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Image 192 of University of Kentucky Catalog, Vol. 63, No. 4, 1971-1972

Part of University of Kentucky course catalogs, 1865-

371 Foundations of Mathematics. (3) 501-SO2 Seminar in Selected Topics. (3 ea.) Set theory including cardinal numbers, ordered sets, and ordinal Various topics from the basic graduate courses. Designed as s. course l numbers. Prereq; MA 213 or equivalent. for teachers of lower division mathematics and usually offered in ` connection with a summer institute. May bc repeated once. Prereq: , Problem Seyninmy €g_) Teaching experience in the field of mathematics and consent of in- é lleports on current research papers. Problems from various fields of structon mathematics. Prereq: Consent of instructor. Discrete , l71(l€f)C71Cl€71l lx/OTl< in Mdlll€mdllCS. C21.) fample sp;§e, combinaforial methods, cognbinlatiotn of evients, lawsiof i . Y . .. . . _ argc num ers, norma approximanon 0 e moima generating . SONS? umgcg gil/Aslgjn Sgudfxi (gt hlgh smndmg Prereq' functions, convolutions, random walks, branching processes, recurrent ‘ dl ‘m il S an 1 g 0 ' ' I E €p‘ E ‘ events. (Same as STA 524.) Prereq: MA 432 or 471 or consent of | i · ` t t . -l·Zl lglcnzeutary l\lumerzcal l\Iet/zods. (3) ms mc °r l I Outline nf capabilities. andf llllllliltliifli 0; lthe CDI'l;}[;lllC€:‘·. Fumber Theory Of Statistical Inference ·····' ··i · ‘ * .. . ‘ i *8- .. .. . ripHMm`ml)ll' .Pmp`m"l1O" ?,.("0m_t nin}? nlm qn· mt lm iopu _ Sample space, concept of probability, conditional probability, random { tions. AppIm.1t¤ons of analysis to trror estimation. Linear ant non _ , _ _ _ _ , i- · .,- , - · , -. _ I ,, variables, dens1ty and distribution functions, mathematical expecta- , umir crnuitum solving. Matrix cngcnxalues. (This course could stru t_ _ t t_ f t, _ f t, f d ri bl _ 4 as an introduction both for the specialist and the non-specialist.) lm? mclmen genera lng, unclonsi uncfcns Q ¥an,°m Ya ades’ , (Sumo M CS 421.) I,l_(_wq: MA ZM or equivalent. limit laws, usual distributions, certain derived distnbutmns, intro uc- ` tion to estimation and hypothesis testing. (Same as STA 531.) . , Prereq: MA 432 or 471 or consent of instructor. i 423 Introductory ProlJabzl1ty. (3) Set theory; fundamental concepts of probability, including conditional Ordiiiary Differeiitial Equations. l and marginal probability; random variables and probability distribu- S _ __ _ d I _ h f tions (discrete and continuous); expected values and moments; uiccsslved "Pp"°"“““t’°"€ ““ E ;’l“6lm“'Yb ixlslmceft °‘{"fl"S or moment-generating and characteristic functions; random experiments; im mj an fv?°F°?rl €¤¤=§z¢¤ll<¢ l’$’n2?r$3s,Z$§’.§¥mlOS *Z.?`v§l?£)1Z2?”Sy§2;i "ZIES€£If§E§..“£?€r€Z§T“i?X Elementary complex variable theory with applications. Complex Held, 532 and MA 472 or equivalent. analytic functions, Cauchy theorum, power series, residue theory. Prereq: MA 432 or 471. V · ector and Tensor Analysis. ( 3) ~ Gcoiiictr 3 The algebra and calculus of vectors, cartesian tensors, curvilinear A · 4 _ y _ _ _ ( > coordinates, Christol·l`el symbols, determinants, exterior forms, integra- ‘ ‘ Euclidean, affine, proiective spaces, and the classical groups. Prereq: Hom Prereq: MA 214_ j MA 362 or equivalent. j 536 Operational Calculus and Generalized ++2 Geometry II (3) i » ‘ ' '7 I Selected topics chosen from among: hyperbolic geometries, spherical _ Functlonsx _ _ (D) i and elliptical geometries, differential geometry, geometric inequalities, T€$U¤§_ f¤¤¤¤0¤$j