67 COURSE DESCRIPTIONS

321 Numerical Analysis (3) Functions of one variable, approximate numerical solutions of non-linear equations and systems of linear equations, interpolation theory, numerical differentiation and integra tion, numerical solutions of ordinary differen tial equations. Prerequisites: 291, Computer Science 101. Fee: $25. Alternate years. 331 Probability (3) Samples spaces, axioms and elementary theorems of probability, combinatorics, in dependence, conditional probability, Bayes' Theorem, one and higher dimensional ran dom variables, special and multivariate dis tributions. Prerequisites: 112, 205. Alternate years. 332 Statistics (3) Estimation: consistency unbiasedness, maximum likelihood, confidence intervals. Testing hypothesis; type I and II errors, likelihood ratio tests, test for means and variances; regression and correlation, Chisquare tests, decision theory, nonpara metric statistics; application of statistical methods. Prerequisite: 331 or consent. Alternate years. 333 Operations Research (3) Mathematical foundations of model building, optimization, linear programming models, game theoretic models. Cross list ed with COS 325. Prerequisites: 105, Computer Science 101. Fee: $25. 410 Topics in Advanced Calculus (3) Implicit function theorems, main theo rems in integral calculus. Jacobian transfor mations, 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, di visibility, 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 in variants, 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.

112 Discrete Structures (3) Elementary properties of sets, discrete probability and combinatorial analysis, graphs, relations, orderings, functions, sim ple algebraic structures, binary arithmetic and other bases, methods of proof. Prerequisite: three years of high school mathematics or consent. Spring. 131 Classical Algebra and Geometry (3) Cubic and quartic equations, inequalities, complex roots of unity, plane geometry of conics and constructions, coordinate geome try of two and three dimensions, advanced trigonometric identities, 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 integration, curves and surfaces in three dimensional space. Prerequisite: 106. Fall. 210 Introduction to Probability and Statistics (3) Nature of statistical methods, descrip tion of sample data, fundamental concepts of probability, probability distributions, sam pling, estimation, correlation and regres sion; application of same. Spring. 291 Linear Algebra (3) Topics from matrices, determinants, lin ear transformations and vector spaces. Prerequisite: 106 or consent. Fall.

COURSES 100 Intermediate Algebra (3) Review of elementary algebra, graphs and polynomials. Study of linear and quadratic equations and inequalities, factor ing, fractions, exponents and radicals. Prerequisite: one year of high school alge bra. Not counted for general education re quirement or toward graduation. Fall. 101 Precalculus Mathematics (3) Sets, the real number system, relations, functions, graphs, algebraic processes, inequalities, trigonometric functions, matri ces and determinants, complex numbers, exponential and logarithmic functions, in troduction to sequences, probability and statistics. Prerequisite: three years of high school mathematics or consent. Cannot be counted toward the major. Fall, Spring. 103 Calculus for Management Sciences (3) Fundamental principles of differential and integral calculus. Applications chosen mainly from the management sciences. Prerequisite: passing proficiency exam ad ministered by Mathamatics Department or receiving a "C" or better grade in math 100 the prior year. Fall, Spring. 105 Analytic Geometry and Calculus I (4) An introduction to analytic geometry, dif ferentiation and integration of polynomial functions, with applications. Prerequisite: four years of high school mathematics or consent. Fall. 106 Analytic Geometry and Calculus II (4) Differentiation and integration of trigonometric, logarithmic and exponential functions , various methods of integration, sequences and series, and vectors in the plane. Prerequisite: 105. Spring. 111 Fundamentals ofMathematics (3) Set theory, relations and functions , num ber systems and algebraic structures, nu meration systems, elementary number the ory, mathematical systems,concepts of probability, introduction to statistics, infor mal geometry. Designed for prospective ele mentary school teachers and to fulfill liberal arts requirements. Cannot be counted to ward the major. Fall, Spring.

302 Introduction to Modern Mathematics (3)

Methods of constructing proofs and the logic used in these methods, set theory, re lations, functions, cardinality, algebraic structures and properties of real numbers. Prerequisites: 205, 291 or consent. Spring. 305 Advanced Calculus (3) The real number system, elementary topological concepts in Cartesian spaces, convergence, continuity, derivatives and in tegrals. 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 integers, congruences, polynomial domains, permutation groups. Prerequisite: 302 or consent Alternate years.

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