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Catalog 05-07 - Biola University

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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

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