Graduate and Postdoctoral
Studies 2008-09
Studies 2008-09
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Graduate and Postdoctoral Studies 2008-09 |
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47 Mathematics and Statistics
Department of Mathematics and Statistics
Burnside Hall, Room 1005
805 Sherbrooke Street West
Montreal, QC H3A 2K6
CanadaTelephone: (514) 398-3800
Fax: (514) 398-3899
E-mail: grad.mathstat@mcgill.ca
Website: www.math.mcgill.caChair
David Wolfson
Graduate Program DirectorGeorg Schmidt
47.1 Staff
Emeritus Professors
Michael Barr; A.B., Ph.D.(Penn.) (Peter Redpath Emeritus Professor of Pure Mathematics)
Marta Bunge; M.A., Ph.D.(Penn.)
Jal R. Choksi; B.A.(Cant.), Ph.D.(Manc.)
Joachim Lambek; M.Sc., Ph.D.(McG.), F.R.S.C. (Peter Redpath Emeritus Professor of Pure Mathematics)
Sherwin Maslowe; B.Sc.(Wayne St.), M.Sc., Ph.D.(Calif.)
Arak M. Mathai; M.Sc.(Kerala), M.A., Ph.D.(Tor.)
William O.J. Moser; B.Sc.(Man.), M.A.(Minn.), Ph.D.(Tor.)
Vanamamalai Seshadri; B.Sc, M.Sc.(Madr.), Ph.D.(Okl.)
George P.H. Styan; M.A., Ph.D.(Col.)
John C. Taylor; B.Sc.(Acad.), M.A.(Qu.), Ph.D.(McM.)
Professors
William J. Anderson; B.Eng., Ph.D.(McG.)
William G.Brown; B.A.(Tor.), M.A.(Col.), Ph.D.(Tor.)
Henri Darmon; B.Sc.(McG.), Ph.D.(Harv.), F.R.S.C. (James McGill Professor)
Stephen W. Drury; M.A., Ph.D.(Cant.)
Kohur N. GowriSankaran; B.A., M.A.(Madr.), Ph.D.(Bom.)
Pengfei Guan; B.Sc.(Zhejiang), M.Sc., Ph.D.(Princ.) (Canada Research Chair)
Jacques C. Hurtubise; B.Sc.(Montr.), D.Phil.(Oxf.) F.R.S.C.
Vojkan Jaksic; B.S.(Belgrade), Ph.D.(Cal. Tech.)
Niky Kamran; B.Sc., M.Sc.(Bruxelles), Ph.D.(Wat.), F.R.S.C. (James McGill Professor)
Olga Kharlampovich; M.A.(Ural St.), Ph.D.(Lenin.), Dr. of Sc., (Steklov Inst.)
Michael Makkai; M.A., Ph.D.(Bud.) (Peter Redpath Professor of Pure Mathematics)
Alexei Miasnikov; M.Sc.(Novosibirsk), Ph.D., Dr. of Sc.(Lenin.) (Canada Research Chair)
Charles Roth; M.Sc.(McG.), Ph.D.(Hebrew)
Karl Peter Russell; Vor. Dip.(Hamburg), Ph.D.(Calif.)
Georg Schmidt; B.Sc.(Natal), M.Sc.(S.A.), Ph.D.(Stan.)
F. Bruce Shepherd; B.Sc.(Vic.,Tor.), M.Sc., Ph.D.(Wat.) (James McGill Professor)
David A. Stephens; B.Sc., Ph.D.(Nott.)
John A. Toth; B.Sc., M.Sc.(McM.), Ph.D.(MIT) (William Dawson Scholar)
David Wolfson; B.Sc., M.Sc.(Natal), Ph.D.(Purd.)
Keith J. Worsley; B.Sc., M.Sc., Ph.D.(Auck.), F.R.S.C. (James McGill Professor)
Jian-Ju Xu; B.Sc., M.Sc.(Beijing), M.Sc., Ph.D.(Renss.)
