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Course Criteria
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3.00 Credits
Introduction to abstract algebra with topics from elementary ring, field and group theories Emphasis on ring of integers, congruences, polynomial domains, permutation groups Prerequisite: 112 and 291 or consent Alternate years
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3.00 Credits
Functions of one variable, approximate numerical solutions of non-linear equations and systems of linear equations, interpolation theory, numerical differentiation and integration, numerical solutions of ordinary differential equations Prerequisites: 291, Computer Science 105 Alternate years
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3.00 Credits
Samples spaces, axioms and elementary theorems of probability, combinatorics, independence, conditional probability, Bayes' Theorem, one and higher dimensional random variables, special and multivariate distributions Prerequisites: 112, 205 Alternate years
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3.00 Credits
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, nonparametric statistics; application of statistical methods Prerequisite: 331 or consent Alternate years
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3.00 Credits
Mathematical foundations of model building, optimization, linear programming models, game theoretic models Prerequisites: 105, Computer Science 105
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3.00 Credits
Theorems of Pythagoras, incenters, circumcenters, circles, Euler line, Fermat center Compass constructions Solid geometry Spherical geometry of arcs Coordinate geometry Prerequisite: Consent Alternate years
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1.00 Credits
Reading of material in a special topic Colloquium participation Writing and oral presentation of a research paper Prerequisite: Consent of the department May be repeated for credit
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3.00 Credits
Implicit function theorems, main theorems in integral calculus Jacobian transformations, infinite series Prerequisite: 305 Alternate years
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3.00 Credits
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
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3.00 Credits
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
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