EIJIIIII COURSE DESCRIPTIONS Department of Mathematical and Computer Sciences
All concentrations must include 24 upper division units. The general educotion requirement far aforeign language far those fallowing amathematicol sciences major may be met by tv.lJ 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. Studentsmust consult wi th department advisor. Thebasic curriculum for aminor is 105, l 06, 205, 290, 298, tv.lJ courses at the 300 level or above and computer science lO l . l 00 INTERMEDIATE AlGEBRA (3) Review of elementary algebra, graphs and polynomials. Study of linear and quadrat ic equations and inequalities, factoring, fractions, exponents and radicols. Prerequisi te: one year of high school algebra. 101 PRECAlCUlUSMATHEMATICS (3) Sets, the real number system, relations, functions, graphs, algebraic processes, inequalities, trigonometric functions, matrices and determinants, complex numbers, exponential and laganthmic functions, introduction ta sequences, probability and stat istics. Prerequisite: three yearsof high school mathemati cs or consent. Cannot be counted toward the major. 103 CAlCUlUSFOR MANAGEMENT SCI ENCES(4) Fundamental principles of differential and integral calculus. Applications chosen mainly from the management sciences. Pre requisite : passing proficiency exam administered by business department or receiving a "C" or better grade in math l 00 the pnar year. 105 ANAlYTIC GEOMETRY AND CAlCUlUS I (4) An introduction taanalytic geometry, differentiation and inte grat ion of polynomial functions, with applications. Prerequisite: four years of high school mathematics or consent. 106 ANAlYTICGEOMETRY AND CAl CU lUSII (4) Differentiation and integration of trigonometric, logarithmic and exponential functions, 111riaus methods of integration, se quences and series, and vectors in the plane. Prerequisite: l 05. l l l FUNDAMENTAlS OFMATHEMATICS (3) Set theory, relations and functions, number systems and algebraic structures, numeration systems, elementary number theory, mathematical systems, conceptsof probability, introduction to statistics, informal geometry. Designed far prospective elementary school teachersand ta fulfill liberal arts requirement s. Cannot be counted toward the major. Either semester. l l 2 DISCRETE STRUCTURES(3) Elementary properties of sets, discrete probability and combinatorial analysis, graphs, relations, orderings, functions, simple algebraic structures, binary arithmetic and other bases, methods of proof. Prerequisite: threeyearsof high school math ematics or consent. 205 INTERMEDIATE CAl CULUS(4) Functions of tv.lJ and three 111riables, partial differentiation, multiple integration, curves and surlaces in three dimensional space. Prerequisite: 106. 210 INTRODUCTION TO PROBABILITY AND STATISTICS (3) Nature of statisticol methods, description of sample data, fundamental concepts of probability, probability distributions, sampling, estimation, correlation and regression; applicotian of same. 291 LIN EAR ALGEBRA (3) Topicsfrom matrices, determinants, linear transformations and vector spaces. Prerequisite: 106 or consent. 298 INTRODUCTION TO MODERN MATHEMATICS (3) Methods of constructing proofs and the logic used in these methods, set theory, relations, functions, cardinality, algebraic structures and properties of real numbers. Prerequisites: 205, 291 or consent.