diE€¤'€¤ti¤ti0¤ imd i¤t€g1'6U0¤ of d1$U”ib¤¤0¤5 OY ` circular transfomiations, manifolds and differential manifolds. Prereq: generalized fl-m¢U0¤$§ COHVOIUUOHSS Fourier and I-·¤·P1a€€ ¤'9·¤$f0m"*$§ ` IMA 441 0; consent gf jnsu-uctm; applications to linear differential equations. Prereq: MA 432 or 481. ' 462 A Iatrxx /\nalys1s. (3) 538 Elementary Numerical Analysis. (3) Vectors, matrices, vcctor—valucd and matrix-valued functions, differ- Interpolation. Gaussian quadrature, orthogonal polynomials. Richard- ‘ cntiation, integration, Jacohians, Wronskians, inversion of matrices, son process. Numerical treatment of ordinary differential equations · eigenvalues, matrices of special forms, inner product spaces and tensors. and intermediate linear algebra. Linear difference equations. Prereq: Prereq: MA 214 or equivalent. MA 421. (Same as CS 538.) ` +71 Aclvancccl Calculus I. (3) $51 Topology 1. (3) The first half of a year sequencevwhieh urill cover the standard topics General topology, separation axioms, normal spaces, connectedness and of uniformity, integrals and derivatives m n—space, St0kes’ theorem, eompactness. Prereq: Consent of instructor. and selected other topics. Prereq: MA 214 and 351 or equivalent. $61 Modem Algebra I (3) V Q +/2 ‘/j\dv(}nCcd Calculus ()) Algebraic structures, quotient structures, substructures, product struc- é A continuation of MA 471. Prereq: MA 471 or consent of instructor. tures, groups, permutation groups, groups with operators, and the I ' _ _ _ ]0rdan-Holder theorum. Prereq: Consent of instructor. i 481 Drffcrentzal Igquatzons. (3) 6 L_ Al b 3 Brief review of linear differential equations and matrix algebra, S 5 lnear ge Ta· ( ) , eigenvalues and eigenvectors of matrices, systems of linear differential Fields, vector spaces, rings of linear transformations, matrices as- _ equations with constant coefficients, applications, Sturm separation sociated with linear transformations, dual spaces, eigenvectors, canon- and comparison theorems, Sturm-Liouville theory for second-order ical forms, adjoint matrices, and tensor products. Prereq: MA 214 l equations and applications. Prereq: MA 214 or equivalent. OT €ql1iV¤l€¤f· i 482 Discrete Methods and Xloclels in Applied $66 Theory of Numbem (3) ~ ~ D'·‘ 'l'l‘t , ' b , . d 'd D' b t' A l¢ll’ll€Il1(ll’ICS, c(;;:t‘i;];·Y EEIECEQS 0f¤?:§;3;;¤(;2:S 'ln rest ues, iop an me Probability on finite sample spaces, combinatorial mathematics, Hnitc ‘ Marker chains, linear programrning. tlicorx of games. Prereq: MA 214 A/Iulfjvgrjgfg Cg[Culug_ i or (lqumllmh (sdmv as S YA 48'“‘ CS 48"") A self-contained course in n-dimensional analysis, including the general j _ , , form of Stokes’ theorem. Prereq: MA 432 or equivalent. . —lS> Fourier Serres and Boundary Value Problems. (3) 1, An introductory treatment of Fourier series and its application to A71(1l}’SlS i_ the solution of boundary value problems in the partial differential This ennrse is designed fer ndvnneed undergraduates and beginning l l"l“¤U0“$ vf Dh>'$¤C$ Fmd <‘“g¤¤¤¤"“K· O*'*h¤S0¤¤l $@5 of functwns. graduate students. Topics include metric spaces, metric space topology, i Fourier scrics andiintcgrals, solution. of boundary value problems, continuous functions on mgtrig spaces, Ascglfs thggrumr Stone- theory and application of Bcsscl functions and Legendre polynomials. Wpierstmgg theorum and Riemann-Stieltjes integration. Prereq: MA (Same as EM 585.) Prereq: MA 432 or equivalent. 471 or equivalgnh ` il 188 { il

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