Associate Professors
Masoud Asgharian; B.Sc.(Shahid Beheshti), M.Sc., Ph.D.(McG)
Peter Bartello; B.Sc.(Tor.), M.Sc., Ph.D.(McG.) (joint appt. with Atmospheric and Oceanic Sciences)
Eyal Z. Goren; B.A., M.S., Ph.D.(Hebrew)
Antony R. Humphries; B.A., M.A.(Cant.), Ph.D.(Bath)
Dmitry Jakobson; B.Sc.(MIT), Ph.D.(Princ.) (William Dawson Scholar)
Wilbur Jonsson; M.Sc.(Man.), Dr.Rer.Nat.(Tübingen)
Ivo Klemes; B.Sc.(Tor.), Ph.D.(Cal.Tech.)
James G. Loveys; B.A.(St. Mary's), M.Sc., Ph.D.(S. Fraser)
Neville G.F. Sancho; B.Sc., Ph.D.(Belf.)
Alain Vandal; B.Sc., M.Sc.(McG.), Ph.D.(Auck.)
Daniel T. Wise; B.A.(Yeshiva), Ph.D.(Princ.)
Assistant Professors
Nilima Nigam; B.Sc.(IIT, Bom.), M.S., Ph.D.(Delaware)
Russell Steele; B.S., M.S.(Carn. Mell), Ph.D.(Wash.)
Paul Tupper; B.Sc.(S. Fraser), Ph.D.(Stan.)
A. Vetta; B.Sc., M.Sc.(LSE), Ph.D.(MIT) (joint appt. with SOCS)
Thomas P. Wihler; M.S., Ph.D.(ETH)
Associate Members
Xiao-Wen Chang (Computer Science), Luc P. Devroye (Computer Science), Pierre R.L. Dutilleul (Plant Science), Leon Glass (Physiology), Jean-Louis Goffin (Management), James A. Hanley (Epidemiology & Biostatistics), Lawrence Joseph (Epidemiology & Biostatistics), Michael Mackey (Physiology), Lawrence A. Mysak (AOS), Christopher Paige (Computer Science), Prakash Panangaden (Computer Science), Robert Platt (Epidemiology & Biostatistics), James O. Ramsay (Psychology), Peter Swain (Physiology), George Alexander Whitmore (Management), Christina Wolfson (Epidemiology & Biostatistics)
Adjunct Professors
Donald A. Dawson; Martin Gander; Andrew Granville; Ming Mei; Ram Murty; Vladimir Remeslennikov; Robert A. Seely
Faculty Lecturers
José Correa; Axel Hundemer
47.2 Programs Offered
The Department of Mathematics and Statistics offers programs which can be focused on applied mathematics, pure mathematics and statistics leading to Masters degrees (M.A. or M.Sc.), as well as M.Sc, program options in Bioinformatics and in CSE (Computational Science and Engineering). In the basic Masters programs students must choose between the thesis option and the non-thesis option, which requires a project. The Bioinformatics and CSE Options require a thesis. In addition to the Ph.D. Program in Mathematics and Statistics, there is a Ph.D. option in Bioinformatics.
The department Website (www.math.mcgill.ca) provides extensive information on the department and its facilities, including the research activities and the research interests of individual faculty members. It also provides detailed information, supplementary to the calendar, concerning our programs, admissions, funding of graduate students, thesis requirements, advice concerning the choice of courses, etc.
Students are urged to consult the Website (www.math.uqam.ca/ISM) of the Institut des Sciences Mathématiques (ISM), which coordinates intermediate and advanced level graduate courses among Montreal and Quebec universities. A list of courses available under the ISM auspices can be obtained from the ISM Website. The ISM also offers fellowships and promotes a variety of joint academic activities greatly enhancing the mathematical environment in Montreal and in the province of Quebec.
