2008-2009 Graduate Catalog - Graduate School @ the University of ...

MATH 7330
Theory of Numbers (3).
Divisibility, factorization, arithmetic
functions, means value
theorems, distribution of prime
numbers, congruencies, primitive
roots, character theory, Riemann
zeta function, and Dirichlet Lfunctions.
Prerequisites: graduate
standing and MATH 2300;
recommended 2320 or 2340, and
4940/7940.
MATH 7335
College Geometry (3).
Euclidean geometry from an advanced
viewpoint. Synthetic and
coordinate methods will be used.
The Euclidean group of transformations
will be studied. Prerequisite:
graduate standing and
MATH 2300.
MATH 7340
Projective Geometry (3).
Basic ideas and methods of projective
geometry built around
the concept of geometry as the
study of invariants of a group.
Extensive treatment of collineations.
Prerequisite: graduate
standing and MATH 2300.
MATH 7345
Foundations of Geometry (3).
Coordination of affine, projective
planes by means of various
kinds of algebraic structures:
planar ternary rings, Veblen-
Wedderburn systems, divisions
rings, skew fields, and fields. Prerequisite:
graduate standing and
MATH 2300.
MATH 7350
Introduction to Non-Euclidean
Geometry (3).
Account of rise, development of
non-Euclidean geometries. Intensive
study of plane hyperbolic
geometry. Prerequisite: graduate
standing and MATH 2300.
MATH 7355
Investment Science I (3).
Deterministic cash flow streams.
The present value. Bonds, bonds’
yield, duration. The term structure
of interest rates. Single-period
random yield analysis. Random
returns. Portfolio mean-variance
analysis. Markovitz model. Prerequisites:
graduate standing
and MATH 2300 and STAT 2500
or instructor’s consent.
MATH 7360
Actuarial Mathematics (3).
Basic actuarial methods, mathematical
population studies and
and models of population growth.
Compound interest and annuities
certain. Values of endowment
and annuities, calculation
of premiums, surrender values.
Stochastic models of populations
growth. Prerequisite: graduate
standing and MATH 2300 and
STAT 2500, or instructor’s consent.
No variable credit.
MATH 7370
Actuarial Modeling I (3).
This course covers the main probability
tools applied to financial
risk modeling, and the financial
mathematics concepts used in
calculating present and accumulated
values for various cash
flows. It is a helpful tool in preparing
for the Society of Actuaries
exams P (Probability) and FM
(Financial Mathematics), and it is
oriented towards problem solving
techniques illustrated with
previous exam problems. Prereq-
uisites: MATH 2300, MATH 4320/
STAT 4750. Students are encouraged
to take MATH 4355 prior to
this course
MATH 7371
Actuarial Modeling II (3).
This course covers the actuarial
models and their applications to
insurance and other business decisions.
It is a helpful tool in preparing
for the Society of Actuaries
exam (M) (Actuarial Models),
and it is oriented towards problem
solving techniques illustrated
with previous exam problems.
Prerequisites: MATH 2300, MATH
4320/STAT 4750. Student are encouraged
to take MATH 4355 prior
to this course.
MATH 7400
Introduction to Topology (3).
Topics from topology of Euclidean
spaces, generalizations to
metric spaces and topological
spaces. Fundamentals of point
set topology. Prerequisite: graduate
standing and MATH 2300.
MATH 7500
Applied Analysis (3).
Solution of the standard partial
differential equations (wave,
heat, Laplace’s eq.) by separation
of variables and transform methods;
including Eigenfunction expansions,
Fourier and Laplace
transform. Boundary value problems,
Sturm-Liouville theory, orthogonality,
Fourier, Bessel, and
Legendre series, spherical harmonics.
Prerequisite: graduate
standing and MATH 4100/7100.
PAGE 479
University of Missouri Graduate School • 2008-2009 Catalog • http://gradschool.missouri.edu
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MATHEMATICS GRADUATE PROGRAMS