2005/2006 - Registrar - McMaster University

244 MATHE,MATlCSAND STATISTICS'MATH 2U03 TEACHING MATHEMATICSMATH 3H03* 'NUMBER THEORY, " ,I. ''This course is designed to give a maximum 01.20 students practical ' Selected topics from: congruence and residues', continued fractions,experience with teachi'ng methods in mathematics. The course also providesan introduction to mathematics writing and development of communicationapproximation of irrationals" arithmetic. in 'selected quadratic numberfields. Diophantine equations, partitions, geometry of numbers, quad~skills relevant to mathematics. " ratic reciprocity.Two lectures' a'nd one practic'um; one term'Three lectures; one term'Prerequisite: A grade of A~ in both MATH1A03 and 1AA3 or in ARTS&SCI , Prerequisite: Credit ,in at/east 12 units of Levell"Matti~ematics'or Statistics1DQ6; and permission of the instructor. Applications mustbesubmitt~dto the instructor by May 1 of the academic year prior tQ registration, with, MATH 3103,' PARTIAL DIFFERENTIALEQUATIONS FOR ENGINEERINGselection for' placements announced by September 9.See the heading Limited Enrolment Courses in the! Faculty of Science ,Topicsin partial differential equ'ationsof interestto mechanical, materialand ceramic engineering, including the wave equation, the heat diffusions$ction of the Calendar. ' , ,equation and Laplace equation" in various co-ordinate systems.Enrolment is limited.Three lectures; first termMATH 3A03 REAL ANALYSIS IPrerequisite: MATH 2M06; or MATH 2P04 and 2Q04; or registration' in 'nie realnumber system, metric spaces, compactness, sequences and Level III or IV of a program in the Department·of Materials Science and, Engineering , ' ','series, continuity; differentiabili~y, the Riemann~Stieltjes integral, uniformconvergence.Three lectures; one termPrerequisite: MATH 2AB3,2C03, 2ROS"MATH 3K03 ENGINEERING MATHEM.ATICS III,Complex variable theory ,with applications', to. eiectrical and computerengineering.'MATH'3AA3 'REAL ANALYSIS IIThree lectures; 'one term'Equicontinuousfunctions, ,functions of several variables, the inversePrerequisite: MATH 2P04,' 2Q04, Antirequisite: MATH 3003function theorem, the implicit function theorem, the rank theorem, Stokes'Theorem, the Lebesgue 'integral.' MATH '3N03 " MATHEMATICAL BIOLOGYThree lectures; one termPopqlation dynamics:' models of discrete and continuous growth; competitionand predation; epidemic models., Partial differential equations: diffu~Prerequisite:' MATH 3A03s,ion and pattern formation in biological settings. Biological oscillators.MATH 3B03 GEOMETRYThree lectures; one termSelected topics from: affine and proJective 'geometry, Euclidean, spherical,Prerequisite: MATH 2Eq3, 3F03and hyperbolic g,eometry, differential geometry of curves and surfaces.,Three lectures; one te,rm'MATH 3Q03 NUMERICAL ANALYSIS IIPrerequisite: MATH 2A03, 2R03Interpolation and approximation, numerical integration and differe~tiation,solution of ordinary differential equation systems, partial differential equatioris"study .of stiffness and stability.MATH 3C03 MA niEMATICAL PHYSICS iLinear algebra and eigenvalue problems; partial differential equations, Three lectures; one termorthogonal functions, Fourier' series, Legendre functions,spherical Prerequisite: MATH 2A03, 2T03harmonics. i ' ,,' ,Antirequisite: MATH 4Q03 , " ' 'Three lectures; orie term MATH 3S03 SET THEORY AND GENERAL TOPOLOGYPrerequisite:'MATH 2A03 or2Q04; and MATH 2C03 or 2P04. One of .Naive set theory, Zorn's Lemma, metric spaces, point set topblogy., PHYSICS 2BO~, 2003 ()r 2K03 is recomme'nded. Three lectures; one term 'Not open to students with credit or'registration in MA TH 3FF3 or creditin MATH. 3J04. " \ ' , 'Prerequisite: MATH 2R03MATH 3D03 MATHEMATICAL PHYSICS II MATH'3X03 '" COMPLEX ANALYSIS I ,. f' I . bl b b'I' ' d '..' b ' " Analytic functions, Cauchy',s,theorem, Cauc,hy'sintegral,formula, residues,F unctions 0 a camp ex varia e, pro.a, IIty" an statistics, oun, dary' zeroes of analytic functions;' Laurentseri~s, the maximum principle.value problems, Bessel functions. ' 'Three lectures; one termThree lectures; one term'Prerequisite: MATH3C03P "t MATH 2AB3 2C03 2R03rereqUisl e:. " , ,MATH 3Z03 ,INQUIRY: HISTORY OF MATHEMATICSAntirequisite: MATH 3K03 ", An introduction to the history-bfmathematics, including interaction with otherNot open to students with creditor registration in MA TH 3X030r cr,edit in ,phases, 0, f culture, With special emph" as is, ,on the past three centuries.MATH 3J04.' ' "Three lectures; one term'Not open to students registered in Honours Mathematics and Physics., flrerequisite: At leasttwo Level II Mathl?matics or·Statistics courses other 'MATH 3E03 ALGEBRA I , than MATH 2K03, 2L03' " 'An introduction to group theory, including Sylow theorems and structure ,', Enrolmentls limited.. Seethe heading Limited EnfolmentC,ourses in t1;reof finitely generated Abelian groups; applications of group theory. . Facultyiof Science section ofthe Calendar. \' "Three lectures; one term " , MATH 4B03 ' CALCULUS ON MANIFOLDS , ,Prerequ,isite: MATH 2R03 ' Review of"multivariable calculus, basic properties "of inanifolds~ differen~MATH 3EE3 ALGEBRA II ' , tialforms, Stokes' theorem, de Rham cohomology and applications:, Topics in ring and module theory, in particular principal ideal 'domains, ,Three hours; one term ' ,unique factorization domains, "Euclidean rings; field theory and Galois Prerequisite: MATH 3C03; or MATH2S03 and e!ther MATH 2AA3 or2AB3theory. ' ,Three lectures; one term MATH 4C03* COMBINATORICSPrerequisite: MATH 3E03Inversion formulae, systems of distinct representatives, block designsMATH 3F03 ADVANCED DIFFERENTIAL ,EQUATIONS and other configurations; and other topics.-Systems of ordinary, differential equations; autonomous systems in the Three lectures; one termPrerequisite: MATH2A03, 2R03'plane, phase portraits,linear systems, stability, Lyapunov's method, MATH 4E03 ALGEBRA IIIPoiricare-Bendixson theorem, applications. :Three lectures; oneferm ,Selected topics in algebra, such' as an 'introduction to algebraic, numberPrerequisite: MATH 2A03;and MATH 2C03 or 2P04; and credit orrE3gistrationin MATH 2R03 ' ,Three lectures; one 'termttieory, commutative algebra o( algebraic geometry. ,; .MATH3FF3 ' PARTIAL DIFFERENTIAL EQUATIONS IPrerequisite: MATH 3EE3 ,First order equations, well-posed ness, ,characteri~tics, wave equation, MATH 4G03 DYNAMICAL SYSTEMSheat equation, Laplace equation, boundaryconditions,Fourier series,applications.Three lectures; one term ' ,Prerequisite: MATH 2A03,2C03, 2B03\ 'ITopics to be ~elected from ordinarydifferentiaJ equations theory; bifurcationand stability theory.'Three lectures; one term, PrElrequisite:MATH 3F03. MATH3A03 is recommended.