MUSIC409 Modern GeometryA course intended to provide a broad survey ofmany different geometries, in particular stressingthe more general notion of non-euclideangeometry. Topics typically include Finite geometries,advanced Euclidean (including higherdimensional) geometry, Spherical geometry,Hyperbolic geometry, Projective geometry, andan introduction to the Topology of Surfaces.Highly recommended for prospective teachersof secondary school mathematics. Prerequisite:Mathematics 252. (Spring <strong>2008</strong>)450 Advanced Topics in MathematicsThis course will explore special topics in mathematics.Prerequisite: Mathematics 252. Maybe repeated with permission of instructor whentopic varies. (Offered on an occasional basis.)460 Advanced Directed Study(Variable course credit)464 Teaching/Learning ParticipationAn individualized study that includes sharingin the instructional process for a particularmath course under the supervision of the facultymember teaching the course. Open only tocertain highly qualified juniors and seniors byinvitation. (Additional details given in the sectionon Other Learning Opportunities.)472 Modern AlgebraA study of the basic abstract algebraic objects(groups, rings and fields, et cetera) and thestructure-preserving maps between them. Prerequisite:Mathematics 252, or permission ofinstructor. (Fall <strong>2007</strong>)473 TopologyAn introductory study typically covering the topologicalproperties of Euclidean spaces, generaltopological spaces, generalized continuity,homeomorphisms, connectedness, compactness,separation properties, and metrization.An introduction to the topology of compactsurfaces may also be included. Prerequisite:Mathematics 252. (Spring 2009)482 Real AnalysisA rigorous study of the calculus of functions of oneand several real variables. Emphasis is placed onthe topology of euclidean spaces, the conceptsof limit and convergence, and a detailed analysisof the corresponding fundamental theorems.Prerequisite: Mathematics 252. (Spring <strong>2008</strong>)483 Complex AnalysisAn introduction to the study of the calculus offunctions of a complex variable. Topics typicallyinclude basic Cauchy theory, analysisof basic holomorphic functions, zeroes andsingularities, Taylor and Laurent series, andresidue theory. Prerequisite: Mathematics 252.(Fall <strong>2008</strong>)490, 491 Independent Study492 Independent StudyOff-Campus/NSOC495 Senior ConferenceMUSICWayne Crannell, chair; DanielDominick, Ricky DuhaimeJennifer Sadoff Auerbach (VisitingInstructor)Robert Archer, Mike Cantwell, BarbaraCase, Michael Lively, Masako Narikawa,Megan Pettitt, Cathy Richardson, SylviaRivers, Heather Thayer, and Mike Walker(Adjuncts)Cecil Isaac and Richard Tappa (Emeritiand Adjunct)Courses in music are designed to provideexperiences with serious music forthe general student as well as the musicmajor or minor. The curriculum fora major in music is intended to preparestudents either for graduate work or, withspecific coursework and in conjunctionwith the Master of Arts in Teaching, forpreparation and certification as a publicschool music educator (see Music EducationTrack below). The major in musicalso may well serve as preparation forvarious immediate occupations and interestsin music and can be successfullycombined with other majors.Individual instruction in piano, organ,voice, strings, winds, brass, percussion,and composition is provided forall music majors and minors and maybe available to other qualified studentsCOURSES OF INSTRUCTION| 123
MUSICwhen faculty are available. Instructionfor beginners is not available. The variousmusical organizations provide additionalopportunity for participation inmusical activity.A major in music requires a minimumof 10 course credit units includingwork in theory, history and literature,and applied music. The followingcourses are required: Music 120, 121,220, 221, 222, 240, 241, at least threeclassroom courses at the 300-level andabove, at least one-half credit in appliedmusic at the 300-level or aboveand Senior Recital (Music 495). Additionalrequirements include the Junior-Level Examination (Music 091) that isrequired for entrance into the major,and Piano Proficiency (Music 090) thatmust be attempted by the end of thejunior year and completed for graduation.A major also requires participationin ensemble music each semester.Membership in any single departmentalperforming group will satisfy therequirement. Pianists are required toparticipate in ensembles but, in specialsituations, may satisfy the requirementthrough supervised accompanying ofvocalists and/or instrumentalists withthe approval of the music faculty. Studentmajors are required to attend aminimum of seven approved concertseach term.Applied music below the 300-level maynot be counted toward credits requiredfor the major in music.Composition Track: Students intendingan emphasis in Theory/Compositionare required to complete the equivalentof four semesters of applied music ona major instrument. Upon successfulcompletion of the Junior-Level Examinationon that instrument, the student beginsprivate composition study and presentsa Senior Recital in composition.Composition students are required tostudy three semesters of applied pianoconcurrently with composition lessons.Theory/Composition students also areexpected to complete Music 271 (CompositionSeminar) before taking privatecomposition lessons, and acceptanceinto the Composition track is contingentupon approval of the Theory/Compositionfaculty. Please consult with the musicfaculty for more information.Music Education Track: Students intendingto pursue the master of arts in teachingdegree through the <strong>Austin</strong> TeacherProgram with an undergraduate major124 |COURSES OF INSTRUCTION