Statist ics ... ... .. ..................................................... ......... .... ........... 3 Estimation: consistency, unbiasedness, maximum likelihood, confidence intervals. Hypothesis-testing; type I and II errors, likelihood ratio tests, test for means and variances; regression and correlation, Chi-square tests, decision theory, nonpara metric statistics; application of statistical methods. Prerequi· site: 331 or consent. Alternate years. . ....... .. .. .. ........... .3 Mathematical foundations of model building, optimization, linear programming models, game theoretic models. Prereq uisites: I 05, Computer Science 105. Operations Research ................. . Classica l Geometry .. .. .. .. ................. ........................ ............ .. 3 Theorems of Pythagoras, incenters, circumcenters, circles, Euler line, Fermat center. Compass constructions. Solid geometry. Spherical geometry of arcs. Coordinate geometry. Prerequisite: Consent. Alternate years. Readings in Mathematics ...................................... .. .......... . 1 Reading of material in a special topic. Colloquium participa tion. Writing and oral presentation of a research paper. Prereq· uisite: Consent of the department. May be repeated for credit.

Top ics in Abstract Algebra .. ................................................. 3 Topics from groups, ring and fi elds. Ga lois theory. Prerequisite: 315. Alternate years.

MATH 332

MATH 450

Research Seminar. ..... ···· ··· ···· ·· ·· ·· · ·· ·· ·· ·· ·· · ··· ···· ··· · ··· ··· ·1~ Special studies in mathematics. Prerequisite: senior standing or consent. May be repeated fo r credit.

MATH4so

MATH 333

MATH 341

MATH37o

Topics in Advanced Calculus ............. . ............ .. ....... .

MATH 410

.. 3

Implicit funcuon theorems, main theorems in integra l calcu lus. Jacobian transformations, infinite series. Prerequisite: 305. Alternate years.

Number Theory & the History of Mathematics .. ......... 3 The history of mathematics from Euclid through the 19th century as seen by exploring developments in number theory including congruences, Diophantine equations, divisibility, theorems of Fermat and Wilson, primitive roots, indices, quadratic reciprocity and the distribution of prime numbers. Prerequisite: 112. Alternate years. Modern Geometry. ... ... ............................ .............. .. ....... .... 3 Projective geometry, cross ratios theorems of Menelaus, Cevas, Pappus, Desargues and Brianchon. Hyperbolic and elliptic geometries. Differential geometry, curvature, torsion. Prerequisite: 341 or consent. Alternate years. Differential Equations ........................ .. ... ......... .. .. .. ... .. ... ....... 3 First order differential equations and second order linear equa tions, series solutions, Laplace transforms. numerical methods, partial differential equations and Fourier series, boundary value problems and Sturm-Liouville theory. Prerequisite: 205, 291 or consent. Alternate years. Complex Variables .. ... .. .. ........ ........... ...... . .. .. ..... .. ................... 3 Complex variables, analytic functions, complex integral theo rems, power series, conformal mappings. Prerequisite: 205 or consent. Alternate years.

MATH415

MATH 420

MATH435

MATH 440

Undergraduare Programs

121

2005 2007 l. ATALOG

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