Sciences 321, 331 or 333.
290
LINEAR ALGEBRA WITH DIFFERENTIAL
Teaching: 410 (Number Theory), 420 (Modern Geometry).
EQUATIONS (3) Topics from matrices , determinants , linear transformations and vector spaces. Application to the theory of ordinary differential equations. Prerequisite: Math 106 or consent . 305 ADVANCED CALCULUS (3) The real number system, elementary topological concepts in Cartesian spaces, convergence, continuity, derivatives and inte grals. Prerequisites: 205 , 290. 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: 290 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 , 290. 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 di s 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 290. Fee: $ IO. 400 DISCRETE STRUCTURES (3) Logical and algebraic structures, combinatorial mathematics , graph theory. Prerequisite: 205 , 290 . Fee: $10. 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 290. Topology. Topics from elementary point set topology. Pre requisite: 305 or consent.
Department Minor: 27 units , six of which must be upper divi sion . Students must consult with department advisor. The basic curriculum for a minor is 105, 106 , 205, 290, computer science IO I, one of computer science 202 or 210 and two 300 or 400 level courses. The general education requirement for a foreign language for those following a mathematical sciences major may be met by two years of high school language or the first four units of a college language. The science/ mathematics requirement may be met by three units of science. 100 INTERMEDIATE ALGEBRA (3) Review of elementary algebra , graphs and polynominals. Study of linear and quadratic equations and inequalities , factoring , fractions, exponents and radicals (semi se lf-paced). Prerequisite: one year of high school algebra. IOI PRECALCULUS MATHEMATICS (3) Sets , the real number system , relation s, functions , graphs , alge braic processes, inequalities, trigonometric functions , matrices and determinants, complex numbers, exponential and logarith mic functions, introduction to sequences, probability and statis tics . Prerequisite: three years of high school mathematics or consent. Cannot be counted toward the major. 103 CALCULUS FOR MANAGEMENT SCIENCES (4) Fundamental principles of differenti al and integral calculus. Applications chosen mainly from the management sciences. Pre requisite: three years high school mathematics or consent. 105 ANALYTIC GEOMETRY AND CALCULUS I (4) An introduction to analytic geometry , differentiation and integration of polynomial functions, with applications. Pre requisite: four years of high school mathematics or consent . 106 ANALYTIC GEOMETRY AND CALCULUS II (4) Differentiation and integration of trigonometric, logarithmic and exponential function s, various methods of integration , sequences and series, and vectors in the plane. Prerequisite: I 05. 1 IO MATHEMATICS FOR COMPUTER SCIENCE (3) Elementary properties of sets , discrete probability and com binatorial 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 . 111 FUNDAMENTALS OF MATHEMATICS (3) Set theory , relations and functions, number systems and alge braic structures , numeration systems, elementary number theory , mathematical systems, concepts of probability , introduction to statistics, informal geometry. Designed for prospective elementary school teachers and to fulfill liberal arts requirements. Cannot be counted toward the major. Either semester. (4) Functions of two and three variables , pa11ial differentiation , multiple integration , curves and surfaces in three dimensional space. Prerequisite: 106. 205 INTERMEDIATE CALCULUS
210
INTRODUCTION TO PROBABIUTY AND
STATISTICS (3) Nature of statistical methods , description of sample data , fun damental concepts of probability , probability distributions , sam pling, estimation, correlation and regression ; application of same.
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