~ COURSE DESCRIPTIONS Department of Mathematical and Computer Sciences
All concentrotions must include 24 upper div1sron units. The general educolion requirement for a foreign language for those following o malhemalrcol sciences major may be mel by I\\IJ years al high school language or the first four units of a college language. The science/malhem □ IICS requirement may be mel by three units of science. Departmen t Minor: 27 units, six of wh1Ch must be upper division. Students must consult with deparlmenl advisor. The basic curriculum for omrnor Is 105,106,205,290,298, I\\IJ courses ol the 300 level or above and computer science I Ol. 100 INTERMEDIATE AlGEBRA '3) Review of elementary algebra, graphs and polynomials. Study of linear ond quadratic equallons and inequahlres, faclorrng, fractions, exponents and radicals. Prerequisite: one year of high school algebra. IOI PRECAlCULUS MATHEMATICS (31 Sets, the reol number system, relo11ons, functions, graphs, algebraic processes, rnequohties, lrigonomelric funcl1ons, matrices ond delerm1nonts, complex numbers, exponenliol ond logar1thm1C functions, rnlrodue11on lo sequences, probobility ond slal1stics. Prerequisite three years of high school molhemal1cs or consent. Cannot be counted toward the moIor. I 03 CAlCUlUS FOR MANAGEMENT SCIENCES 4 fundomenlol prrnc1ples of ditterenl1ol ond integral colculus. Applications chosen mornly from the manogemenl sciences. Pre requIsIte: possrng prof1crency exam odm1nistered by business deparlmenl or receiving o "C" or belier grade in moth 100 the prior year. I05 ANAlYTIC GEOMETRY AND CALCULUS I '4 An 1ntroduclron lo onolyt1c geometry, ditterenlmtion and inle gralian al polynomial functions, with applicatmns. Prerequisrte: four years of high school ma thematics or consenl. 106 ANAlYTIC GEOMETRY AND CAlCUlUS II ·4 Ditterent1al1on ond integration of lrrgonomelrrc, logor1lhm1c and exponential functions, various methods of rntegralion, se quences and series, and vectors in the plane Prerequisite: I05. 111 fUNDAMENTAlS Of MATHEMATICS 13\ Set theory, relations ond funcl1ons, number systems and olgebroic slruclures, numeration systems, elementary number theory, mathematical systems, concepts of probability, introduction lo stolrstics, informal geometry. Desrgned for prospeclrve elementary school teachers ond to fulfill liberal arts requirements. Cannot be counted toward the maIor. Either semester. 112 DISCRETE STRUCTURES 3 Elementary propertres of sets, discrete probability and combinatorml analysis, graphs, relolmns, orderings, functions, simple olgebra1C structures, b1nory arithmetic ond 01he1 bases, methods of proof Prerequisite three years of high school moth emolIcs or consenl. 205 INTERMEDIATE CAlCUlUS (4 functions of I\\IJ ond three variables, partial ditteren11ation, multiple integrol1on, curves and surioces in three dimensional space. Prerequisite: 106. 210 INTRODUCTION TO PROBABlllTY ANDSTATISTICS (3) Nature of stot1st1cal methods, description of sample dolo, fundamental concepts of probability, probability distrrbutians, sampling, estImolion, correlation and regressmn; application of some. 291 llNEAR ALGEBRA ,3) Topics from molrrces, determinants, linear tronsformolions and vector spaces. Prerequisite: 106 or consent 298 INTRODUCTION TO MODERN MATHEMATICS '31 Methods of constructing proofs and the logic used rn these methods, set theory, relations, functions, cardinality, algebraic structures and properties of real numbers. Prerequisites: 205, 291 or consent.