47.3 Admission Requirements
In addition to the general Graduate and Postdoctoral Studies Office requirements, the Department requirements are as follows:
Master's Degree
The normal entrance requirement for the Master's programs is a Canadian Honours degree or its equivalent, with high standing, in mathematics, or a closely related discipline in the case of applicants intending to concentrate in statistics or applied mathematics.
Applicants wishing to concentrate in pure mathematics should have a strong background in linear algebra, abstract algebra, and real and complex analysis.
Applicants wishing to concentrate in statistics should have a strong background in linear algebra and basic real analysis. A calculus based course in probability and one in statistics are required, as well as some knowledge of computer programming. Some knowledge of numerical analysis and optimization is desirable.
Applicants wishing to concentrate in applied mathematics should have a strong background in most of the areas of linear algebra, analysis, differential equations, discrete mathematics and numerical analysis. Some knowledge of computer programming is also desirable.
Students whose preparation is insufficient for the program they wish to enter may, exceptionally, be admitted to a Qualifying Year.
Ph.D. Degree
A Master's degree with high standing is required, in addition to the requirements listed above for the Masters program. Students may transfer directly from the Masters program to the Ph.D. program under certain conditions. Students without a Master's degree, but with exceptionally strong undergraduate training, may be admitted directly to Ph.D. 1.
47.4 Application Procedures
Online application is preferred and is available at www.mcgill.ca/applying/online. Applicants unable to apply online can request a paper or PDF form from the department.
Applications will be considered upon receipt of:
1. application form;
2. $80 application fee;
3. two official or certified copies of transcripts;
4. two letters of reference on letterhead with original signatures;
5. one page statement outlining research interests and identifying possible supervisor;
6. TOEFL/IELTS test results (if applicable);
7. applicants in pure and applied mathematics should provide a GRE score report, if available.
For more details, especially concerning items 6 and 7, please consult the Website at www.math.mcgill.ca/students/grad_app.php#necessarybackground.
All information is to be submitted directly to the Graduate Program Secretary in the Department of Mathematics and Statistics.
Deadline:
Applicants are urged to submit complete applications by March 1 for September admission, or by July 1 for January admission.
McGill's online application form for graduate program candidates is available at www.mcgill.ca/applying/graduate.
47.5 Program Requirements
M.A. in Mathematics and Statistics (Non-Thesis)
(45 credits)
or
M.Sc. in Mathematics and Statistics (Non-Thesis)(45 credits)
Complementary Courses
(minimum 29 credits)
At least 8 approved graduate courses, at the 500 level or above, of 3 or more credits each.
Project Component - Required (16 credits)
MATH 640
(8)
Project 1
MATH 641
(8)
Project 2
M.A. in Mathematics and Statistics (Thesis)
(45 credits)
or
M.Sc. in Mathematics and Statistics (Thesis)(45 credits)
Complementary Courses
(minimum 21 credits)
M.Sc. in Mathematics and Statistics (Thesis) - Bioinformatics (48 credits)
Required Course
(3 credits)
M.Sc. in Mathematics and Statistics (Thesis) - Computational Science and Engineering (CSE) (47 credits)
Required Course
(1 credit)Complementary Courses
(minimum 22 credits)Ph.D. Degree in Mathematics and Statistics
Complementary Courses
Ph.D. in Mathematics and Statistics - Bioinformatics
Students will meet the Ph.D. degree requirements of the Department of Mathematics and Statistics and the following requirements for the option.
Required Course
(3 credits)
47.6 Courses
Students preparing to register should consult the Web at www.mcgill.ca/minerva (click Class Schedule) for the most up-to-date list of courses available; courses may have been added, rescheduled or cancelled after this Calendar went to press. Class Schedule lists courses by term and includes days, times, locations, and names of instructors.
Approximately 15 of the 600- and 700-level courses will be given.
Term(s) offered (Fall, Winter, Summer) may appear after the credit weight to indicate when a course would normally be taught. Please check Class Schedule to confirm this information.
