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 , 33 1. 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 sections of computer science at the 300 level or above. Teaching (45 total units): 331, 332, 410 (Number Theory) and 420 (Modern Ge ometry). All concentrations must include 24 up per division units. 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, I 06, 205, 290, 298, two courses at the 300 level or above and computer science IO I . The general education requir·ement for a foreign language for those followi ng 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. I00 INTERMEDIATE ALGEBRA (3) Review of elementary algebra, graphs and polynominals. Study of linear and quadratic equations and inequalities, factoring, frac tions, exponents and r·adicals (semi self paced). Prerequisite: one year of high school algebra. IO I PRECALCULUS MATHEMATICS (3) Sets, the real number system, relations, fuctions, graphs, algebraic processes, in equalities, trigonometric functions, matri ces and determinants, complex numbers, exponential and logarithmic functions, in
33 1 PROBABILITY (3) Sample spaces, axioms and elementary theorems of probabili t y, combi natorics, 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 STAT IST ICS (3) Estimation: consistency unbiasedness, maximum likelihood, confidence intervals. Testing hypothesis: Type I and II errors, likelihood rat io tests, test fo r means and variances ; regression and correlation , Chi square tests, decision theory, nonparamet ric statistics; application of sta tistical methods. Prerequisite: 331 or con sent. 333 OPERATIO NS RESEARCH (3) Mathematical foundations of mode l build ing, optimizat ion, linear programming models, game theoretic models. Prerequi sites: 205 and 290. Fee: $10. 400 DISCRETE STRUCTURES (3) Logical and algebraic structures, combinator ial mathematics, graph theory. Prerequisite: 205, 290. Fee $ I0.
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 PROBABILITY AND STATISTICS (3) Nature of statist ical methods, description of sample data, fundamental concepts of probability, probability distributions, sam pling, estimation, correlation and regres sion; application of same.
troduction to sequences, probability and statistics. Prerequ isite three years of high school mathematics or consent. Cannot be counted toward the major. I 03 CALCULUS FOR MANAGEMENT SCIENCES (4) Fundamental principles of differential and integral calculus. Applications chosen main ly from the management sciences. Prereq uisite: three years high school mathematics or consent. Proficiency exam administered by the business department. 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 t rigono metric, logarithmic and exponential func tions, various methods of integration, se quences and series, and vectors in the plane. Prerequisite: I05. I IO MATHEMATICS FOR COMPUTER SCIENCE (3) Element ary 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 requisi te: three years of high school math ematics or consent.
290 LINEAR ALGEBRA W ITH DIFFERENTIAL EQUATIONS (3)
Topics from matrices, determinants, linear transformations and vector spaces. Appli cation to the theory of ordinary differential equations. Prerequisite: Math I06 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 , ca r·dinality, algebraic structures and properties of real numbers. Pre~equisite: 205 or consent. 305 ADVANCED CALCULUS (3) The real number system, elementary to pological concepts in Cartesian spaces, convergence, continu ity, derivatives and in tegrals Prerequisites: 205, 290. 315 MODERN ALGEBRA (3) Introduction to abstract algebra with topics from elementary ring, fie ld and group the ories. Emphasis on ring of integers, congru ences, polynomial domains, permutation groups. Prerequisite: 290 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 differentiati on and integration, numerical solutions of ordinary differential equations. Prerequisites: 205, 290. Fee $ 10.
410 STUDIES IN ADVANCED MATHEMATICS(3)
One section offered each year upon suffi cient demand. Course may be repeated with different content (section title). Topics in Advanced Calculus. Implicit func tion theorems, main theorems in integral calculus. Jacobian transformations, infinite series. Prerequ isite: 305. Number Theory. Congruences, Diophant ine equations, divisi bility, theo rems of Fermat and Wilson, primitive roots, indices, quadratic reciprocity. Pre requisite: 205 or 290. Topology. Topics from elementary point set topology. Prerequisite: 305 or consent.
I I I FUNDAMENTALS O F MATHEMATICS (3)
Set theory, relations and functions, number systems and algebraic st ructures, numera tion systems, elementary number theory, mathemat ical systems, concepts of prob abi lity, introduction to statist ics, informal geometry. Designed for prospective elementary school teachers and to fulfill liberal arts requ irements . Cannot be counted toward the maJor Ei ther semes ter.
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