305 ADVANCED CALCULUS (3) The real number system, elementary topological concepts in Cartesian spaces, convergence, continuity, deri111tives and inte grals. Prerequisite: 298 or consent. 315 MODERN ALGEBRA (3) Introduction ta abstract algebra with topics from elementary ring, field and group theories. Emphasis an ring of integers, congruences, polynomial domains, permutation groups. Prerequi site: 298 or consent. 321 NUMERICALANALYSIS(3) functions of one 111riable, approximatenumerical solutions of non-linear equationsand systemsof linear equations, interpola tion theory, numerical differentiation and integration, numencal solutions of ordina ry differential equations. Prerequisites: 291, COS lOl. Fee: $10. 331 PROBABILITY (3) Sample spaces, axiomsand elementary theorems of probabil ity, combinatancs, independence, conditional probability, Bayes' Theorem, one and higher dimensional random 111riables, discrete and continuous random 111riables, special and multi111riate distri butions. Prerequisites: l l 2, 205. 332 STATISTICS (3) Estimation: consistency unbiasedness, maximum likelihood, confidence inter111ls. Testing hypothesis; Type I and II errors, likel ihood ratio tests, test far means and 111riances; regression and correlation, Chisquare tests, decision theory, nonparametric statis tics; application of statistical methods. Prerequisite: 331 or con sent. 333 OPERATIONS RESEARCH (3) Mathematical founda tions of model building, optimization, linear programming models, game theoretic models. Prerequisi tes: 291, COS 101. Fee $10. 4lOTOPICS IN ADVANCED CALCULUS (3) Implicit function theorems, main theorems in integral colculus. Jacobian transformations, infinite series. Prerequisite: 305. 415 NUMBER THEORY AND THE HISTORY OF MATHEMATICS (3) The history of mathematics from Euclid through the nineteenth century as seen by exploring developments in number theory including congruences, Diophantine equations, divisibility, theo rems of Fermat and Wilson, primitive roots, indices, quadratic reciprocity and the distribution of prime numbers. Prerequisite: 298. 420 MODERN GEOMETRY (3) Homogeneous projective coordinates, in111riants, duality, Desargues's and Pappus's theorems, transformations, paint and line conics, 111riaus axioms systerns far Euclidean and nan Euclidean geometry. Prerequisite: 298. 435 MATHEMATICS FOR THE PHYSICALSCIENCES (3) First order differential equations and second order linear equations, series solutions, Laplace transforms, numerical meth ods, partial differential equations and Fourier series, boundary wive problems and Sturm-liouville theory. Prerequisite: 205, 291 or consent. 440 COMPL EX VARIABLES (3) Complex 111riables, analytic functions, complex integral theo rems, po1Wr series, conformal mappings. Prerequisite: 205 or consent. 450 TOPICS IN ABSTRACT ALGEBRA (3) Topics from groups, rings and fields. Galois theory. Prerequisite: 315. 480 RESEARCH SEMINAR (l-3) Special studies in mathematics. Prerequisite: senior standing or consent.
Edward Thurber, Ph.D., Chair Faculty Professor: Thurber Associate Professors: Stangl, Wolfe Assistant Professors: Converse, Karman Mathematical Sciences
The depar tment of mathematical sciences at Biola University provides several areas of concentra tion in addition to a basic core curriculum. The student is allowed considerable flexibil ity in the major depending upon his vocational or professional goals. The department has available a Digital Equip ment Corporation VAX. 11 /780 computer in addition to twenty Apple lie microcomputers. Objectives: The department endeavors to pro vide (l) astrong foundational core curriculum for the student desiring topursue graduate study in both the pure and applied fields of mathematical science, (2) course work and training to prepare students for applied mathematical sciences (s tatistics, computer science, operations research and actuarial science) and the field of teaching, (3)support courses for the curriculum of other majors (biological science, phys ical science, business and nursing) and (4) courses basic togaining some knowledge of mathematics as part of a liberal arts education. The department provides an attractive and thorough offering in mathematics os part of God 's creation and there is a concerted effort to integrate fa ith and learning. Department Major: All majors are required to toke o core curriculum of 105, 106, 112, 205, 291, 298, 305, 315 ond computer science101. \\Jrious sequences of courses which depend on the area of concentrotion ore recommended ta complete the requirements. Those who plan to pursue groduate studies should take at least tv.lJ of 410, 450 or 480 regardless of the area of concentration. The fallowing course sequences are recommended far: Applied Math (48 total units): 321, 331, 332, 333, one section of 435 ar 440. Computer Science (54 total units): at least tv.lJ of 321,331, 332, 333, computer science l 02, 202, 300, 400, one or tv.lJ courses at the 300 or 400 level in math or computer science if needed. Teaching (48 total units): 331,332,415,420, tv.lJ courses at the 300 or 400 level.
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