# Course Offerings

## 3000-level Courses

AS/SC/AK/MATH3010.03W Vector Integral Calculus

1995-95 York Calendar: Integrability of continuous functions over suitable domains, iterated integrals and Fubini's theorem, counterexamples, change of variables, Jacobian determinants, polar and spherical coordinates, volumes, vector fields, divergence, curl, line and surface integrals, Green's and Stokes' theorems, differential forms, general Stokes' theorem.

Prerequisite: AS/SC/MATH2010.03; or AS/SC/AK/ MATH2310.03; or AS/SC/MATH2015.03 and written permission of the Mathematics Undergraduate Director (normally granted only to students proceeding in Honours programmes in Mathematics or in the Specialized Honours Programme in Statistics)

Corequisite: (or prerequisite) AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03.

Degree credit exclusion: AS/SC/MATH3310.03.

Coordinator: N. Purzitsky

AS/SC/AK/MATH3020.06 Algebra I

1995-95 York Calendar: Introduction to the basic concepts of abstract algebra, with applications: groups (cyclic, symmetric, Lagrange's theorem, quotients, homomorphism theorems); rings (congruences, quotients, polynomials, integral domains, principal-ideal and unique-factorization domains); fields (field extensions, constructions with ruler and compass, coding theory).

Algebra is the study of algebraic systems, that is, sets of elements endowed with certain operations. A familiar example is the set of integers with the operations of addition and multiplication.

Algebra is used in almost every branch of mathematics; indeed it has simplified the study of mathematics by indicating connections between seemingly unrelated topics. In addition the success of the methods of algebra in unravelling the structure of complicated systems has led to its use in many fields outside of mathematics.

One aim of this course is to help students learn to write clear and concise proofs, read the mathematical literature, and communicate mathematical ideas effectively, both orally and in writing.

Any student having the prerequisite is, of course, welcome, but THIS COURSE IS INTENDED PRIMARILY FOR STUDENTS WHO HAVE TAKEN THE HONOURS VERSIONS OF FIRST AND SECOND YEAR COURSES.

The text has not yet been chosen.

The final grade breakdown has not yet been determined.

Prerequisite: AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03.

Degree credit exclusion: AK/MATH3420.06

Coordinator: J.W. Pelletier

AS/SC/MATH3033.03F Classical Regression Analysis

1995-95 York Calendar: General linear model. Properties and geometry of least-squares estimation. General linear hypothesis, confidence regions and intervals. Multicollinearity. Relationship between ANOVA models and linear models. Residual analysis, outliers, partial and added variable plots.

This course is closely linked with MATH3034.03W, Modern Regression Analysis, for which it is a prerequisite. The emphasis, in contrast to MATH3330.03 and MATH3230.03, will be a more mathematical development of linear models including modern regression techniques. To develop a solid knowledge of regression models, it is strongly advised that you take both MATH3033.03 and MATH3034.03.

Students will use the computer for some exercises. No previous courses in computing are required. The statistical software package SPLUS in a UNIX enrivonment will be used and instructions will be given in class.

The text is R. H. Myers ed., Classical and Modern Regression with Applications (Duxbury).

The final grade may be based (in each term) on assignments, quizzes, a project, one midterm, and a final examination.

Prerequisites: prerequisites{AS/SC/MATH1132.03 , or an average of B or higher in AS/SC/AK/MATH2560.03 and AS/SC/AK/MATH2570.03; AS/SC/MATH2022.03 or AS/SC/AK/MATH2222.03.

Corequisite: AS/SC/AK/MATH3131.03 or permission of the course coordinator.

Degree credit exclusion: AS/SC/MATH3330.03, AS/SC/ GEOG3421.03, AS/SC/PSYC3030.06, AK/GEOG4200.06, AK/PSYC3110.03.

AS/SC/MATH3034.03W Modern Regression Analysis

1995-95 York Calendar: Selecting best model, cross-validation. Influence diagnostics. Weighted least squares, correlated errors, transformations, Box-Cox transformations. Logistic and Poisson regression. Generalized linear models. Multicollinearity, ridge regression. Topics selected from non-linear regression, scatterplot smoothing, non-parametric regression, additive non-linear regression, projection pursuit, robust regression.

For course description see AS/SC/MATH3033.03F.

Prerequisite: AS/SC/MATH3033.03.

Degree credit exclusion: AS/SC/AK/MATH3230.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06, AK/GEOG4200.06, AK/PSYC3110.03.

