COURSE DESCRIPTIONS
112 Discrete Structures (3) Elememary propenies of sets, discrete probab ility and combinatoria l analy- sis, graphs, relations, orderings, func- tions, simple algebraic structures, binary arithmetic and other bases, methods of proof. Prerequisite: three years of high sc hool mathematics or consent. Spring. 120 The Nature of Mathematics (3) Selected topics in mathematics with consideration of historical develop- mem and related philosophi cal issues. Designed Lo meet the general educa- tion requirement in mathematics fo r liberal arts students. Cannot be counted toward the mathematics major. Fall, spring. 131 Classical Algebra and Geometry (3) Cubic and quartic equations, inequali- ties, complex roots of unity, plane geomeuy of conics and constructions, coordinate geometq•of two and three dimension s, advanced trigonometric ident ities, infinite series and conver- gence, binomial ser ies, symmetric fun ctions. Focus is on theory and prob lem-solving techniques. Prereq- uisite: four years of high school math or consent. Fall. 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, busi ness forecasti ng with simple and mu ltiple regression , index numbers. Prerequisite: consent. Fall , spr ing. For business majors only. 205 Intermediate Calculus (4) Functions of two and three variables, partial differentiation , mult iple integration , curves and surfaces in three dimensional space. Prerequi- site: I06. Fall. 21 OIntroduction to Probability and Statistics (3) Nature of stati stical methods, descrip- tion of sample data, fundamental con- cepts of probabi lity, probabili ty distr i- butions, sampling, estimation, correla- tion and regress ion, app lication of same. Fall, spring. 291 Linear Algebra (3) Topics from mau·ices, dete1minants, lin- ear u·ansformations and vector spaces. Prerequisite: I06 or consent. Fall. 305 Advanced Calculus (3) The real number system, elementary topo log ica l conce pts in Ca rtes ian
spaces, convergence, continuity, deriv- atives and integrals. Prerequisite: 112 and 205 or consent. Alternate years. 315 Modern Algebra (3) lmroduction to abstract algebra with topics from elemema, 1• ring, field and group theories. Emphasis on ring of intege rs , co ngruenc es, pol ynomia l domains, permut ation groups. Pre- requi site: 112 and 291 or consent. Alternate years. 321 Numerical Ana lysis (3) Functions of one var iable, approxi- mate numerical solutions of non-li n- ear equations and systems of li near equations, int erpolat ion theory, numerical differentiation and imegra- tion, numerical solutions of ordina1y differential equations. Prerequisites: 291, Computer Science I05. Alter- nate yea rs. 331 Probability (3) Samples spaces, axioms and elementa1y theorems of probabili ty, combinatorics, independence, conditional probability, Bayes ' Theorem, one and higher dimensional random variables, special and multivariate disu-ibutions. Prereq- uisites: 112, 205. Alternate years. 332 Statistics (3) Estimation: consistency, unbiasedness, maximum likelihood , confidence intervals. Hypothesis-testing; type I and II errors, likelihood ratio tests, test fo r mea ns and variances; regres- sion and correlation , Chi-square tests, decision 1heo1y, nonparametric statis- tics; application of stati stical methods. Prerequisite: 33 1 or consent. Alter- nate years. 333 Operations Research (3) Mathematical foundat ions of mode l bui lding , optimization, linea r pro- gramming models , game theoret ic mode ls. Cross listed with Computer Science 325. Prerequisites: l 05, Com- puter Science 105. 410 Topics in Advanced Calculus (3) Implicit function th eorems, main the- orems in in tegral calculus. Jacobian transformations, infi nite seri es. Pre- requisite: 305. Alte rn ate years. 415 Number Theory and the History of Mathematics (3) The history of mathemat ics from Eucl id through the 19th century as seen by exp loring developments in numbe r theo ry includ in g congru- ences, Diophanti ne equations, divis i- bili ty, th eorems of Fermat and Wilson, primitive roo ts, indices, quadra tic reci-
procity and the distribution of prime numbers . Prerequisite: 112. Alter- nate yea rs. 420 Modern Geometry (3) Homogeneous projective coordinates invariants, duality, Desargues's and Pappus's theorems, transformations, point and line conics, various axioms systems for Euclidean and non-Eucl id- ean geometry. Prerequisite: 112 or
Lions and Four ier se ries , bo undary value problems and Sturm-Liouville theoq'. Prerequisite : 205, 291 or con- sent. Alternate years. 440 Complex Variables (3) Complex variables, analytic functions , complex integra l theorems, power series, conformal mappings. Prerequi- site: 205 or consent. Alternate years. 450 Topics in Abstract Algebra (3) Topics from groups, ring and fie lds. Ga lois theor y. Prerequisite: 315. Alternate years. 480 Research Seminar (1-3) Special stud ies in mathematics. Pre- requisite: sen ior standing or consent.
consent. Alternate years. 435 Mathematics fo r the Physical Sciences (3)
First order differential equations and second order li near equations, series solutions, Laplace transforms, numeri- ca l methods, partial differential equa-
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