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Master of Financial Mathematics with Additional Mathematics
For Additional Mathematics, please make one of the following
three choices:
- probability choice:
please take MATH 8651, MATH 8652 and MATH 8659
- numerical analysis choice:
please take MATH 8651, MATH 8441 and MATH 8442
- differential equations choice:
please take MATH 8651, MATH 5587 and MATH 5588
Note that MATH 8651 (a probability course) is required
in all three choices.
These courses are offered by the School of Mathematics, and are
recommended to those students in our program who wish to enhance their
knowledge of mathematics beyond the level covered in the regular
FM courses.
WARNING:
Courses listed on this website may have prerequisites; see the syllabi
to check on those. If you have any question about whether you are
ready to take a certain course, please speak to the course instructor
and/or your advisor.
NOTE:
Completion of these "with additional Mathematics" requirements
also also fulfills the requirements for a Master's level minor in
Mathematics. If you wish to obtain that minor, you'll need to get the
signature of the Mathematics DGS on your degree program form.
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MATH 8651
Theory of Probability Including Measure Theory
3 credits
Syllabus
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Probability spaces. Distributions/expectations of random
variables. Basic theorems of Lebesque theory. Stochastic
independence, sums of independent random variables, random walks,
filtrations. Probability, moment generating functions,
characteristic functions. Laws of large numbers.
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MATH 8652
Theory of Probability Including Measure Theory
3 credits
Syllabus
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Conditional distributions and expectations, convergence of
sequences of distributions on real line and on Polish spaces,
central limit theorem and related limit theorems, Brownian motion,
martingales and introduction to other stochastic sequences.
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MATH 8659
Stochastic Processes
3 credits
Syllabus
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In-depth coverage of various stochastic processes and related
concepts, such as Markov sequences and processes, renewal
sequences, exchangeable sequences, stationary sequences, Poisson
point processes, Levy processes, interacting particle systems,
diffusions, and stochastic integrals.
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MATH 8441
Numerical Analysis and Scientific Computing
3 credits
Syllabus
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Approximation of functions, numerical integration. Numerical
methods for elliptic partial differential equations, including
finite element methods, finite difference methods, and spectral
methods. Grid generation.
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MATH 8442
Numerical Analysis and Scientific Computing
3 credits
Syllabus
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Numerical methods for integral equations, parabolic partial
differential equations, hyperbolic partial differential
equations. Monte Carlo methods.
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MATH 5587
Elementary Partial Differential Equations I
4 credits
Syllabus
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Emphasizes partial differential equations w/physical applications,
including heat, wave, Laplace's equations. Interpretations of boundary
conditions. Characteristics, Fourier series, transforms, Green's
functions, images, computational methods. Applications include wave
propagation, diffusions, electrostatics, shocks.
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MATH 5588
Elementary Partial Differential Equations II
4 credits
Syllabus
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Heat, wave, Laplace's equations in higher dimensions. Green's
functions, Fourier series, transforms. Asymptotic methods, boundary
layer theory, bifurcation theory for linear/nonlinear
PDEs. Variational methods. Free boundary problems. Additional topics
as time permits.
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