AS/SC/AK/MATH3110.03F Introduction to Mathematical Analysis

1995-95 York Calendar: Proofs in calculus and analysis. Topics include sets, functions, axioms for $\Bbb{R}$, applications of the completeness axiom, countability, sequences and their limits, monotone sequences, limits of functions, continuity.

This course provides a path towards an honours degree for those students who have not taken the honours first year calculus course MATH1010.03. The course MATH3210.03, which is required for several honours programmes, has this course as an alternative to MATH1010.03 as a prerequisite.

The course will emphasize the theoretical aspects of the subject. A principal goal of the course is learning to understand the various definitions and to use them to prove basic properties of the objects being defined. The structure of proofs and the basic logic underlying them will be carefully considered. Relatively little effort will be devoted to problems involving calculations, except when they are useful for explaining the concepts.

The text has not yet been selected.

The final grade will be based 60% on term work, 40% on the final exam.

Prerequisite: AS/SC/AK/MATH1310.03 or AS/SC/MATH1014.03.

Corequisites: AS/SC/AK/MATH2310.03 or AS/SC/ MATH2010.03 or AS/SC/MATH2015.03; AS/SC/MATH 2021.03 or AS/SC/MATH2221.03 or AS/SC/MATH1025.03.

Degree credit exclusion: AS/SC/MATH1010.03, AK/MATH2400.06.

Coordinator: S. Scull

AS/SC/AK/MATH3131.03F Mathematical Statistics I

1995-95 York Calendar: Topics include common density functions, probability functions, principle of likelihood, the likelihood function, the method of maximum likelihood, likelihood regions, tests of hypotheses, likelihood ratio tests, goodness of fit tests, conditional tests, and confidence sets with a view towards applications.

This course is intended for students who need a theoretical foundation in mathematical statistics. It continues where MATH2030 left off, while providing a theoretical foundation for many of the statistical procedures learned in MATH1131/1132. Students who have taken this course normally take MATH3132 in the second term. Further topics will include some aspects of probability theory including change of variables and common distributions, as well as tests of significance.

Prerequisite: AS/SC/AK/MATH2030.03 or permission of the course coordinator.

Degree credit exclusion: AS/SC/MATH3030.03 (before 1993/94), AK/MATH3030.03 (before SU95), AK/MATH 3530.06.

Coordinator: Y. Wu

AS/SC/AK/MATH3132.03W Mathematical Statistics II

(formerly MATH3031)
1995-95 York Calendar: Important examples and methods of statistical estimation and hypothesis testing are discussed in terms of their mathematical and statistical properties. Topics include sufficiency, Bayesian statistics, decision theory, most powerful tests, likelihood ratio tests.

A survey of basic methods of statistical inference: sufficiency, conditionality, likelihood, information, asymptotics.

The text will be D.A.S. Fraser, Probability and Statistics; Theory and Applications, ITS.

The final grade will be based 20% on assignments, 30% on test, 50% on final exam.

Prerequisite: AS/SC/AK/MATH3131.03.

Degree credit exclusion: AS/SC/MATH3031.03 and AS/SC/MATH3130.03, AK/MATH3530.06.

Coordinator: D.A.S. Fraser

AS/SC/AK/MATH3140.06 Number Theory and Theory of Equations

1995-95 York Calendar: A study of topics in number theory and theory of equations using relevant methods and concepts from modern algebra, such as Abelian groups, unique factorization domains and field extensions.

The theory of numbers is concerned with properties of the natural numbers (positive integers) 1, 2, 3, .... These numbers have fascinated amateur as well as professional mathematicians through the ages. A peculiarity of the subject is the great difficulty experienced in verifying results which are simple to state and which are suggested quite naturally by numerical evidence. "It is just this," said Gauss, "which gives the higher arithmetic [number theory] that magical charm which has made it the favorite science of the greatest mathematicians."

One fascinating aspect of number theory is that its methods come from algebra, analysis, and geometry. A major aim of the course is to show how that comes about, namely through the solution of important number-theoretic problems arising in the study of diophantine equations and distribution of primes.

Examples of diophantine equations are $x^2 + y^2 = z^2$ and $x^2 + 2 = y^3$ . In both cases one seeks integer solutions. Algebra comes to our aid if we factor the left sides here, to get $(x + yi)(x - yi) = z^2$ and $(x + \sqrt2 i)(x - \sqrt2 i) = y^3$ . These are now equations in important algebraic domains.

