic analysis and its use in solutions to differential equations, including asymptotic sequences and series, boundary layers, internal layers, and shocks in ODEs and PDEs, multiscale methods, WKB methods, and analysis of turning points. Prerequisite/Restriction: Math 5420 or equivalent experience solving ODE/PDE
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• MATH 6500: Methods of Secondary School Mathematics Teaching

  3.00 Credits

  Utah State University

  
  A teaching methods course required of all prospective secondary school mathematics teachers. To receive graduate credit, students must complete an extra project. Students having a Methods of Secondary Math Teaching Methods course on their transcripts will not be allowed to apply credit for this course toward a master's degree. Prerequisite/Restriction: Matriculation into the Master's of Education Plan C program, the Master's of Mathematics program, or the USOE Alternative Route to Licensure Program. Cross-listed as: MATH 4500.
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• MATH 6510: Topology

  3.00 Credits

  Utah State University

  
  Homotopy theory, fundamental groups, covering spaces, singular homology with applications to spheres and Euclidean spaces, CW complexes, cohomology ring, and Poincare duality. Prerequisite/Restriction: C- or better in MATH 4310, MATH 5510; and C- or better in MATH 5310 or consent of instructor. MATH 6510 must be completed prior to MATH 6520.
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• MATH 6520: Topology

  3.00 Credits

  Utah State University

  
  Homotopy theory, fundamental groups, covering spaces, singular homology with applications to spheres and Euclidean spaces, CW complexes, cohomology ring, and Poincare duality. Prerequisite/Restriction: C- or better in MATH 4310, MATH 5510; and C- or better in MATH 5310 or consent of instructor. MATH 6510 must be completed prior to 6520.
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• MATH 6530: Advanced Algebraic Topology

  3.00 Credits

  Utah State University

  
  This course focuses on topics in research-level algebraic topology, including functoriality in topology, homotopy groups, singular homology and cohomology, and topological manifolds. Prerequisite(s): MATH 4310, MATH 5310, and MATH 5510 with a C- or better
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