COURSE DESCRIPTIONS
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Chair: Edward Thurber, Ph.D. FACULTY Professor: Thurber Associate Professors: Stangl, Woo Assistant Professor: Seitz OBJECTIVES The Department of Mathematics at Biola University provides several areas of concentration in addition to a basic core curriculum. The student is allowed considerable flexibility in the major, depending upon vocational or professional goals. Our student labs are equipped with numerous Pentium and Apple PowerPC workstations. We also have a Computer Science Alcove equipped with the latest Pentium, Pen tium Pro and Pentium Il platforms run ning either Windows Nr or Linux. The department endeavors to pro vide ( 1) a strong foundational core cur riculum for the student desiring to pur sue graduate study in both the pure and applied fields of mathematical science, (2) course work and training to prepare students for applied mathematical sci ences (statistics, computer science, operations research and actuarial sci ence) and the field of teaching, (3) sup port courses for the curriculum of other majors (biological science, physical sci ence, engineering, business and nurs ing) and ( 4) courses basic to gaining some knowledge of mathematics as part of a liberal arts education. The depart ment provides an attractive and thor ough offering in mathematics as part of God's creation and there is a concerted effort to integrate faith and learning. DEGREE PROGRAM A &didor of Scitna dtgn!t in Malhemal ical Samas is offered upon completion of the university baccalaureate and the math major in one of the emphases. Those who plan to pursue graduate studies should take at lea!it two of 410, 450 or 480 regard less of the area of concentration. MAJORS Applied Math (47 units) Students who are interested in preparing for careers in business or industry should choose this emphasis. Courses introduce a variety of areas of applied mathematics. This emphasis must complete: Math 105, 106,112, 205, 291, 305, 315, 321, 331 , 332, 333, two units of 370, 435 or 440, one course (3 units) at the 300 or 400 level in Math, and Computer Science 105.
120 The Nature of Mathematics (3) Selected topics in mathematics with consideration of historical develop ment and related philosophical issues. Designed to meet the general educa tion requirement in mathematics for libera l arts students. Cannot be counted toward the mathematics major. Fall, spring. 190 Business Statistics (3) Collection and presentation of busi ness data, central tendency and dis persion measures for business analysis, sampling and inference for confi dence intervals and hypothesis testing, business forecasting with simple and multiple regression , index numbers. Prerequisite: consent. Fall, spring. For business majors only. 205 Calculus Ill (4) Functions of two and three variables, partial differentiation , multiple integration, curves and surfaces in three dimensional space. Prerequi site: 106. Fall. 210 Introduction to Probability and Statistics (3) Nature of statistical methods, descrip tion of sample data, fundamental con cepts of probability, probability distri butions, sampling, estimation, correla tion and regression, application of same. Fall, spring. 291 Linear Algebra (3) Topics from matrices, determinants, lin ear transformations and vector spaces. Prerequisite: 106 or consent Fall. 305 Advanced Calculus (3) The real number system, elementary topological concepts in Cartesian spaces, convergence, continuity, deriv atives and integrals. Prerequisite: 112 and 205 or consent. Alternate years. 315 Modem Algebra (3) Introduction to abstract algebra with topics from elementary ring, field and group theories. Emphasis on ring of integers, congruences, polynomial domains, permutation groups. Pre requisite: 112 and 291 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 solutions of ordinary differential equa tions. Prerequisites: 291, Computer Science 105. Alternate years.
Computer Science (53 units)
quadratic equations and inequalities, factoring, fractions, exponents and radicals. Prerequisite: one year of high school algebra. Not counted for general education requirement or toward graduation. Fall. 101 Precalculus Mathematics (3) Sets, the real number system, relations, functions, graphs, algebraic processes, inequalities, trigonometric functions, exponential and logarithmic functions, introduction to sequences. Prerequi site: three years of high school mathe matics or consent. Cannot be counted toward the major. Spring. 102 Topics In Mathematics (1-2) Selected topics in mathematics. Arranged in conjunction with the individual needs of the student Pre requisite: consent 103 calculus tor Management Sciences (3) Fundamental principles of differential and integral calculus. Applications chosen mainly from the management sciences. Prerequisite: passing profi ciency exam administered by Mathe matics Department or receiving a "C" or better grade in Math 90 the prior
This emphasis allows a mathematics major the opportunity to focw on the more mathematical aspects of computer science. This emphasis must complete: Math 105, 106, 112, 205, 291, 305, 315, at least two of 321, 331, 332, 333, two units of 370; Computer Science 105, 106, 202, 400; and three courses (9 units) at the 300 or 400 level in math or computer science. Mathematics (47 units) This emphasis allows the student flexibility in the selection of upper division courses. The student plan ning to pursue mathematics in gradu ate school would find this particularly appropriate. Afaculty advisor will aid the student in making these choices. This emphasis must complete: Math 105, 106, 112, 205, 291, 305, 315, two units of 370; Computer Science 105; and six courses (18 units) in math at the 300 or 400 level. Mathematics Secondary Teaching (59 units) Students who wish to prepare to teach mathematics at the high-school level should select this emphasis . These students work toward a prelimi nary single-subject credential and should consult the Education Depart ment This emphasis must complete: Math 105, 106, 112, 205, 291, 305, 315, 331, 332, 341 , two units of 370, 415, two courses (6 units) at the 300 or 400 level; Computer Science 105, and Education 300, 330, 425, and 435. All concentrations must include 24 upper division units. Noll: The general education requirt mmt for a fomgn language for those fol lowing a mathematical sciences major may be met l,y two years ofhigh school language or the first four units of a rollege language. The science/mathematics requimnent may be met l,y three units of science. MINOR A Mathematical Sciences Minor is offered with the completion of 27 units, six of which must be upper division. Students must consult with a depart ment adviser. The basic curriculum for a minor is 105, 106, 112, 205, 291, two courses (6 units) at the 300 or 400 level and Computer Science 105. COURSES 90 Intermediate Algebra (3) Review of elementary algebra, graphs and polynomials. Study of linear and
year. Fall, spring. 105 Calculus I (4)
Limits, differentiation and integration of rational and trigonometric func tions, with applications. Introduction to use of Mathematica. Prerequisite: four years of high school mathematics
or consent Fall. 106 Calculus II (4)
Differentiation and integration of loga rithmic, exponential and inverse trigono metric functions; various methods of integration; infinite sequences and series; parametric equations, polar coordinates. Prerequisite: 105. Spring. 111 Fundamentals of Mathematics for Elementary Teachers (3) Set theory, relations and functions, number systems and algebraic struc tures, numeration systems, elementary number theory, informal geometry, use of manipulatives. For elementary edu cation majors only. Cannot be counted toward the mathematics major. Fall. 112 Discrete Structures (3) Elementary properties of sets, discrete probability and combinatorial analy sis, graphs, relations, orderings, func tions , simple algebraic structures, binary arithmetic and other bases, methods of proof. Prerequisite: three years of high school mathematics or consent. Spring.
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