If we write the equation $x^2 + y^2 = z^2$ as $(x/z)^2 + (y/z)^2 = 1$, $z$ unequal to zero, its solutions can be thought of as points with rational coordinates on the unit circle. Similarly, the Fermat equation $x^3 + y^3 = z^3$ , rewritten as $(x/z)^3 + (y/z)^3 = 1$ , gives rise to an "elliptic curve". We are in both cases in the domain of geometry. Such ideas were instrumental in the recent solution of what was perhaps the most celebrated open math problem of all time: to show the unsolvability in nonzero integers of $x^n + y^n = z^n$ for $n > 2$ .

The primes (2, 3, 5, 7, 11, ...) are the building blocks of the integers: every integer is a unique product of primes. But how are the primes distributed among the integers? There is no simple algebraic formula which yields the "answer", but there are analytic ones (involving ideas from calculus).

The solution of the quadratic equation $ax^2 + bx + c = 0$ was known to the Babylonians ca. 4000 years ago. Algebraic solutions of the cubic and quartic equations were found in the 16th century. But can cubics (like quadratics) be solved using only square roots? This question is related to the famous ancient geometric problems of trisecting angles and doubling cubes. We shall explore some of the above ideas.

The text is not yet determined.

The final grade will be based on class tests and assignments (60--70%) and a final exam (40--30%). Prerequisites: AS/SC/MATH2022.03 or AS/SC/AK/ MATH2222.03 or permission of the Course Coordinator.

Coordinator: I. Kleiner

AS/SC/AK/MATH3170.06 Operations Research I

(formerly ACMS3050.06)
1995-95 York Calendar: A study of linear programming; transportation problems, including network flows, assignment problems and critical path analysis; integer programming; dynamic programming and an introduction to stochastic models. Application to a set of problems representative of the field of operations research.

This course deals with standard optimization techniques used in Operations Research. The main topics include:

• Linear Programming: the theory and applications of linear programming including the simplex algorithm, duality theorem, postoptimality analysis, and a discussion of the types of problems that lead to linear programming problems.
• Transportation Problems: the transportation algorithm with applications to network flows, assignment problems, shortest-route problems, and critical path scheduling.
• Integer Programming: a study of the situations leading to integer-programming problems, branch-and-bound algorithm for solving such problems.
• Dynamic Programming: an introduction to the concepts of dynamic programming with a discussion of typical problems and their solutions.

The text will be W.L. Winston, Operations Research. Applications and Algorithms, 3rd ed. (Wadsworth Publishing Co., Duxbury Press), 1994.

The final grade will be based on two computer assignments (5%), three tests (55%), and a final examination (40%).

Prerequisites: AS/SC/MATH2022.03 or AS/SC/AK/ MATH2222.03, plus SC/AS/COSC1530.03 or SC/AS/ COSC1540.03 or equivalent. Students who have not taken these courses need the permission of the course coordinator.

Degree credit exclusion: AK/MATH2751.03, AK/MATH3490.06, AK/ADMS3351.03, AK/COSC3450.06, AK/ECON3120.03.

Coordinator: Silviu Guiasu

AS/SC/AK/MATH3210.03W Principles of Mathematical Analysis

1995-95 York Calendar: Rigorous presentation, with proofs, of fundamental concepts of analysis: limits, continuity, differentiation, integration, fundamental theorem, power series, uniform convergence.

The origins of some ideas of mathematical analysis are lost in antiquity. 300 years ago, Newton and Leibniz independently created the calculus. This was used with great success, but rather part uncritically, for nearly two hundred years. In the 19th century mathematicians began to examine the foundations of analysis, giving such concepts as "function", "continuity", "convergence", "derivative" and "integral" the firm basis they required. These developements continue today. For example, one major theme in 20th century mathematics has been the study of "functional analysis", or calculus in infinite-dimensional spaces.

The course is a prerequisite, or at least a good background, for several 4000-level courses, including MATH 4010.06, MATH4030.06, MATH4080.06, and MATH4210.06. Notions such as uniform continuity and uniform convergence will play a central role; examples will illustrate the theory. The course emphasizes rigor, and the development of the skills required in the study of advanced mathematics.

The course is a natural continuation of the first and second year honours calculus courses. An alternate route into the course is to take the ordinary calculus courses, then MATH3110. The latter will not cover all topics as deeply as the honours courses, but it provides sufficient background and exposure to rigorous mathematical argument to prepare students for MATH3210.

The text has not yet been chosen.

