112 Discrete Structures (3) Elcrncnrary properti es of sets, di s c rete probabi lir:y and combinacoria l ,1na lys is, gr::1phs, rclaci ons 1 order in gs, fun c ti ons, simp le a lge brai c s tru ct ures. bina ry a rithrn ct ic a nd mhcr bases, rnerhods of proof. Pre req ui sire: th ree vea rs of high schoo l 111athema ti cs or consent. Spring. 11 7 Fundamentals of Mathematics for Elementary Teachers I (3) Probl e m so l l'i n g, se t th corl', whole nurnbers, nurnber theo rl', inccgc rs 1 rat io na l numbe rs as frac tions, d ecima ls, percents, a nd real nurnb e rs. Use of manipular ives. Fo r e leme n ta ry educat io n maj o rs on ly. Ca nnot be co unted toward the ma th e mati cs major. 11 8 Fundamentals of Mathematics for Elementary Teachers II (3) ln uoducmry geometry, congruence, ,;ymn1crry 1 mea"urcment. a lge bra and coord inate gcomcrry. stat istics, probab ility. l'sc of manipularivcs. For elcmcn ran· e d ucat ion majors only. Cannot be counted coward the mathematics major. 120 The Nature of Mathematics (3) Selected mpics in marhemari cs with cons iderat ion of hi storica l develop m e nt and re lated ph il osophica l iss ues. Dcsig ncd to meet rhe gcn cral education requirement in math e m a ti cs for l ibera l arts swdc n ts. Ca nnot be counte d toward the marhemarics majo r. Fal l, sp ring. 130 Honors Nature of Mathe matics (3) A hi stori ca l, themati c and integra ti ve swd y of the natu re of math e matics using selected topics. Rcad i ngs in p rima ry sou rce ma terial. 1\l a rhcmar ical conte nt in c lud es number t heorv, geo111erri es and con cepts of ca lculus. 1\ lal' be counted toll'ard the 111arhcmarics mino r. Pre requ isite: 10 1 o r cq ui l'a le nt, o r con sem of the instructor. 190 Business Statistics (3) Co llect io n and pr ese ntati o n o f bu s inc ss data, ce ntral tendency a nd di spe rs ion rncas urc s for bu s i ness a n alys is, sa mplin g and infe r e nce for confide nce interva ls a nd hy pothesis rest ing, b us in ess fore casti ng w it h s imple and multipl e regress io n. in dex nu111bers. P re requi s ite: co nse nt. Fall , s pring . Fo r business majors on lv. 205 Calculus 111 (4) Functions o f two and three vari ab le,, part ia l d ifferent iat io n, mul t ip le inrcgra ri o n. cun·cs a nd s ur fa ces in three dim e n s io nal s pace. Prerequisite : 106. Fal l.
210 Introduction to Probability and Statistics (3) Nat ur e of s rari s ric a l meth o d s, d escri ption o f sa mpl e darn. fun da 111 enra l concepts of probabil ity, probability di st ri butions , sa m p ling, es ti111 a ti o n, co rre lat ion a nd reg ress io n , ap pli cat io n of sa m e. Fal l, sp ri ng. 291 Linear Algebra (3) Topi cs fr om matri ces. d ete rmi nan ts, linear tr~tn'=iformar ions and 1·ector spaces . Prerequ is ite: 106 or eonsc nt. Fall. 305 Advanced Calculus (3) Th e rea l numb e r svstem, e lc menrar y w po logical concepts in Cartes ian ,p,1ces. conl'ergenee. co n tin ui ty. dc ri\'at ives and intc gr:d s. Pre req ui s ite: 11 2 and 20.'i o r conse nt. Alternate \'ears. 315 Modern Algebra (3) ln rroducrion t0 a b s tra c t algebra \\'ith wpics from e le m enrar, ring, field and group theories. Emphas is on r ing of integers, cong;rucnccs, pol y norni a l domai ns, perrnu rnrion gro ups. Pn:rcqu is ite : 11 2 and 29 1
341 Classical Geometry (3 ) Th co re m s of P y rhagora ,, ince n te rs, c irc um eenters, c irc les, Euler lin e, F e rm at center . Compa" cons tr uct ions. Sol id geom err,·. Spher ica l geo merr v of arcs. Coo rdinate geornem· . Pre req ui site: Consent. Alternate Yea rs. 370 Readings in Mathematics (1) Reading of mate ri al in a spcc ia l topic. Co ll oqu ium part ic ipat ion. \\ "r icing and oral presentation of a resea rc h p a p e r. Prerequisite: Consent of the departrncnt. ti la, be repeated fo r c red it. 410 Topics in Advanced Calculus (3) Impli cit fu nction rhcorcm,. 111a1n thco rc111s in integral ca lcu lm. Jaco bian tran\formations, infinite scric~. Prerequisite: 305. Alte rnate vc,ir,. 415 Number Theory and the History of Mathematics (3) The hi smrv of mathematic, from Eucl id throug h th e 19th cc nrur, as seen by ex pl oring de, ·e lop ments in nurn bc r rheor, incl udin g co ngr uences , Diophantine e qu a tions. div is ibilitv, theorem, of Fer mat and Wil son, p rimi r i1·e roots, indices, quadratic rcciprocit, and t he distrib ution of prirnc nurnbcrs. P rereq ui s ite: 112. Alternate years. 420 Modern Geometry (3) l'rojccti1 c geo rnetn, era" ratios t h eo rems of :\ l cnclau s. Ccl'a,. Pappw,, Desargues and Brianchon. I l vpcrbo li c a nd ellipt ic geome tries. Diffe rential gcomem·, c ur n1w rc, tors io n. Pre requ isi te : 3-t I o r co nsent. Alte rn ate yea rs. 435 Differential Equations (3) First orde r differe nti a l cqu,1rio n s and seco nd o rd er linear equa tions, se ri es so lution,, Laplace r ran,forrns, nurner ica l met hod,, parti,il d iffe re nti a l equ,1rions and Fourier series. bound:ir, \",due prob lerns and Sturrn-Li o u,· il lc theory. Pre re q uisite: 20.'i, 29 1 o r consent. Alternate years. 440 Complex Variables (3) Com pl ex va riables, analyt ic func ti ons, com pl ex integra l th eorems, p owcr se ri es, co nform a l m ap pings. Prereq ui site : 20.'i or con sen t. i\ltcrnare years. 450 Topics in Abstract Algebra (3) T o pi cs from g roup s, ring and fields. Ga lois t heor,. Prerequ i s ite: 3 1.'i. Alternate ,·ca rs. 480 Research Seminar (1-3) Spec ia l swdi es in m athemat ics. Pre requi site: senior standing or con se nt. ti lay be repeatcd for credit.