Notes:
All undergraduate courses administered by the Faculty of Science (courses at the 100- to 500-level) have limited enrolment. With the permission of the instructor, prerequisites and corequisites for courses may be waived in individual cases.The course credit weight is given in parentheses after the title.
H Denotes courses taught only in alternate years.
MATH 523 Generalized Linear Models.
(4) (Winter) (Prerequisite: MATH 423 or EPIB 697.) (Restriction: Not open to students who have taken MATH 426.) Modern discrete data analysis. Exponential families, orthogonality, link functions. Inference and model selection using analysis of deviance. Shrinkage (Bayesian, frequentist viewpoints). Smoothing. Residuals. Quasi-likelihood. Sliced inverse regression. Continency tables: logistic regression, log-linear models. Censored data. Applications to current problems in medicine, biological and physical sciences. GLIM, S, software.
MATH 524 Nonparametric Statistics.
(4) (Fall) (Prerequisite: MATH 324 or equivalent.) (Restriction: Not open to students who have taken MATH 424.) Distribution free procedures for 2-sample problem: Wilcoxon rank sum, Siegel-Tukey, Smirnov tests. Shift model: power and estimation. Single sample procedures: Sign, Wilcoxon signed rank tests. Nonparametric ANOVA: Kruskal-Wallis, Friedman tests. Association: Spearman's rank correlation, Kendall's tau. Goodness of fit: Pearson's chi-square, likelihood ratio, Kolmogorov-Smirnov tests. Statistical software packages used.
MATH 525 Sampling Theory and Applications.
(4) (Winter) (Prerequisite: MATH 324 or equivalent.) (Restriction: Not open to students who have taken MATH 425.) Simple random sampling, domains, ratio and regression estimators, superpopulation models, stratified sampling, optimal stratification, cluster sampling, sampling with unequal probabilities, multistage sampling, complex surveys, nonresponse.
MATH 533 Honours Regression and Analysis of Variance.
(4) (Prerequisites: MATH 357, MATH 247 or MATH 251.) (Restriction: Not open to have taken or are taking MATH 423.) (Note: An additional project or projects assigned by the instructor that require a more detailed treatment of the major results and concepts covered in MATH 423.) This course consists of the lectures of MATH 423 but will be assessed at the 500 level.
H
MATH 550 Combinatorics.
(4) (Intended primarily for honours and graduate students in mathematics.) (Restriction: Permission of instructor.) Enumerative combinatorics: inclusion-exclusion, generating functions, partitions, lattices and Moebius inversion. Extremal combinatorics: Ramsey theory, Turan's theorem, Dilworth's theorem and extremal set theory. Graph theory: planarity and colouring. Applications of combinatorics.
MATH 552 Combinatorial Optimization.
(4) (Prerequisite: MATH 350 or COMP 362 (or equivalent).) (Restriction: Not open to students who have taken or are taking COMP 552.) Algorithmic and structural approaches in combinatorial optimization with a focus upon theory and applications. Topics include: polyhedral methods, network optimization, the ellipsoid method, graph algorithms, matroid theory and submodular functions.
H
MATH 555 Fluid Dynamics.
(4) (Fall) (Prerequisite (Undergraduate): MATH 315 and MATH 319 or equivalent.) Kinematics. Dynamics of general fluids. Inviscid fluids, Navier-Stokes equations. Exact solutions of Navier-Stokes equations. Low and high Reynolds number flow.
MATH 556 Mathematical Statistics 1.
(4) (Fall) (Prerequisite: MATH 357 or equivalent.) Probability and distribution theory (univariate and multivariate). Exponential families. Laws of large numbers and central limit theorem.
MATH 557 Mathematical Statistics 2.
(4) (Winter) (Prerequisite: MATH 556) Sampling theory (including large-sample theory). Likelihood functions and information matrices. Hypothesis testing, estimation theory. Regression and correlation theory.
MATH 560 Optimization.
