damental concepts of probability, probability distributions, sam pling, estimation, correlation and regression ; application of same. 295 LINEAR ALGEBRA (3) Topics from matrices, determinants , linear transformations and
may be repeated with different content (section title). Pre, requisite: 202. Fee: $15. Discrete Structures. Logical and algebraic structures , com binatorial mathematics , graph theory. Theory ofAlgorithms. Analytic techniques for the determina tion of algorithmic efficiency. NP - complete problems, complexity hierarchies , provably intractable problems. Theory of Computation. An introduction to the formal theory of computation, concepts of decidability , the halting problem, algorithms , procedures and the theoretical foundations of computer science. 410 STUDIES IN ADVANCED MATHEMATICS (3) One section offered each year upon sufficient demand . Course may be repeated with different content (section title). Topics in Advanced Calculus. Implicit function theorems, main theorems in integral calculus. Jacobian transformations , infinite series. Prerequisite: 305. Number Theory. Congruences, Diophantine equations, divisi bility , theorems of Fermat and Wilson , primitive roots , in dices , quadratic reciprocity. Prerequisite: 205 or 295. Topology. Topics from elementary point set topology. Pre requisite: 305 or consent. 420 STUDIES IN HIGHER GEOMETRIES (3) One section offered each year upon sufficient demand. Course may be repeated with different content (section title) . Modem Geometry. Homogeneous projective coordinates, in variants, duality , Desargues 's and Pappus's theorems, trans formations, point and line conics, various axioms systems for Euclidean and non-Euclidean geometry. Prerequisites: 205, 295. Differential Geometry. General curve theory , surfaces in the three-dimensional space, fundamental quadratic forms of a surface; the intrinsic geometry of surfaces, extrinsic properties of surfaces. Prerequisites : 205, 295. 430 STUDIES RELATED TO APPLIED MATHEMATICS (3) One section offered each year upon sufficient demand. Course may be repeated with different content (section title) . Complex Variables. Complex variables, analytic functions, complex integral theorems , power series, conformal map pings. Prerequisite: 205. Mathematics for the Physical Sciences. First order differential equations and second order linear equations, series solutions, Laplace transforms , numerical methods , partial differential equations and Fourier series, boundary value problems and Sturm-Liouville theory. Prerequisite: 296. Topics in Numerical Analysis. Approximate numerical solu tions to partial differential equations, finite difference methods , numerical computations of eigenvectors, error analysis. Prerequisite: 321. Fee: $10. 480 RESEARCH SEMINAR (1-3) Special studies in mathematics. Prerequisite: senior standing or consent.
vector spaces. Prerequisite: 106 or consent. 296 DIFFERENTIAL EQUATIONS (3)
Linear differential equations, power series solutions of differen tial equations, systems of differential equations, Laplace trans forms and numerical methods. Prerequisites: 205, 295 . 300 DATA STRUCTURES (3) Linear lists, strings, arrays and orthogonal lists; graphs, trees, binary trees, multilinked structures, searching and sorting tech niques, dynamic storage allocation; applications. Prerequisite: 202. Fee: $15. 305 ADVANCED CALCULUS (3) The real number system, elementary topological concepts in Cartesian spaces, convergence , continuity, derivatives and inte grals. Prerequisites: 205, 296. 315 MODERN ALGEBRA (3) Introduction to abstract algebra with topics from elementary ring, field and group theories. Emphasis on ring of integers , congru ences, polynomial domains , permutation groups. Prerequisite: 295 or consent. 321 NUMERICAL ANALYSIS (3) Functions of one variable , approximate numerical solutions of non-linear equations and systems of linear equations, interpola tion theory, numerical differentiation and integration , numerical solutions of ordinary differential equations. Prerequisites: 205, 295. Fee: $10. 331 PROBABILITY (3) Sample spaces, axioms and elementary theorems of probability , combinatorics, independence, conditional probability , Bayes' Theorem, one and higher dimensional random variables , discrete and continuous random variables , special and multivariate dis tributions. Prerequisite: 205 or consent. 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, Chi-square tests , decision theory , nonparametric sta tistics; application of statistical methods. Prerequisite: 331 or consent. 333 OPERATIONS RESEARCH (3) Mathematical foundations of model building, optimization , linear programming models , game theoretic models. Pre requisites: 205 and 295. Fee: $10. 341 MANAGEMENT INFORMATION SYSTEMS (3) Information systems, their design, implementation and contribu tion to management planning, decision making and control. Pre requisites: 103 , or 105, 200 . 400 STUDIES IN COMPUTER SCIENCE (3) One section offered each year upon sufficient demand. Course
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