MTH U545 Fourier Series and PDEs 4 SH
Provides a first course in Fourier series, Sturm-Liouville
boundary value problems, and their application to solving the
fundamental partial differential equations of mathematical
physics: the heat equation, the wave equation, and Laplace’s
equation. Green’s functions are also introduced as a means of
obtaining closed- form solutions . Prereq. MTH U345.
MTH U550 Real Analysis 4 SH
Provides the theoretical underpinnings of calculus and the
advanced study of functions. Emphasis is on precise definitions
and rigorous proof. Topics include the real numbers and
completeness, continuity and differentiability, the Riemann
integral, the fundamental theorem of calculus, inverse function
and implicit function theorems, and limits and convergence.
Required of all mathematics majors . Prereq. MTH U165,
MTH U341, and MTH U371.
MTH U555 Complex Variables 4 SH
Provides an introduction to the analysis of functions of a
complex variable . Starting with the algebra and geometry of
complex numbers, basic derivative and contour integral
properties are developed for elementary algebraic and
transcendental functions as well as for other analytic functions
and functions with isolated singularities. Power and Laurent
series representations are given. Classical integral theorems,
residue theory, and conformal mapping properties are studied.
Applications of harmonic functions are presented as time
permits. Prereq. MTH U341.
MTH U560 Geometry 4 SH
Studies classical geometry and symmetry groups of geometric
figures, with an emphasis on Euclidean geometry. Teaches how
to formulate mathematical propositions precisely and how to
construct and understand mathematical proofs. Provides a line
between classical and modern geometry with the aim of
preparing students for further study in group theory and
differential geometry . Prereq. MTH U343 or MTH U371.
MTH U565 Topology 4 SH
Introduces the student to fundamental notions of topology.
Introduces basic set theory, then covers the foundations of
general topology (axioms for a topological space, continuous
functions, homeomorphisms, metric spaces, the subspace,
product and quotient topologies, connectedness, compactness,
and the Hausdorff condition). Also introduces algebraic and
geometric topology (homotopy, covering spaces, fundamental
groups, graphs , surfaces, and manifolds) and applications.
Other topics are covered if time permits. Prereq. MTH U341
and MTH U371.
MTH U571 Advanced Linear Algebra 4 SH
Provides a more detailed study of linear transformations and
matrices: LU factorization, QR factorization, Spectral theorem
and singular value decomposition, Jordan form, positive
definite matrices, quadratic forms , partitioned matrices, and
norms and numerical issues. Topics and emphasis change
from year to year. Prereq. MTH U371.
MTH U575 Group Theory 4 SH
Presents basic concepts and techniques of the group theory:
symmetry groups, axiomatic definition of groups, important
classes of groups (abelian groups, cyclic groups, additive and
multiplicative groups of residues, and permutation groups),
Cayley table, subgroups, group homomorphism, cosets, the
Lagrange theorem, normal subgroups, quotient groups, and
direct products. Studies structural properties of groups.
Possible applications include geometry, number theory,
crystallography, physics, and combinatorics. Prereq.
MTH U165, MTH U341, and MTH U371.
MTH U576 Rings and Fields 4 SH
Introduces commutative rings, ideals, integral domains, fields,
and the theory of extension fields. Topics include Gaussian
integers, Galois groups, and the fundamental theorem of
Galois theory. Applications include the impossibility of angletrisection
and the general insolvability of fifth- and higherdegree
polynomials. Other topics are covered as time permits.
Prereq. MTH U371.
MTH U581 Statistics and Stochastic Processes 4 SH
Continues topics introduced in MTH U481. The first part of
the course covers classical procedures of statistics including the
t-test, linear regression, and the chi- square test . The second
part provides an introduction to stochastic processes with
emphasis on Markov chains, random walks, and Brownian
motion, with applications to modeling and finance. Prereq.
MTH U481.
MTH U585 Introduction to Actuarial Math 4 SH
Introduces basic aspects of life contingencies. The theory is
illustrated by worked examples and reinforced through
numerous exercises. Prepares students to take the relevant
actuarial exam. Prereq. MTH U481 is recommended.
MTH U606 Mathematical and Computational Methods
for Physics 4 SH
Covers advanced mathematical methods topics that are
commonly used in the physical sciences, such as complex
calculus, Fourier transforms, special functions, and the
principles of variational calculus. Applies these methods to
computational simulation and modeling exercises. Introduces
basic computational techniques and numerical analysis, such
as Newton’s method, Monte Carlo integration, gradient
descent, and least squares regression. Uses a simple
programming language, such as MATLAB, for the exercises.
Same as PHY U606. Prereq. PHY U303, MTH U341, and
MTH U343 or MTH U345.
MTH U681 Probability and Risks 4 SH
Reviews main probability and statistics concepts from the point
of view of decision risks in actuarial and biomedical contexts,
including applications of normal approximation for evaluating
statistical risks. Also examines new topics, such as distribution
of extreme values and nonparametric statistics with examples.
May be especially useful for students preparing for the first
actuarial exam on probability and statistics. Prereq. MTH U481.
MTH U682 Theory of Interest and Basics of Life
Insurance 4 SH
Reviews basic financial instruments in the presence of interest
rates, including the measurement of interest and problems in
interest ( equations of value , basic and more general annuities,
yield rates, amortization schedules, bonds and other securities).
Examines numerous practical applications. Also introduces
problems of life insurance with examples. May be especially
useful for students preparing for the second actuarial exam on
theory of interest. Prereq. MTH U481.
MTH U725 Applied Mathematics Capstone 4 SH
Offers students of mathematics the experience of utilizing their
skills to study problems that arise in industry and other realworld
settings. Provides students the opportunity to build on
exciting industrial experiences they may have had through coop
or other employment. Fulfills the Arts and Sciences
experiential education requirement, and is intended for juniors
and seniors with some experience or interest in applications of
mathematics. Prereq. Two years calculus and junior or senior
standing.
MTH U921 Directed Study 1 SH
MTH U922 Directed Study 2 SH
MTH U923 Directed Study 3 SH
MTH U924 Directed Study 4 SH
Offers independent work under the direction of members of
the department on a chosen topic. Course content depends on
instructor. Prereq. Permission of instructor.
MTH U951 Experiential Education Directed Study 4 SH
Draws upon the student’s approved experiential activity and
integrates it with study in the academic major. Restricted to
those junior and senior mathematics majors who are using it to
fulfill their experiential education requirement; for these
students it may count as a mathematics elective, subject to
approval by instructor and adviser. Prereq. Math major with
junior or senior standing.
MTH U970 Junior/Senior Honors Project 1 4 SH
Focuses on in-depth project in which a student conducts
research or produces a product related to the student’s major
field. Culminating experience in the University Honors
Program. Combined with Junior/Senior Project 2 or collegedefined
equivalent for 8-credit honors project. Prereq. Honors
program participation.
MTH U971 Junior/Senior Honors Project 2 4 SH
Focuses on second semester of in-depth project in which a
student conducts research or produces a product related to the
student’s major field. Culminating experience in the University
Honors Program. Prereq. MTH U970 and honors program
participation.
