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math 332 statistics......................................................................................3<br />
Estimation: consistency, unbiasedness, maximum likelihood,<br />
confidence intervals. Hypothesis-testing; type I and II errors,<br />
likelihood ratio tests, test for means and variances; regression<br />
and correlation, Chi-square tests, decision theory, nonpara-<br />
metric statistics; application of statistical methods. Prerequi-<br />
site: 331 or consent. Alternate years.<br />
math 333 operations research ..............................................................3<br />
Mathematical foundations of model building, optimization,<br />
linear programming models, game theoretic models. Prereq-<br />
uisites: 1<strong>05</strong>, Computer Science 1<strong>05</strong>.<br />
math 341 Classical Geometry .................................................................3<br />
Theorems of Pythagoras, incenters, circumcenters, circles,<br />
Euler line, Fermat center. Compass constructions. Solid<br />
geometry. Spherical geometry of arcs. Coordinate geometry.<br />
Prerequisite: Consent. Alternate years.<br />
math 370 readings in mathematics .....................................................1<br />
Reading of material in a special topic. Colloquium participa-<br />
tion. Writing and oral presentation of a research paper. Prereq-<br />
uisite: Consent of the department. May be repeated for credit.<br />
math 410 Topics in advanced Calculus ...............................................3<br />
Implicit function theorems, main theorems in integral calcu-<br />
lus. Jacobian transformations, infinite series. Prerequisite: 3<strong>05</strong>.<br />
Alternate years.<br />
math 415 number Theory & the history of mathematics ............3<br />
The history of mathematics from Euclid through the 19th<br />
century as seen by exploring developments in number theory<br />
including congruences, Diophantine equations, divisibility,<br />
theorems of Fermat and Wilson, primitive roots, indices,<br />
quadratic reciprocity and the distribution of prime numbers.<br />
Prerequisite: 112. Alternate years.<br />
math 420 modern Geometry ..................................................................3<br />
Projective geometry, cross ratios theorems of Menelaus,<br />
Cevas, Pappus, Desargues and Brianchon. Hyperbolic and<br />
elliptic geometries. Differential geometry, curvature, torsion.<br />
Prerequisite: 341 or consent. Alternate years.<br />
math 435 Differential equations ............................................................3<br />
First order differential equations and second order linear equa-<br />
tions, series solutions, Laplace transforms, numerical methods,<br />
partial differential equations and Fourier series, boundary<br />
value problems and Sturm-Liouville theory. Prerequisite: 2<strong>05</strong>,<br />
291 or consent. Alternate years.<br />
math 440 Complex Variables ..................................................................3<br />
Complex variables, analytic functions, complex integral theo-<br />
rems, power series, conformal mappings. Prerequisite: 2<strong>05</strong> or<br />
consent. Alternate years.<br />
math 450 Topics in abstract algebra ...................................................3<br />
Topics from groups, ring and fields. Galois theory. Prerequisite:<br />
315. Alternate years.<br />
math 480 research seminar .................................................................1-3<br />
Special studies in mathematics. Prerequisite: senior standing<br />
or consent. May be repeated for credit.<br />
20<strong>05</strong> – 20<strong>07</strong> C ATA LO G Undergraduate Programs 121