74 COURSE DESCRIPTIONS
333 OPERATIONS RESEARCH (3) Mathematical foundations of model building, optimizati®, linear program ming models, game theoretic models . Cross listed with Computer Science 325. Prerequisites: 105, Computer Science 101. Fee: $25.
291 LINEAR ALGEBRA (3) Topics from matrices, determinants, linear transformations and vector spaces. Prerequisite: 106 or consent. Fall. 302 INTRODUCTION TO MODERN MATHEMATICS (3) Methods of constructing proofs and the logic used in these methods, set theo ry, relations, functions, cardinality, alge braic structures and properties of real numbers. Prerequisites: 205, 291 or con sent. Spring. 305 ADVANCED CALCULUS (3) The real number system, elementary topological concepts in Cartesian spaces, convergence, continuity, derivatives and integrals. Prerequisite: 302 or consent. Alternate years. 315 MODERN ALGEBRA (3) Introduction to abstract algebra with topics from elementary ring, field and group theories. Emphasis on ring of inte gers, congruences, polynomial domains, permutation groups. Prerequis ite: 302 or consent. Alternate years . 321 NUMERICAL ANALYSIS (3) Functions of one variabl e, approximate numerical solutions of non-linear equa tions and systems of linear equations, interpolation theory, numerical differenti ation and integration, numerical solutions of ordinary differential equations. Prerequisites: 291, Computer Science 101. Fee: $25. Alternate years. 331 PROBABILITY (3) Samples spaces, axioms and elemen tary theorems of probability, combina torics, independence, conditional proba bility, Bayes' Theorem, one and higher dimensional random variables, special and multivariate distributions. Prerequisites: 112, 205. Alternate years . 332 STATISTICS (3) Estimation: consistency, unbiasedn ess, maximum likelihood, confidence inter vals. Hypothesis-testing; type I and II erro rs, likelihood ratio tests, test for means and variances; regression and cor relation, Chi-square tests, decision th eory, nonparametric statistics; application of statistical methods. Prerequisite: 331 or consent. Alternate years.
111 FUNDAMENTALS OF MATHEMATICS FOR ELEMENTARY TEACHERS (3) Set theory, relations and functions, number systems and algebraic structures, numeration systems, elementary number theory, informal geometry, use of manipu latives. For elementary education majors only. Cannot be counted toward the mathematics major. Fall. 112 DISCRETE STRUCTURES (3) Elementary properties of sets, discrete probability and combinatorial analysis, graphs, relations, orderings, functions, simple algebraic structures, binary arith metic and other bases, methods of proof. Prerequisite: three years of high school mathematics or consent. Spring. 120 THE NATURE OF MATHEMATICS (3) Selected topics in mathematics with consideration of historical deve lopment and related philosophical issues. Designed to meet the general education requirement in mathematics for liberal arts students. Cannot be counted toward the mathematics major. Fall ,Spring. 131 CLASSICAL ALGEBRA AND GEOMETRY (3) Cubic and quartic equa tions , inequali ties, complex roots of unity, plane geome try of conics and constructions, coordi nate geometry of two and three dimensions, advanced trigonometric iden tities, infinite series and convergence, binomial series, symmetric funtions. Focus is on theory and problem-solving techniques. Prerequisite: four years of high school math or consent. Fall. 205 INTERMEDIATE CALCULUS (4) Functions of two and three variables, partial differentiation, multiple integra tion, curves and surfaces in three dimen sional space. Prerequisite: 106. Fall. 210 INTRODUCTION TO PROBABILITY AND STATISTICS (3) Nature of statistical methods, descrip tion of sample data, fundamental con cepts of probability, probability distribu tions, sampling, estimation, correlation and regression; application of same. Spring.
410 TOPICS IN ADVANCED CALCULUS (3)
Implicit function theorems, main theo rems in integral calculus. Jacobian trans formations, infinite series. Prerequisite: 305. Alternate years. 415 NUMBER THEORY AND THE HISTORY OF MATHEMATICS (3) The history of mathematics from Euclid through the 19th century as seen by explor ing developments in number theory includ ing congruences, Diophantine equations, divisibility, theorems of Fermat and Wilson, primitive roots, indices, quadratic reciproci ty and the distribution of prime numbers. Prerequisite: 302. Alternate years. 420 MODERN GEOMETRY (3) Homogeneous projective coordinates invariants, duality, Desargues 's and Pappus 's theorems, transformations, point and line conics, various axioms systems for Euclidean and non-Euclidean geometry. Prerequisite: 302. Alternate years. 435 MATHEMATICS FOR THE PHYSICAL SCIENCES (3) First order differential equations and second order linear equations, series solu tions, Laplace transforms , numerical methods, partial differential equations and Fourier series, boundary value prob
lems and Sturm-Liouville theory. Prerequisite: 205, 291 or consent. Alternate years.
440 COMPLEX VARIABLES (3) Complex variables, analytic functions, complex integral theorems, power series, conformal mappings. Prerequisite: 205 or consent. Alternate years. 450 TOPICS IN ABSTRACT ALGEBRA (3) Topics from groups, ring and fields. Galois theory. Prerequisite: 315. Alternate years. 480 RESEARCH SEMINAR (1-3) Special studi es in mathematics._ Prerequisite: senior standing or consent.
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