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• MATH 313: Introductory Analysis I

  3.00 Credits

  Slippery Rock University of Pennsylvania

  
  This course begins the rigorous mathematical study of the real numbers. Topics include cardinality of sets; sequences of real numbers; completeness of the real numbers; topology of the real line including open sets, closed sets, and compact sets; and continuous, real-valued functions. Students will be expected to communicate using mathematical proofs throughout the course.
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• MATH 314: Introductory Analysis II

  3.00 Credits

  Slippery Rock University of Pennsylvania

  
  This course continues the rigorous mathematical treatment of the real numbers that begins in MATH 313. The concepts of differentiation and Riemann integration of real-valued functions on the real line from calculus are explored and made rigorous. Additionally, series of functions are explored, including convergence (pointwise and uniform) and Taylor series. Students will be expected to communicate using mathematical proofs throughout the course.
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• MATH 315: Numerical Mathematics

  3.00 Credits

  Slippery Rock University of Pennsylvania

  
  The mathematics of computation and approximation, interpolation, calculating the roots of equations, curve fitting linear systems, numerical differentiation and integration and error analysis.
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• MATH 316: Advanced Methods of Operations Research

  3.00 Credits

  Slippery Rock University of Pennsylvania

  
  Topics include Brownian motion, stationary processes, weak convergence of stochastic processes, regenerative phenomena, random walks, simulations.
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• MATH 317: Complex Variables

  3.00 Credits

  Slippery Rock University of Pennsylvania

  
  Complex numbers, analytic functions, complex integration, convergence of sequences and series, and applications.
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• MATH 320: Theory of Numbers

  3.00 Credits

  Slippery Rock University of Pennsylvania

  
  A study of the properties of natural numbers and number theoretic functions.
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• MATH 325: Abstract Algebra I

  3.00 Credits

  Slippery Rock University of Pennsylvania

  
  An introduction to groups. Topics include integers mod n, cyclic groups, permutation groups, normal subgroups, isomorphisms, finite Abelian groups.
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• MATH 326: Abstract Algebra II

  3.00 Credits

  Slippery Rock University of Pennsylvania

  
  An introduction to rings. Topics include integral domains, fields, polynomial rings.
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• MATH 331: Mathematical Methods of Physics and Engineering

  3.00 Credits

  Slippery Rock University of Pennsylvania

  
  The course covers a broad spectrum of mathematical methods relevant to physics and engineering. The emphasis is on the use of methods rather than on proofs and derivations. Topics include vector analysis, complex variables, Fourier and Laplace transforms, linear algebra, and some boundary value problems. Cross-listed with PHYS 331. This course may be counted as a physics course or as a mathematics course, but not both.
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• MATH 335: Mathematical Modeling

  3.00 Credits

  Slippery Rock University of Pennsylvania

  
  A general introduction to mathematical modeling involving optimization, dynamic and probabilistic models. Specific topics selected from dimensional analysis, optimization techniques, continuous and discrete modeling, stability analysis, linearization, eigenvalue methods, qualitative analysis, Markov chains, regression models, simulation techniques, and others as time permits.
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