(4) (Prerequisite: Undergraduate background in analysis and linear algebra, with instructor's approval.) Classical optimization in n variables. Convex sets and functions, optimality conditions for single-objective and multi-objective nonlinear optimization problems with and without constraints. Duality theories and their economic interpretations. Optimization with functionals. Connections with calculus of variations and optimal control. Stability of mathematical models. Selected numerical methods.
MATH 564 Advanced Real Analysis 1.
(4) (Fall) (Prerequisites: MATH 354, MATH 355 or equivalents.) Review of theory of measure and integration; product measures, Fubini's theorem; Lp spaces; basic principles of Banach spaces; Riesz representation theorem for C(X); Hilbert spaces; part of the material of MATH 565 may be covered as well.
MATH 565 Advanced Real Analysis 2.
(4) (Winter) (Prerequisite: MATH 564) Continuation of topics from MATH 564. Signed measures, Hahn and Jordan decompositions. Radon-Nikodym theorems, complex measures, differentiation in Rn, Fourier series and integrals, additional topics.
MATH 566 Advanced Complex Analysis.
(4) (Winter) (Prerequisites: MATH 366 (formerly MATH 466), MATH 564.) Simple connectivity, use of logarithms; argument, conservation of domain and maximum principles; analytic continuation, monodromy theorem; conformal mapping; normal families, Riemann mapping theorem; harmonic functions, Dirichlet problem; introduction to functions of several complex variables.
MATH 570 Higher Algebra 1.
(4) (Fall) (Prerequisite: MATH 371 or equivalent.) Review of group theory; free groups and free products of groups. Sylow theorems. The category of R-modules; chain conditions, tensor products, flat, projective and injective modules. Basic commutative algebra; prime ideals and localization, Hilbert Nullstellensatz, integral extensions. Dedekind domains. Part of the material of MATH 571 may be covered as well.
MATH 571 Higher Algebra 2.
(4) (Winter) (Prerequisites: MATH 570 or consent of instructor.) Completion of the topics of MATH 570. Rudiments of algebraic number theory. A deeper study of field extensions; Galois theory, separable and regular extensions. Semi-simple rings and modules. Representations of finite groups.
H
MATH 574 Dynamical Systems.
(4) (Winter) (Prerequisites: MATH 325 and MATH 354 or permission of the instructor.) Dynamical systems, phase space, limit sets. Review of linear systems. Stability. Liapunov functions. Stable manifold and Hartman-Grobman theorems. Local bifurcations, Hopf bifurcations, global bifurcations. Poincare Sections. Quadratic maps: chaos, symbolic dynamics, topological conjugacy. Sarkovskii's theorem, periodic doubling route to chaos. Smale Horseshoe.
MATH 575 Intermediate Partial Differential Equations.
(4) (Prerequisite: MATH 375) A continuation of topics introduced in MATH 375.
MATH 576 Geometry and Topology 1.
(4) (Fall) (Prerequisite: MATH 354) Basic point-set topology, including connectedness, compactness, product spaces, separation axioms, metric spaces. The fundamental group and covering spaces. Simplicial complexes. Singular and simplicial homology. Part of the material of MATH 577 may be covered as well.
MATH 577 Geometry and Topology 2.
(4) (Winter) (Prerequisite: MATH 576) Continuation of the topics of MATH 576. Manifolds and differential forms. De Rham's theorem. Riemannian geometry. Connections and curvatures 2-Manifolds and imbedded surfaces.
MATH 578 Numerical Analysis 1.
(4) (Fall) (Prerequisites: MATH 247 or MATH 251; and MATH 387; or permission of the instructor.) Development, analysis and effective use of numerical methods to solve problems arising in applications. Topics include direct and iterative methods for the solution of linear equations (including preconditioning), eigenvalue problems, interpolation, approximation, quadrature, solution of nonlinear systems.
MATH 579 Numerical Differential Equations.
