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MTH 555: Numerical Analysis
3.00 Credits
University of Dayton
Solutions of nonlinear equations, Newton's methods, fixed point methods, solutions of linear equations, LU decomposition, iterative improvement, QR decomposition, SV decomposition.
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MTH 555 - Numerical Analysis
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MTH 556: Numerical Analysis
3.00 Credits
University of Dayton
Interpolating functions, numerical differentiation, numerical integration including Gaussian quadrature, numerical solutions of differential equations.
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MTH 556 - Numerical Analysis
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MTH 558: Financial Math I
3.00 Credits
University of Dayton
Discrete methods in financial mathematics. Topics include introduction to financial derivatives, discrete probability theory, discrete stochastic processes (Markov chain, random walk, and Martingale), binomial tree models for derivative pricing and compu
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MTH 558 - Financial Math I
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MTH 559: Financial Math II
3.00 Credits
University of Dayton
Continuous methods in financial mathematics. Topics include review of continuous probability theory, Ito's Lemma, the Black-Scholes partial differential equation, option pricing via partial differential equations, analysis of exotic options, local and sto
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MTH 559 - Financial Math II
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MTH 561: Modern Algebra I
3.00 Credits
University of Dayton
Groups, rings, integral domains and fields; extensions of rings and fields; polynomial rings and factorization theory in integral domains; modules and ideals.
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MTH 561 - Modern Algebra I
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MTH 562: Modern Algebra II
3.00 Credits
University of Dayton
Finite and infinite field extensions, algebraic closure, constructible numbers and solvability by use of radicals, Galois theory, and selected advanced topics.
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MTH 562 - Modern Algebra II
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MTH 563: Computational Finance
3.00 Credits
University of Dayton
The purpose of this course is to introduce students to numerical methods and various financial problems that include portfolio optimization and derivatives valuation that can be tackled by numerical methods. Students will learn the basics of numerical ana
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MTH 563 - Computational Finance
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MTH 565: Linear Algebra
3.00 Credits
University of Dayton
Vector spaces, linear transformations and matrices; determinants, inner product spaces, invariant direct-sum decomposition and the Jordan canonical form.
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MTH 565 - Linear Algebra
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MTH 571: Topology I
3.00 Credits
University of Dayton
An axiomatic treatment of the concept of a topological space; bases and subbases; connectedness, compactness; continuity, homeomorphisms, separation axioms and countability axioms; convergence in topological spaces.
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MTH 571 - Topology I
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MTH 572: Topology II
3.00 Credits
University of Dayton
Compactification theory, para-compactness and metrizability theorems, uniform spaces, function spaces, and other advanced topics of current interest.
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MTH 572 - Topology II
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