COURSE DESCRIPTIONS
120 The Nature of Mathematics (3) Selected topics in mathematics with con- sideration of historical development and related philosophical issues. Designed to meet the general education require- ment in mathematics for liberal ans stu· dents. Cannot be counted toward the mathematics major. Fall, spring. 131 Classical Algebra and Geometry (3) Cubic and quartic equations, inequali- ties, complex roots of unity, plane geom- etry of conics and constructions, coordi- nate geomeuy of two and three dimen- sions, advanced trigonometric identities, infinite series and convergence, bino- mial series, symmetric functions. Focus is on theory and problem-solving tech- niques. 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: I06. Fall. 210 Introduction to Probability and Statistics (3) Nature of statistical methods, description of sample data, fundan1en ta! concepts of probability, probability distributions, sampling, estimation, correlation and regression , application of same. Spring. 291 Linear Algebra (3) Topics from matrices, determinants, lin- ear 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 theory ," relations, functions , cardinal- ity, algebraic structures and properties of real numbers. Prerequisites: 205,
for Euclidean and non-Euclidean geom- etry. Prerequisite: 302. Alternate years. 435 Mathematics for the Physical Sciences (3) First order differential equations and second order linear equations, series solutions, Laplace transforms, numeri- cal methods, partial differential equa- tions and Fourier series, boundary value problems and Stu rm-Liouville theory. Prerequisite: 205, 29 I or con- sent. Alternate years. 440 Complex Variables (3) Complex variables, analytic functions, comp lex integral theorems , power series, conformal mappings. Prerequi- site: 205 or consent. Alternate years. 450 Topics in Abstract Algebra (3) Topics from groups, ring and fields. Ga lois theory. Prerequisite: 315. Alternate years. 480 Research Seminar (1 ·3) Special studies in mathematics. Pre- requisite: senior standing or consent.
solutions of ordinary differemial equa- tions. Prerequisites: 291, Computer Science l05. Fee: S25. Alternate years. 331 Probability (3) Samples spaces, axioms and elementary theorems of probability, combinatorics, independence, conditional probability, Bayes ' Theorem , one and higher dimensional random variables, special and multivariate distributions. Prereq- uisites: 112, 205. Alternate years. 332 Statistics (3) Estimation : consistency, unbiasedness, maximum likelihood, confidence inter- vals. Hypothesis-testing; type I and II errors, likelihood ratio tests, test for means and variances; regression and correlation, Chi-square tests, decision theory, nonparametric sta ti sti cs; appli- cation of statistical methods. Prerequi- site: 331or consent. Alternate years. 333 Operations Research (3) Mathematical foundations of model building, optimization, lin ear pro·
gramming models , game theoretic models. Cross li sted with Computer Science 325. Prerequisites: I05, Com- puter Science I05. Fee: S25. 410 Topics in Advanced Calculus (3) Implicit function theorems, main the- orems in integral calculus. Jacobian transforma tions, infinite seri es. Pre- requisite: 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 exploring developments in number theory including congruences, Diophantine equations, di\~sibility, the- orems of Fermat and Wilson, primitive roots, indices, quadrat ic reciprocity and the distribution of prime numbers. Prerequisite: 302. Alternate years. 420 Modern Geometry (3) Homogeneous projective coordinates invariants, duality, Desargues's and Pap- pus's theorems, transformations, point and line conics, various axioms systems
291or consent. Spring. 305 Advanced Calculus (3)
The real number system, elementary topo log ical concepts in Cartesian spaces, convergence, continuity, deriv- atives and integrals. Prerequisite: 302 or consent. Alternate years. 315 Modern Algebra (3) Introduction LO abstract algebra with topics from elementary ring, field and group theories. Emphasis on ring of integers , congruences, polynomial domains, permutation groups. Prereq- uisite: 302 or consent. Alternate years. 321 Numerical Analysis (3) Functions of one variable, approximate numerical solutions of non-linear equa- tions and systems of linear equations, interpolation theory, numerical differ- entiation and integration , numerical
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