(4) (Winter) (Prerequisites: MATH 375 and MATH 387 or permission of the instructor.) Numerical solution of initial and boundary value problems in science and engineering: ordinary differential equations; partial differential equations of elliptic, parabolic and hyperbolic type. Topics include Runge Kutta and linear multistep methods, adaptivity, finite elements, finite differences, finite volumes, spectral methods.
MATH 580 Applied Partial Differential Equations 1.
(4) (Fall) (Prerequisites: MATH 316, MATH 375 or equivalent.) (Restrictions: Not open to students who have taken MATH 586.) Linear and nonlinear partial differential equations of applied mathematics. Uniqueness, regularity, well posedeness and classification for elliptic, parabolic and hyperbolic equations. Method of characteristics, conservation laws, shocks. Fundamental solutions, weak and strong maximum principles, representation formulae, Green's functions.
MATH 581 Applied Partial Differential Equations 2.
(4) (Winter) (Prerequisite: MATH 580.) Continuation of topics from MATH 580. Transform methods. Weak solutions. Advanced topics in partial differential equations.
MATH 587 Advanced Probability Theory 1.
(4) (Fall) (Prerequisite: MATH 356 or equivalent and approval of instructor.) Probability spaces. Random variables and their expectations. Convergence of random variables in Lp. Independence and conditional expectation. Introduction to Martingales. Limit theorems including Kolmogorov's Strong Law of Large Numbers.
MATH 589 Advanced Probability Theory 2.
(4) (Winter) (Prerequisites: MATH 587 or equivalent.) Characteristic functions: elementary properties, inversion formula, uniqueness, convolution and continuity theorems. Weak convergence. Central limit theorem. Additional topic(s) chosen (at discretion of instructor) from: Martingale Theory; Brownian motion, stochastic calculus.
H
MATH 590 Advanced Set Theory.
(4) (Prerequisites: MATH 318, either MATH 355 or MATH 371, or permission of the intructor.) (Restriction: Not open to students who have taken or are taking MATH 488.) Students will attend the lectures and fulfill all the requirements of MATH 488. In addition, they will study an advanced topic agreed on with the instructor. Topics may be chosen from combinatorial set theory, Goedel's constructible sets, forcing, large cardinals.
H
MATH 591 Mathematical Logic 1.
(4) (Winter) (Prerequisites: MATH 488 or equivalent or consent of instructor.) Propositional logic and first order logic, completeness, compactness and Löwenheim-Skolem theorems. Introduction to axiomatic set theory. Some of the following topics: introduction to model theory, Herbrand's and Gentzen's theories, Lindström's characterization of first order logic.
H
MATH 592 Mathematical Logic 2.
(4) (Winter) (Prerequisites: MATH 488 or equivalent or consent of instructor.) Introduction to recursion theory; recursively enumerable sets, relative recursiveness. Incompleteness, undecidability and undefinability theorems of Gödel, Church, Rosser and Tarski. Some of the following topics: Turing degrees, Friedberg-Muchnik theorem, decidable and undecidable theories.
MATH 600 Master's Thesis Research 1.
(6) (Restriction: Not open to students who have taken or are taking MATH 640.) Thesis research under supervision.
MATH 601 Master's Thesis Research 2.
(6) Thesis research under supervision.
MATH 604 Master's Thesis Research 3.
(6) Thesis research under supervision.
MATH 605 Master's Thesis Research 4.
(6) Thesis research under supervision.
MATH 606 Algebraic Topology.
(4) (Prerequisite: MATH 577) Homology and Cohomology theories. Duality theorems. Higher homotopy groups.
MATH 626 Advanced Group Theory 1.
(4) The structure of groups. Special classes of groups. Representation theory. Additional topics to suit the class.
MATH 627 Advanced Group Theory 2.
(4) A continuation of the topics listed in the description of MATH 626.
MATH 635 Functional Analysis 1.
(4) (Prerequisite: MATH 564, MATH 565, and MATH 566.) Banach spaces. Hilbert spaces and linear operators on these. Spectral theory. Banach algebras. A brief introduction to locally convex spaces.
