112 Discrete Structures (3) Elementary properties of sets, discrete probability and combinatorial analysis, graphs, relations, orderings, functions, simple algebraic structures, binary ari th­ 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 111th con­ sideration of histmical development and related phi losophical issues. Designed lO meet the general education requi re­ ment in mathematics for liberal arts stu­ dents. Cannot be counted toward the mathematics major. Fall , sp1ing. 131 Classical Algebra and Geometry (3) Cubic and quartic equations, inequali­ ties, complex roots of uni ty, plane geom­ eu-y of conics and consu-uctions, coordi­ nate geomeuy of two and three dimen­ sions, advanced uigonomeuic identi ties, infi nite series and convergence, bi no­ mial se1ies, symmeuic functions. Focus is on theory and problem-solving tech­ niques. Prerequisite: four years of high

school math or consen t. Fal l. 190 Business Statistics (3)

Collection and presentation of business data, central tendency and dispersion measures for business analysis, sampli ng and inference for confidence intervals and hypothesis testing, business forecast­ ing with simple and multi ple regression, index numbers. Prerequisite: consent. Fall, sp1ing. For business majors only. 205 Intermediate Calculus (4) Functions of two and three variables, partial differentiation, multiple in tegra­ tion, curves and swfaces in three dimen­ sional space. Prerequisite: I06. Fall. 210 Introduction to Probability and Statistics (3) Nature of statistical me thods, description of sample data, fi.mdamental concepts of probabili ty, probabili ty distributions, sampli ng, estima tion, correlati on and regression, application of same. Spring. 291 Li near Algebra (3) Topics from mauices, determinants, lin­ ear transformations and vector spaces. Prerequisite: l06 or consent. Fall. 305 Advanced Calculus (3) The real number system, elementary topologica l co ncepts in Ca rtes ian spaces, convergence, continuity, deriv­ atives and integrals. Prerequisite: 11 2 and 205 or consent. Alternate years.

315 Modern Algebra (3) In troduction to abstract algebra 111 th top­ ics fromelementaty ting, fi eld and group theories. Emphasis on ring of integers, congruences, polynomial domains, per­ mutation groups. Prerequisite: 11 2 and 291or consent. Alternate years. 321 Numerical Analysis (3) Functions of one variable, approximate numerical solutions of non-linear equa­ ti ons and systems of linear equations, in terpolation theory, numerical differ­ entia tion and in tegration , nume ri cal solutions of ordi na1y diffe rential equa­ tions. Prerequ is ites: 29 1, Compu ter Science 105. Fee: $25. Alternate years. 331 Probability (3) Samples spaces, axioms and elementary theorems of probabili ty, combinatorics, independence, condi tional probabili ty, Bayes' Theorem, one and hi gher dimensional random variables, special and mul tivariate distributions. Prereq­ uisi tes: 11 2, 205. Al ternate years. 332 Statistics (3) Estimation: consistency, unbiasedn ess, maximum li ke lihood, confidence inter­ vals. Hypothesis-testing; type I and II errors, li ke lih ood ratio tes ts, tes t for

420 Modern Geometry (3) Homogeneous projective coordinates invariants, dua lity, Desargues's and Pappus's theorems, transformations, point and line coni cs, various axioms systems fo r Euclidean and non-Eucl id­ ean geometry. Prerequisite: 11 2 or

means and variances; regression and correlation, Chi-square tests, decision theory, nonparametri c stati stics; appli­ cation of sta ti stical methods. Prerequi­ site: 331or consent. Al ternate years. 333 Operations Research (3) Ma thematical foundat ions of model bui ld ing, optimization, li nea r pro­ gramming models, game th eore ti c models. Cross listed with Compu ter Science 325. Prerequi sites: I05, Com­ puter Science 105 . Fee: $25. 410 Topics in Advanced Calculus (3) Implicit fu nct ion th eorems, main the­ orems in integral calculus. Jacobian transformations, infi nite se ri es. Pre­ requisite: 305. Al te rn ate years. 415 Number Theory and the History of Mathematics (3) The hi story of mat hemat ics fr om Euclid th rough the 19th centu ry as seen by expl oring deve lopments in number theory including congruences, Diophantine equations, divisibili ty, the­ orems of Fermat and Wilson , primitive roots, in dices, quadratic rec iprocity and the dis tribution of prime numbers. Prerequisite: 112. Alternate years.

consent. Al ternate years. 435 Mathematics for the Physical Sciences (3)

Fi rs t order differential equations and second order linear equations, series solutions, Laplace transforms, numeri­ cal methods, partial differential equa­ ti ons and Fouri er series, boun dary va lue pro bl ems and Sturm-Liouville theory. Prerequisite: 205, 29 1or con­ sen t. Alternate years. 440 Complex Variables (3) Complex variables, analytic functions, comp lex integ ral theo rems , powe r series, confo rmal mappings. Prerequi­ site: 205 or consent. Al ternate years. 450 Topics in Abstract Algebra (3) Topics from groups, ring and fi elds. Ga lois th eory. Prerequi site: 315. Alternate years. 480 Research Seminar (1-3) Special studies in mathemati cs . Pre­ req uisite: senior standing or consent.

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