# Biola_Catalog_19850101NA

ability, introduction to statistics, informal geometry. Designed for prospective elementary school teachers and to fulfill liberal arts requirements. Cannot be counted toward the major. Either semes­ ter. 205 INTERMEDIATE CALCULUS (4) Functions of two and three variables, par­ tial differentiation, multiple integration, curves and surfaces in three dimensional space. Prerequisite: I06. 210 INTRODUCTION TO PROBABILITYAND STATISTICS (3) Nature of statistical methods, description of sample data, fundamental concepts of probability, probability distributions, sam­ pling, estimation, correlation and regres­ sion; application of same. Topics from matrices, determinants, linear transformations and vector spaces. Appli­ cation to the theory of ordinary differential equations. Prerequisite: Math I 06 or con­ sent. 298 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, 290 or consent. 305 ADVANCED CALCULUS (3) The real number system, elementary to­ pological concepts in Cartesian spaces, convergence, continuity, derivatives and in­ tegrals. Prerequisites: 298 or consent. 290 LINEAR ALGEBRA WITH DIFFERENTIAL EQUATIONS (3) 315 MODERN ALGEBRA (3) Introduction to abstract algebra with topics from elementary ring, field and group the­ ories. Emphasis on ring of integers, congru­ ences, polynomial domains, permutation groups. Prereq~isite: 298 or consent.

321 NUMERICAL ANALYSIS(3) Functions of one variable, approximate nu­ merical 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, COS IO I . Fee: \$ I 0. 33 I PROBABILITY (3) Sample spaces, axioms and elementary theorems of probability, combinatorics , in­ dependence, conditional probability, Bayes' Theorem, one and higher dimensional ran­ dom variables, discrete and continuous random variables, special and multivariate distributions. 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 statistics; application of sta­ tistical methods. Prerequisite: 331 or con­ sent. 333 OPERATIONS RESEARCH (3) Mathematical foundations of model build­ ing, optimization, linear programmi ng models, game theoretic models. Prerequi­ sites 290, COS IO I . Fee: \$ I 0. 400 DISCRETE STRUCTURES (3) Logical and algebraic structures, combin­ ational mathematics, graph theory. Prereq­ uisites 290, COS IO I . Fee: \$1 0. 410 TOPICS IN ADVANCED CALCU­ LUS (3) Implicit function theorems, main theorems in integral calculus. Jacobian transforma­ tions, infinite series. Prerequisite: 305.

provides an attractive and thorough offer- ing in mathematics as part of God's cre­ ation and there is a concerted effort to in­ tegrate faith and learning. Department Major: All majors are re­ quired to take a core curriculum of I05, I06, 205, 290, 298, 305, 315 and comput­ er science IO I . Various sequences of courses which depend on the area of con­ centration are recommended to complete the requirements. Those who plan to pursue graduate studies should take 410 (Topics in Ad­ vanced Calculus) and 480 (a research semi­ nar) regardless of the area of concentra­ tion. The following course sequences are recommended for: Applied Math (45 total units): 321, 331, 332, 333, one section of 430. Computer Science (48 total units): 333, 400 and two of 321, 331 or 332. Comput­ er science I02 or 202 and two courses in computer science at the 300 level or above. Teaching (45 total units): 331, 332, 415 (Number Theory) and 420 (Modern Ge­ ometry). All concentrations must include 24 up­ per division units. 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. Department Minor: 27 units, six of which must be upper division. Students must consult with department advisor. The basic curriculum for a minor is I05, I06, 205, 290, 298, two courses at the 300 level or above and computer science IO I . I00 INTERMEDIATE ALGEBRA (3) Review of elementary algebra, graphs and polynominals. Study of linear and quadratic equations and inequalities, factoring, frac­ tions, exponents and radicals (semi self­ paced). Prerequisite: one year of high school algebra.

IO I PRECALCULUS MATHEMATICS (3) Sets, the real number system, relations, functions, graphs, algebraic processes, in­ equalities, trigonometric functions, matri­ ces and determinants, complex numbers, exponential and logarithmic functions, in­ troduction to sequenes, probabil ity and statistics. Prerequ isite: three years of high school mathematics or consent. Cannot be counted toward the major. Fundamental principles of differential and integral calculus. Applications chosen main­ ly from the management sciences. Prereq­ uisite: passing proficiency exam adminis­ tered by business department or receiving a "C" or better grade in math I00 the pri­ or year. I03 CALCULUS FOR MANAGEMENT SCIENCES (4) I05 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. I06 ANALYTIC GEOMETRYAND CALCULUS II (4) Differentiation and integration of trigono­ metric, logarithmic and exponential func­ tions, various methods of integration, se­ quences and series, and vectors in the plane. Prerequisite: I05. 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. Pre­ requisite: three years of high school math­ ematics or consent. I IO MATHEMATICS FOR COMPUTER SCIENCE (3)

111 FUNDAMENTALS OF MATHEMATICS (3)

Set theory, relations and functions, number systems and algebraic structures, numera­ tion systems, elementary number theory, mathematical systems, concepts of prob-

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