MATH 640 Project 1.
(8) (Restriction: Not open to students who have taken or are taking MATH 600.) Project research under supervision.
MATH 641 Project 2.
(8) Project research under supervision.
MATH 651 Asymptotic Expansion and Perturbation Methods.
(4) Asymptotic series. Summation. Asymptotic estimation of integrals. Regular and singular perturbation problems and asymptotic solution of differential equations.
MATH 666 Seminar Mathematics and Statistics 1.
(2) (Restriction: Departmental approval required.) Study on an advanced topic in mathematics or statistics.
MATH 667 Seminar Mathematics and Statistics 2.
(2) (Restriction: Departmental approval required.) Study on an advanced topic in mathematics or statistics.
MATH 690 Reading Course in Number Theory.
(4) A highly specialized study.
MATH 669D1 (0.5), MATH 669D2 (0.5) CSE Seminar.
(Restriction: This seminar course is open only to students who were admitted to the CSE Program Option.) (No credit will be given for this course unless both MATH 669D1 and MATH 669D2 are successfully completed in consecutive terms) (Students must register for both MATH 669D1 and MATH 669D2) Techniques and applications in computational science and engineering.
MATH 669N1 CSE Seminar.
(0.5) (Restriction: This seminar course is open only to students who were admitted to the CSE Program Option.) (Students must also register for MATH 669N2) (No credit will be given for this course unless both MATH 669N1 and MATH 669N2 are successfully completed in a twelve month period) Techniques and applications in computational science and engineering.
MATH 669N2 CSE Seminar.
(0.5) (Prerequisite: MATH 669N1) (No credit will be given for this course unless both MATH 669N1 and MATH 669N2 are successfully completed in a twelve month period) See MATH 669N1 for course description.
MATH 671 Applied Stochastic Processes.
(4) Discrete parameter Markov chains, including branching processes and random walks. Limit theorems and ergodic properties of Markov chains. Continuous parameter Markov chains, including birth and death process. Topics selected from the following areas: renewal processes, Brownian motion, statistical inference for stochastic processes.
MATH 674 Experimental Design.
(4) Review of one-way and two-way analyses of variance; randomized block, Latin square and incomplete block designs; factorial designs, confounding, fractional replications; random and mixed models; split-plot designs; nested and hierarchical designs; response surface analysis. Weighted least squares. Analysis of variance with equal and unequal numbers in cells. Latin squares, complete factorial designs. Prediction and confidence bands, multiple comparisons. Random effects models.
MATH 678 Applied Statistical Methods 1.
(4) Statistical data analysis, with special reference to applications of the main statistical methods to problems in medicine, biology, chemistry, etc. Extensive use of computer methods, especially subroutine packages for statistical data description, display and analysis.
MATH 680 Computation Intensive Statistics.
(4) (Prerequisites: MATH 556, MATH 557 or permission of instructor.) (Restriction: Not open to students who have taken or are taking EPIB 680) Introduction to a statistical computing language, such as S-PLUS; random number generation and simulations; EM algorithm; bootstrap, cross-validation and other resampling schemes; Gibbs sampler. Other topics: numerical methods ; importance sampling; permutation tests.
MATH 681 Time Series Analysis.
(4) Stationary stochastic processes. Autocovariance and autocovariance generating functions. The periodogram. Model estimation. Likelihood function. Estimation for autoregressive moving average and mixed processes. Computer simulation; diagnostic checking, tests with residuals. Estimation of spectral density; Bartlett, Daniell, Blackman-Tukey spectral windows. Asymptotic moments of spectral estimates.
MATH 685D1 (2), MATH 685D2 (2) Statistical Consulting.