The final grade will be based 60% on term work/tests, 40% on final exam.

Prerequisite: AS/SC/MATH2010.03 or AS/SC/AK/MATH3110.03.

Coordinator: S. Scull

AS/SC/AK/MATH3230.03W Analysis of Variance

1995-95 York Calendar: Categorical variables; one factor and two factor analysis; fixed, random and mixed models; nested designs; an introduction to randomized block and Latin square designs. Second term.

A major focus will be on models with categorical variables as predictors (classical ANOVA, or Analysis of Variance). The computer will be used heavily, but no previous computing courses are required. See also the course description for MATH3330, with which this course is closely linked.

Prerequisite: AS/SC/AK/MATH3330.03.

Degree credit exclusion: AS/SC/MATH3034.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06, AK/GEOG4200.06, AK/PSYC3110.03.

Coordinator: Y. Wu

AS/SC/MATH3241.03F Numerical Methods I

1995-95 York Calendar: An introductory course in computational linear algebra. Topics include simple error analysis, linear systems of equations, nonlinear equations, linear least squares and interpolation. (Same as SC/AS/COSC3121.03.)

The course begins with a general discussion of computer arithmetic and computational errors. Examples of ill-conditioned problems and unstable algorithms will be given. The first class of numerical methods we introduce are those for nonlinear equations, i.e., the solution of a single equation in one variable. We then turn to a discussion of the most basic problem of numerical linear algebra: the solution of a linear system of $n$ equations in $n$ unknowns. The Gaussian elimination algorithm will be discussed as well as the concepts of error analysis, condition number and iterative refinement. We then turn to the least squares methods for solving overdetermined systems of linear equations. Finally we discuss polynomial interpolations. The emphasis in the course is on the development of numerical algorithms, the use of mathematical software, and the interpretation of the results obtained on some assigned problems.

A possible textbook is Curtis F. Gerald and Patrick O. Wheatley, Applied Numerical Analysis (5th ed.), Addison Wesley, 1994.

The final grade will be based on assignments (including computer assignments), tests and a final examination. Details will be announced.

Prerequisites: One of AS/SC/MATH1010.03, AC/SC/MATH1014.03, AS/SC/AK/MATH1310.03; one of AS/SC/MATH1025.03, AS/SC/AK/MATH2221.03, AS/SC/MATH2021.03; one of SC/AS/COSC1540.03, SC/AS/COSC2011.03, SC/AS/COSC2031.03.

Degree credit exclusion: SC/AS/COSC3121.03, AK/COSC3511.03.

Coordinator: Martin Muldoon

AS/SC/MATH3242.03W Numerical Methods II

1995-95 York Calendar: Algorithms and computer methods for solving problems of differentiation, integration, and differential equations, and an introduction to systems of non-linear equations. (Same as SC/AS/COSC3122.03.)

The final grade will be based on assignments (including computer assignments), tests and a final examination. Details will be announced.

Prerequisites: AS/SC/AK/MATH2270.03; AS/SC/MATH3241.03 or SC/AS/COSC3121.03.

Degree credit exclusions: SC/AS/COSC3122.03, AK/COSC3512.03.

Coordinator: A.D. Stauffer

AS/SC/AK/MATH3260.03W Introduction to Graph Theory

1995-95 York Calendar: Introductory graph theory with applications. Graphs, digraphs. Eulerian and Hamiltonian graphs. The travelling salesman. Path algorithms; connectivity; trees; planarity; colourings; scheduling; minimal cost networks. Tree searches and sortings, minimal connectors and applications from physical and biological sciences.

This is a first course in graph theory. After an introduction to graphs, we consider trees, circuits, cycles and connectedness. Also included in the curriculum are introductions to extremal problems, counting and labelings of graphs, graph algorithms, and planarity.

Prerequisite: At least six credits from 2000-level (or higher) MATH courses (without second digit 5), or permission of the instructor.

Coordinator: Buks van Rensburg

AS/SC/AK/MATH3270.03F Dynamical Systems

1995-95 York Calendar: Iterations of maps and differential equations; phase portraits, flows; fixed points, periodic solutions and homoclinic orbits; stability, attraction, repulsion; Poincaré maps, transition to chaos. Applications: logistic maps, interacting populations, reaction kinetics, forced Van der Pol, damped Duffing, and Lorenz equations.