305 ADVANCED CALCULUS (3) The reol number system, elementary topological concepts In Cartesian spaces, convergence, continuity, derivatives and inte grals. Prerequisite: 298 or consent. 315 MODERN ALGEBRA (31 Introduction to abstract algebra with topics from elementary rrng, field and group lheorres. Emphasis on rrng of integers, congruences, polynomial domrnns, permutation groups. Prerequi site: 298 or consenl. 321 NUMERICAL ANALYSIS (3) functions of one variable, opproxirnote numerical solutrons of non-linear equations ond systems of linear equolmns, inlerpolo tion theory, numerical ditterentiotmn and integration, numerrcal solutrons of ordinary differential equations. Prerequisites: 291, COS 101. fee SID. 331 PROBABILITY )) Sample spaces, axioms ond elementary theorems of probabil ity, combinotorrcs, independence, conditional probability, Boyes' Theorem, one ond higher dimensional random variables, discrete ond continuous random variables, special ond multivarrate distri butions. Prerequisites: 112, 205. 332 STATISTICS (3; Estimation: consrstency unbiasedness, maximum lrkelihood, confidence intervals. Testing hypothesis; Type I and II errors, likelihood rolio lesls, tesl for means and variances; regression and correlation, Chisquore tests, decision theory, nonporamelrIc stolis llCS; application of statistical methods. Prerequisite: 331 or con sent 333 OPERATIONS RESEARCH (3) Mathematical foundations of model building, opt1m11olion, linear programming models, game theoretic models. Prerequisites: 291, COS IOI fee SIO. 410 TOPICS IN ADVANCED CALCULUS '3\ Implicit function theorems, morn theorems rn rntegral calculus. Jacobian transformations, rnf1nite 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, pr1mil1ve roots, indices, quadratic reciprocity and the distribution of prrme numbers. Prerequisite: 298. 420 MODERN GEOMETRY '.3) Homogeneous proIective coordinates, invar1onts, duality, Desorgues's and Poppus's theorems, lransformotions, pornt and lrne conics, various axioms syslerns for Euclidean and non Euclidean geometry. Prerequisite: 298. 435 MATHEMATICS FOR THE PHYSICAL SCIENCES (3) first order differential equations and second order linear equations, serres solu11ons, Laplace transforms, numerical meth ods, partial ditterenliol equations and Fourier serres, boundary value problems and Sturm-liouville theory. Prerequisite 205, 291 or consent. 440 COMPLEX VARIABLES (3' Complex variables, analytic funclmns, complex integral theo rems, power serres, conformal mappings. Prerequisite: 205 or consent 450 TOPICS IN ABSTRACT ALGEBRA 3) Topics from groups, rings and frelds. Galors theory Prerequ1s1le: 315. 480 RESEARCH SEMINAR (1-3) Special studies in mathematics. Prerequ1s1te: senior standing or consent,
Edward Thurber, Ph.D, Chair Faculty Professor: Thurber Associate Professors: Stangl, Wolfe Assistant Professor: Converse Mathematical Sciences
The department of mathematical sciences ot Biola Uni versity provides several areas of concentra ti on in addition to a basic core curricu lum. The student is allowed considerable fl exibi lity in the major depending upon his vocational or professional goals The department has available aDigital Equip ment Corpora tion VAX 111780 computer in addition toApp le li e, Macintosh and1MB PCmicrocomputers. Objectives: The department endeavors ta pro vide (1) astrong foundational core curriculum for the student desiring to pursue graduate study in boththe pureand applied fields of mathematicol science, (2) course work and training to prepare students for applied mathematical sciences (statistics, computer science, operations research and actuarial science) and thefield of teaching, (3) support courses for the curriculum of other majors (biological science, phys ical science, business end nursing) and (4) courses basic togaining some knowledge of mathematics as par t of a liberal arts educat ion. The department provides an attractive and thorough offering in mathematics as por t of God's creation andthereis a concerted effort to integrate foi th and learning. Department Ma jor: All majors are required to lake acore curriculum of 105, 106,112,205,291,298,305,315 ond computer science 101. Vanous sequences of courses which depend on the areo of concenlralion are recommended lo complete the requirements. Those who plan to pursue groduole studies should toke at leasI I\\IJ of 410, 450 or 480 regardless of the areo of concentration. The following course sequences are recommended for: Applied Moth •48 lotol units): 321, 331, 332, 333, one section of 435 or 440, plus one course ot 300 or 400 level if needed Computer Science (54 lolal units\: al least I\\IJ of 321,331, 332, 333, computer soence I02, 202, 300, 400, one or I\\IJ courses ol the 300 or 400 level in moth or computer science if needed. Teaching (48 total units)· 331,332,415,420, I\\IJ courses ol the 300 or 400 level.
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