Cuny queens Colleg

quantification theory, recursive functions,
Gödel’s incompleteness theorem. Fall
628. Functions of a Complex Variable. 
3 hr.; 3 cr. Prereq.: One year of advanced
calculus (Mathematics 202) or permission
of instructor. Topics covered include ana-
lytical functions, Cauchy’s Integral Theo-
rem, Taylor’s theorem and Laurent series,
the calculus of residues, Riemann surfaces,
singularities, meromorphic functions.
Spring
630. Differential Topology. 3 hr.; 3 cr.
Prereq.: Advanced calculus. Differentiable
manifolds and properties invariant under
differentiable homeomorphisms; differen-
tial structures; maps; immersions, imbed-
dings, diffeomorphisms; implicit function
theorem; partitions of unity; manifolds
with boundary; smoothing of manifolds.
Spring 1998
631. Differential Geometry. 3 hr.; 3 cr.
Prereq.: Advanced calculus. Theory of
curves and surfaces and an introduction to
Riemannian geometry. Fall 1996
632. Differential Forms. 3 hr.; 3 cr. Pre-
req.: Advanced calculus. A study in a coor-
dinate-free fashion of exterior differential
forms: the types of integrands which
appear in the advanced calculus. Fall 1997
633. Statistical Inference. 3 hr.; 3 cr.
Prereq.: A semester of intermediate calcu-
lus (the equivalent of Mathematics 201)
and either an undergraduate probability
course which includes mathematical
derivations or Mathematics 611 or 621.
Basic concepts and procedures of statistical
inference. Spring
634. Theory of Graphs. 3 hr.; 3 cr. Pre-
req.: One semester of advanced calculus.
An introduction to the theory of directed
and undirected graphs. The Four-Color
Theorem. Applications to other fields. Fall
635. Stochastic Processes. 3 hr.; 3 cr.
Prereq.: Mathematics 611 or 621. A study
of families of random variables.††
636. Combinatorial Theory. 3 hr.; 3 cr.
Prereq.: A course in linear algebra. This
course will be concerned with techniques of
enumeration. Spring
650. Studies in Mathematics. Prereq.:
Permission of department. The topic will
be announced in advance. This course may
be repeated for credit provided the topic is
not the same.††
650.1.     1 hr.; 1 cr.
650.2.     2 hr.; 2 cr.
650.3.     3 hr.; 3 cr.
701. Theory of the Integral. 3 hr.; 4
1
⁄
2
cr.
Prereq.: Mathematics 614. The Lebesgue
integral in one dimension and in n dimen-
sions, the abstract case. Spring
702. Modern Abstract Algebra I. 3 hr.;
4
1
⁄
2
cr. Prereq.: Mathematics 613. A course
in the fundamental concepts, techniques,
and results of modern abstract algebra.
Concepts and topics studied are semi-
groups, groups, rings, fields, modules, vec-
tor spaces, algebras, linear algebras, matri-
ces, field extensions, and ideals. Fall
703. Point Set Topology. 3 hr.; 4
1
⁄
2
cr.
Prereq.: Advanced calculus. Topological
spaces, mappings, connectedness, compact-
ness, separation axioms, product spaces,
function spaces. Fall
704. Functional Analysis. 3 hr.; 4
1
⁄
2
cr.
Prereq.: A course in linear algebra and
Mathematics 614. Abstract linear spaces,
normed linear spaces, continuous linear
transformations, dual spaces. Hahn-
Banach theorem, closed graph theorem,
uniform boundedness principle, Hilbert
spaces, the weak-topology, Alaoglu’s theo-
rem, topological linear spaces. Spring 1998
705. Theory of Functions of a Complex
Variable. 3 hr.; 4
1
⁄
2
cr. Prereq.: Mathemat-
ics 701.††
706. Advanced Ordinary Differential
Equations. 3 hr.; 4
1
⁄
2
cr. Prereq.: Mathe-
matics 616.††
707. Partial Differential Equations. 3
hr.; 4
1
⁄
2
cr. Prereq.: Mathematics 706.††
708. Combinatorial Topology. 3 hr.; 4
1
⁄
2
cr. Prereq.: Mathematics 703.††
709. Set Theory. 3 hr.; 4
1
⁄
2
cr.††
710. Mathematics and Logic: Advanced
Course. 3 hr.; 4
1
⁄
2
cr. Prereq.: Mathematics
626.††
711. The Mathematical Structure of
Modern Statistics. 3 hr.; 4
1
⁄
2
cr. Prereq.: A
course in either probability or statistics.††
712. Higher Geometry. 3 hr.; 4
1
⁄
2
cr.††
713. Modern Abstract Algebra II. 3 hr.;
4
1
⁄
2
cr. Prereq.: Mathematics 702.††
717. Theory of Approximation I. 3 hr.;
4
1
⁄
2
cr. Prereq.: Mathematics 614 or permis-
sion of department.††
718. Theory of Approximation II. 3 hr.;
4
1
⁄
2
cr. Prereq.: Mathematics 717.††
790. Independent Research. May be
repeated for credit if the topic is changed.
790.1.     1 hr.; 1 cr.
790.2.     2 hr.; 2 cr.
790.3.     3 hr.; 3 cr.
790.4.     4 hr.; 4 cr.
790.45.   3 hr.; 4
1
⁄
2
cr.
790.5.     5 hr.; 5 cr.
791. Tutorial. May be repeated for credit
if the topic is changed.
791.1.     1 hr.; 1 cr.
791.2.     2 hr.; 2 cr.
791.3.     3 hr.; 3 cr.
791.4.     4 hr.; 4 cr.
791.45.   3 hr.; 4
1
⁄
2
cr.
791.5.     5 hr.; 5 cr.
792. Seminar. May be repeated for credit
if the topic is changed.
792.1.     1 hr.; 1 cr.
792.2.     2 hr.; 2 cr.
792.3.     3 hr.; 3 cr.
792.4.     4 hr.; 4 cr.
792.45.   3 hr.; 4
1
⁄
2
cr.
792.5.     5 hr.; 5 cr.
M A T H E M A T I C S
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