(Prerequisites: MATH 423, MATH 523, MATH 556, MATH 557. Equivalents may be substituted at instructor's discretion) (Password required) (Students must register for both MATH 685D1 and MATH 685D2) (No credit will be given for this course unless both MATH 685D1 and MATH 685D2 are successfully completed in consecutive terms) Statistical consultation skills; overview of widely used statistical techniques; understanding the client's problem; suggesting designs and statistical analyses; performing statistical analyses; communicating with clients orally and in writing. Format: Simulated and real consultations with clients.
MATH 686 Survival Analysis.
(4) (Prerequisites: MATH 556, MATH 557 or permission of instructor.) (Restriction: Not open to students who have taken or are taking EPIB 686.) Parametric survival models. Nonparametric analysis: Kaplan-Meier estimator and its properties. Covariates with emphasis on Cox's proportional hazards model. Marginal and partial likelihood. Logrank tests. Residual analysis. Homework assignments a mixture of theory and applications. In-class discussion of data tests.
MATH 687 Reading Course in Mathematical Logic.
(4) A highly specialized study.
MATH 689 Reading Course in Algebra.
(4) A highly specialized study.
MATH 690 Reading Course in Number Theory.
(4) A highly specialized study.
MATH 691 Reading Course in Geometry/Topology.
(4) A highly specialized study.
MATH 693 Reading Course in Analysis.
(4) A highly specialized study.
MATH 695 Reading Course in Applied Mathematics.
(4) A highly specialized study.
MATH 697 Reading Course in Statistics.
(4) A highly specialized study.
MATH 698 Reading Course in Probability.
(4) A highly specialized study.
MATH 699 Reading Course in Discrete Mathematics.
(4) A highly specialized study.
MATH 700 Ph.D. Preliminary Examination Part A.
(0)
MATH 701 Ph.D. Preliminary Examination Part B.
(0)
MATH 704 Topics in Mathematical Logic.
(4)
MATH 706 Topics in Geometry and Topology 1.
(4)
MATH 707 Topics in Geometry and Topology 2.
(4)
MATH 720 Topics in Algebra 1.
(4) This course covers an advanced topic in some branch of algebra.
MATH 721 Topics in Algebra 2.
(4) This course covers an advanced topic in some branch of algebra.
MATH 722 Topics in Algebraic Geometry.
(4) This course covers an advanced topic in some branch of algebra.
MATH 723 Topics in Group Theory.
(4) This course covers an advanced topic in some branch of algebra.
MATH 726 Topics in Number Theory.
(4) This course covers an advanced topic in number theory.
MATH 727 Topics in Arithmetic Geometry.
(4) This course covers an advanced topic in number theory.
MATH 740 Topics in Analysis 1.
(4) This course covers an advanced topic in some branch of analysis.
MATH 741 Topics in Analysis 2.
(4) This course covers an advanced topic in some branch of analysis.
MATH 742 Topics in Mathematical Physics.
(4) This course covers an advanced topic in some branch of analysis.
MATH 743 Topics in Microlocal Analysis.
(4) This course covers an advanced topic in some branch of analysis.
MATH 744 Topics in Spectral Theory.
(4) This course covers an advanced topic in some branch of analysis.
MATH 756 Topics in Optimization.
(4) This course covers an advanced topic in Optimization.
MATH 758 Topics in Discrete Mathematics.
(4) This course covers an advanced topic in Optimization.
MATH 761 Topics in Applied Mathematics 1.
(4) This course covers an advanced topic in applied mathematics.
MATH 762 Topics in Applied Mathematics 2.
(4) This course covers an advanced topic in applied mathematics.
MATH 763 Topics in Differential Equations.
(4) This course covers an advanced topic in applied mathematics.
MATH 764 Topics in Partial Differential Equations.
(4) This course covers an advanced topic in applied mathematics.
MATH 765 Topics in Numerical Analysis.
(4) This course covers an advanced topic in applied mathematics.
MATH 782 Topics in Statistics 1.
(4) This course covers an advanced topic.
MATH 783 Topics in Statistics 2.
(4) This course covers an advanced topic.
MATH 784 Topics in Probability.
(4) This course covers an advanced topic.
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