co urses (6 units) at th e 300 or -IO0 lcvcl and Computcr Science I05.
COURSES (MATH) 90 Intermediate Algebra (3) Revi e\\ of e lementarY algebra, graphs and polynornials. Swdy of linear and quadrat ic eq uations and inequa liti es, factoring, fra c tions. cxpo ncnt s and ra di ca ls . Prerequisite : one vear of hig h school a lgcbra. Nor counted for ge neral educat ion require rnent o r tow:ird graduat ion. Fall. 101 Precalculus Mathematics (3) Sers. t he rcal nurnbcr syste rn , re la tions, functio ns, grap h s, a lgebraic processes. i ncq ua l i tics. rri go n o rncrric functions. ex ponenti a l a nd logarithrni c functions, introduction to seque nces. Prerequi site: three , ·cars of high schoo l marhernarics or co n,ent. Cannot be co unt e d to\\'ard t he rnajor. Sp ring. 102 Topics in Mathematics (1-2) Topic, in mat he ma t ics se lected from ge neral cclucar ion mathemat ics c lasses. Arra nge d in conjunc tion \\'ith the indi1·idual needs u f rhe st ude nt. l'rc requ isire: co nse nt. 103 Calculus for Management Sciences (3) Fundamental princip les of differ cn ria l and integra l calcul u s. Appl ications chose n rnainly from the manageme nt sc iences. Prc req u isirc: passing proficien cv exam adm ini ste red by tl l arhe macic.:s Departme nt or receiving a "C" or bette r grade in to- l ath 90 the prior year. Fa ll , spr ing. 104 College Algebra (3) Equations. inequalities, sys tems of eq uat ions, functions a nd grap h s, polynorninal and nationa l functions, exponcnr ia l and logari rhrni c func tion,, ,equences and seri es. Pre req uisite: Three ,·cars of hig h sc hool mathematics or c.:onc;;cnc. 105 Calculus I (4) Limits. different iation and integra tio n of rationa l and trigonornerri c function,, " ·irh applica tions. lmro ducr ion to use of I\ lathe matica. Pre rc.:q ui site: fo ur yc.:ars of high school rnar hcmar ics or consem. Fall. 106 Calculus II (4) Differcmiarion and integrat ion of logarithmic , exponent ia l a nd inverse trigonom e tric funct io ns; variou, 111crhods o f int egration; in f inite seq u e n ces an d series; para111erric equa tions. po lar coord i nates . Prerequisite: 105. Sp ring.
or co nsen t. Alterna te years . 321 Numerical Analysis (3)
Functions of one var ia ble, approxi rnar c n11mcrical so luti o n s of non linear equa ti o n s and svsrerns of linear equ atio ns, interpolat io n the o ry. nurnerical diffe rentiation and inrcgrar ion, nu me ri ca l soluti ons of o rdin a ry diffcrcntial e qu atio n s. Pre requi si tes: 29 1. Cornpurcr Sci e nce I0.'i. Altern ate yea rs. 331 Probability (3) Samples s paces, axioms and elc rncn ra ry th eo rems of p ro b ab ility, corn binatori cs, independe nce, con dit ional probab il irv. Baves· Theo rem, o ne and hi g he r dirncmional ra ndom l'ariab les. specia l a nd mu l ri, ·a ri are distr ibu tions. l'rcrcq ui sircs : 11 2. 205 . Alte rnate years. 332 Statistics (3) l·,sr irnat ion: consisrc ncv. unbi ased ncss, rn ax imum likelihood, confi dcncc interva ls . Hvpot hes is- res t in g; ty pe I and Tl e rro rs. like lihood ra tio tcs ts 1 test for means and va ri ances; regress ion and co rre la t ion, Chi-sq uare rests, decision t heo ry. no nparame t ri c sta ti s ti cs; a pplicat ion of stat ist ica l rncthods. Pre re qui site: 33 1 or conse nt. Alternate years. 333 Operations Research (3) :\ l athernatical fo und at ions of rnodel building, up rirni Lat ion, li n ea r programming m ode ls. game rhcoreric rnodcb. Prerequi sites: 105, Com purer Science I05.
80 • Course Descript ion s
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