Dynamical systems is a branch of mathematics which studies processes which change. Such processes occur in all branches of science, and examples of dynamical systems include the motion of stars, the change of stock markets, the variation of the world's weather, the rise and fall of populations, the reaction of chemicals and the motion of a simple pendulum. The central goal of the study of dynamical systems is to predict where the system under consideration is heading and where it will ultimately go (for example, one would like to know when the market goes up or down, whether it will be rainy or sunny, or if interacting populations become extinct). The study of dynamical systems originated from differential or difference equations arising from many applied fields, and has been one of the most fruitful fields of mathematical research in this century. Many profound results have been uncovered and applied to other branches of mathematics as well as to physics, chemistry, biology and economics.

In this course, we will use scalar maps and low-dimensional ordinary differential equations to demonstrate the main contents, methods and applications of dynamical systems. The course will be structured so that students are gradually introduced to more and more sophisticated ideas from analysis as the course proceeds. It starts with only a few elementary notions that can be explained using graphical methods or simple differential calculus. The concentration of the course is on the illustration of main ideas and results by graphical analysis and applications, rather than long calculations. Numerical experiments illustrating mathematical results will also be performed.

The contents of the course also include bifurcations and period doubling.

The text will be J. Hale and H. Kocak, Dynamics and Bifurcations (Springer-Verlag, New York, 1991).

The final grade may be based on assignments, projects, one or more tests and a final exam.

Prerequisites: AS/SC/MATH2021.03 or AS/SC/AK/MATH2221.03 or AS/SC/MATH1025.03; AS/SC/AK/MATH2270.03.

Coordinator: M.W. Wong

AS/SC/MATH3271.03F Partial Differential Equations

1995-95 York Calendar: Partial differential equations of mathematical physics and their solutions in various coordinates, separation of variables in Cartesian coordinates, application of boundary conditions; Fourier series and eigenfunction expansions; generalized curvilinear coordinates; separation of variables in spherical and polar coordinates.

Further topics include Sturm--Liouville theory,the gamma function, Bessel, Legendre, Laguerre, Hermite, Chebyshev, hypergeometric, and confluent hypergeometric equations and functions and their properties.

The principal reference text will be G. Arfken, Mathematical Methods for Physicists.

The final grade may be based on assignments, two tests, and a final exam.

Prerequisites AS/SC/AK/MATH2270.03; one of AS/ SC/MATH2010.03, AS/SC/MATH2015.03, AS/SC/AK/ MATH2310.03; AS/SC/AK/MATH3010.03 is also desirable, though not essential, as prerequisite for students presenting AS/SC/MATH2010.03 or AS/SC/AK/MATH2310.03.

Degree credit exclusion: AS/MATH4200A.06.

Coordinator: H. Freedhoff

AS/SC/MATH3280.06 Actuarial Mathematics

1995-95 York Calendar: Actuarial mathematics at a level appropriate for examination 150 of the Society of Actuaries. Topics include survival distributions and life tables, premiums and reserves for life insurance and annuities, multiple life functions, multiple decrement models, valuation theory of pension plans.

This course is intended for those students contemplating careers in the actuarial profession. It will help to prepare a student for Examination 150 of the Society of Actuaries. We will cover most of the material in Chapters 3-10 of the official textbook, N. L. Bowers et al., Actuarial Mathematics, 2nd ed. (Society of Actuaries).There is not sufficient time in a one-year course to cover Chapters 11, 15 and 16, the remaining material needed for Exam 150. However, students who complete this course should acquire sufficient background to enable them to study the omitted chapters on their own.

The prerequisites are a sound knowledge of both interest theory and probability theory. For the probability prere- quisite, students should have completed MATH2030.03. For interest theory the preferred prerequisite is MATH2280.03. Those who have completed MATH2580.06 with a grade of B+ or better may be allowed to enrol, but such students should note that MATH3280.06 is considerably more advanced, and requires much more mathematical ability, than MATH2580.06.

The final grade will be based on a combination of assignments, midterm tests and a final examination.

Prerequisites: AS/SC/MATH2280.03; AS/SC/AK/MATH2030.03.

Coordinator: T.B.A.

AS/SC/AK/MATH3330.03FW Regression Analysis

1995-95 York Calendar: Simple regression analysis, multiple regression analysis, matrix form of the multiple regression model, estimation, tests (t- and F-tests), multicollinearity and other problems encountered in regression, diagnostics, model building and variable selection, remedies for violations of regression assumptions. First term.

This course is closely linked with MATH3230.03W, Analysis of Variance, for which it is a prerequisite. Students will use the computer heavily in these courses, but no previous courses in computing are required.

MATH3330.03 will focus on linear models for the analysis of data on several predictor variables and a single response. The emphasis will be on understanding the different models and statistical concepts used for these models and on practical applications, rather than on the formal derivations of the models. The approach will require the use of matrix representations of the data, and the geometry of vector spaces, which will be reviewed in the course.

The first term (MATH3330.03) will cover the basic ideas of multiple regression, having reviewed in depth the elements of simple linear regression. The second term (MATH3230.03) will have a major focus on models with categorical variables as predictors (classical ANOVA, or Analysis Of Variance).

The nature of the course requires that students be involved on a constant basis with the material, and not fall behind.

The text will be announced at a later date.

The final grade may be based (in each term) on assignments, quizzes, one or more midterms, and a final examination which will be common to all sections.

Prerequisites: One of AS/SC/MATH1132.03, AS/SC/AK/MATH2570.03, AS/SC/PSYC2020.06, or equivalent; some acquaintance with matrix algebra (such as is provided in AS/SC/MATH1025.03, AS/SC/MATH1505.06, AS/AK/MATH1550.06, AS/SC/MATH2021.03, or AS/SC/AK/MATH2221.03).

Degree credit exclusions: AS/SC/MATH3033.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06, AS/ECON4210.03, AK/GEOG4200.06, AK/PSYC3110.03.

Coordinator: T.B.A.

AS/SC/AK/MATH3410.03F Complex Variables

1995-95 York Calendar: An introduction to the theory of functions of a complex variable with applications to the evaluation of definite integrals, solution of two-dimensional potential problems, conformal mapping and analytic continuation.

Some polynomials, such as $x^2+ 1$ , have no roots if we confine ourselves to the real number system, but do have roots if we extend the number system to the complex numbers, which can be defined as the set of all numbers of the form $a + ib$ , where $a$ and $b$ are real and $i$ is a new kind of number satisfying $i^2= -1$ , where the basic arithmetic operations have the same structure as those of the real numbers. The complex numbers include the reals (case $b = 0$), and the extended system has the desirable property that not only $x^2 + 1$ but every polynomial now has a root. In the system of complex numbers certain connections are seen between otherwise apparently unconnected real numbers. A striking example is Euler's formula $e^{i \pi} + 1 = 0$ , which is a simple consequence of the extension to complex variables of the familiar exponential and trigonometric functions. The concepts and operations of calculus (differentiation, integration, power series, etc.) find their most natural setting in complex (rather than real) variables. The present course is intended to give the student a basic knowledge of complex numbers and functions and a basic facility in their use.

Topics will include: Complex numbers and their representations; functions of a complex variable; extensions of elementary functions from real to complex variables; mapping of elementary functions; complex differentiation; Cauchy-Riemann equations; complex integration; Cauchy's theorem; Cauchy's integral formula and its applications; complex power series; the residue theorem and its applications.

Prerequisites: AS/SC/MATH2015.03 or AS/SC/AK/ MATH3010.03 or permission of the course coordinator.

Coordinator: K. Maltman

AS/SC/AK/MATH3430.03W Sample Survey Design

(formerly ACMS4080.03)
1995-95 York Calendar: Principal steps in planning and conducting a sample survey. Sampling techniques including simple random sampling, stratified random sampling, cluster sampling, and sampling with probabilities proportional to size. Estimation techniques including difference, ratio, and regression estimation.

This course deals with the peculiarities of sampling and inference commonly encountered in sample surveys in medicine, business, the social sciences, political science, natural resource management, and market research. Attention will be focused on the economics of purchasing a specific quantity of information. That is, methods for designing surveys that capitalize on characteristics of the population under study will be presented, along with associated estimators to reduce the cost of acquiring an estimate of specified accuracy. (The emphasis will be on the practical applications of theoretical results.)

The text will be R. L. Scheaffer, W. Mendenhall, and L. Ott, Elementary Survey Sampling (5th ed.), PWS-Kent.

The final grade may be based on assignments (15%), a class test (35%) and a final examination (50%).

Prerequisite: AS/SC/MATH2030.03 or AS/SC/MATH3030.03 (taken before 1993/94) or AS/SC/AK/MATH3330.03 or AS/SC/PSYC3030.06.

Degree credit exclusions: These courses may not be taken for credit after taking MATH3430: AK/MATH2752.03, AK/ADMS3352.03, AK/ECON3130.03.

Coordinator: P. Peskun

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