2001/2002 Calendar copy: 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's theorems, differential forms, general Stokes's theorem.      The course continues the study of vector calculus, begun in the first and second year calculus courses. An introduction to the differential geometry of curves is given thorough a detailed study of curvature. Matrices and determinants are used to extend the concepts of differential calculus from real valued functions of several variables to vector valued functions. The Inverse and Implicit Function Theorems are studied. Lagrange multipliers are used to solve extremum problems with side conditions.       Jacobians are used to study a general change of variables in multiple integrals. Special cases include double integrals in polar coordinates as well as triple integrals in cylindrical and spherical coordinates. Scalar and vector fields are introduced. Line and surface integrals are defined and computed. Green's Theorem for line integrals as well as the Gauss and Stokes Theorems for surface integrals are studied and applications are given.      The course grade will be based on two term tests (50%) and a final exam (50%).  The text will be S.O. Kochman, Calculus: Concepts, Applications and Theory, Parts III and IV. Prerequisite: AS/SC/MATH 2010 3.0 or AS/SC/AK/MATH 2310 3.0; or AS/SC/MATH 2015 3.0 and written permission of the Mathematics Undergraduate Director (normally granted only to students proceeding in Honours programs in Mathematics or in the Specialized Honours Program in Statistics). Precorequisite: AS/SC/AK/MATH 2022 3.0 or AS/SC/AK/MATH 2222 3.0. Coordinator:  S.O. Kochman AS/SC/AK/MATH 3020 6.0 Algebra I              2001/2002 Calendar copy: 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, PID's and UFD's); 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 who performed well in the prerequisite linear algebra course is welcome to enrol, but {\sc this course is intended primarily for students who have taken the honours versions of first and second year courses}.      The text will be Fraleigh, {\it A First Course in Algebra}, 6th Ed. (Addison-Wesley Longman).      The final grade will be based on assignments, class participation, class tests, and a final examination. Prerequisite: AS/SC/AK/MATH 2022 3.0 or AS/SC/AK/MATH 2222 3.0. Coordinator:  Yun Gao AS/SC/MATH 3033 3.0 F Classical Regression Analysis      2001/2002 Calendar copy: 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 intended for students who need a solid knowledge of regression analysis. The emphasis, in contrast to MATH3330.30, will be a more mathematical development of linear models including modern regression techniques.      Students will use the computer for some exercises, but no previous courses in computing are required. The statistical software package SPLUS in a UNIX environment will be used and instructions will be given in class.      The text and grading scheme have not been determined. Prerequisites: AS/SC/AK/MATH 2131 3.0 or permission of the course coordinator; AS/SC/AK/MATH 2022 3.0 or AS/SC/AK/MATH 2222 3.0.  Exclusions: AS/SC/AK/MATH 3330 3.0, AS/SC/GEOG 3421 3.0, AS/SC/PSYC 3030 6.0. Coordinator:  TBA AS/SC/AK/MATH 3034 3.0 W Applied Categorical Data Analysis      2001/2002 Calendar copy: Regression using categorical explanatory variables, one-way and two-way analysis of variance. Categorical response data, two-way and three-way contingency tables, odds ratios, tests of independence, partial association. Generalized linear models.  Logistic regression. Loglinear models for contingency tables.  Note: Computer/Internet use may be required to facilitate course work.      This course is a continuation of MATH 3033 3.0, Classical Regression Analysis, or of MATH 3330 3.0, Regression Analysis.  The focus of the course is on the analysis of categorical data, including regression using categorical explanatory variables, contingency table, logistic regression, log-linear regression and generalized linear models.      Students will use statistical software packages, either SPLUS or SAS, for data analysis.  The text is A. Agresti, An Introduction to Categorical Data Analysis (Wiley).      The final grade will be based on assignments, term tests, a project and a final examination. Prerequisite: AS/SC/MATH 3033 3.0 or AS/SC/AK/MATH 3330 3.0. Exclusion: Not open to any student who has passed or is taking AS/SC/MATH 4130G 3.0. Coordinator:  P. Song AS/SC/AK/MATH 3050 6.0 Introduction to Geometries      2001/2002 Calendar copy: Analytic geometry over a field with vector and barycentric coordinate methods, affine and projective transformations, inversive geometry, foundations of Euclidean and non-Euclidean geometry, applications throughout to Euclidean geometry. Note: This course will NOT be offered in FW 2001.  It will probably be offered in FW 2002. Prerequisite: AS/SC/AK/MATH 2022 3.0 or AS/SC/AK/MATH 2222 3.0 or permission of the Course Coordinator. AS/SC/MATH 3100 3.0 Famous Problems in Mathematics      2001/2002 Calendar copy: An attempt to foster an appreciation of the history, the personalities and some of the content of different areas of mathematics, by means of a study of some specific problems which have exercised the minds of mathematicians. Note: This course will NOT be offered in FW 2001.  It will probably be offered in FW 2002. Prerequisites: At least 12 credits from 2000-level MATH courses without second digit 5, or (Atkinson) second digit 7, or permission of the Course Coordinator. AS/SC/AK/ MATH 3110 3.0 F Introduction to Mathematical Analysis      2001/2002 Calendar copy: 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 MATH 1010 3.0. The course MATH 3210 3.0, which is required for several honours programs, has this course as an alternative to MATH 1010 3.0 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 final grade will be based on written assignments, two class tests, and a final examination. The exact scheme will be announced during the first week of classes.      The text will be Bartle and Sherbert, Introduction to Real Analysis (Wiley). Prerequisite: AS/SC/AK/MATH 1310 3.0 or AS/SC/MATH 1014 3.0. Corequisites: AS/SC/AK/MATH 2310 3.0 or AS/SC/MATH 2010 3.0 or AS/SC/MATH 2015 3.0; AS/SC/AK/MATH 1021 3.0, AS/SC/MATH 2021 3.0 or AS/SC/AK/MATH 2221 3.0 or AS/SC/MATH 1025 3.0. Exclusions: AS/SC/MATH 1010 3.0, AK/MATH 2400 6.0. Coordinator:  Eli Brettler AS/SC/AK/MATH 3131 3.0 F Mathematical Statistics I      2001/2002 Calendar copy: 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. Students who have taken it normally take MATH 3132 in the second term. It continues where MATH 2131 left off, while providing a theoretical foundation for many of the statistical procedures learned in MATH 1131 and in either MATH 1132 (no longer offered) or MATH 2131 (which has replaced 1132).      Topics will include multivariate probability distributions, functions of random variables, sampling distributions, point estimation, confidence intervals, relative efficiency, consistency, sufficiency, minimum variance unbiased estimation, method of moments, maximum likelihood, etc.      The final grade will be based on assignments, two tests, and a final exam. The text has not yet been determined. Prerequisite: AS/SC/AK/MATH 2131 3.0 or permission of the course coordinator. Coordinator:  Y. Wu AS/SC/AK/MATH 3132 3.0 W Mathematical Statistics II      2001/2002 Calendar copy: 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.      This course is a continuation of MATH 3131 3.0. The basic nature of statistical inference will be studied. Topics include likelihoods, testing statistical hypotheses, Bayesian methods, large sample inference, etc.      The final grade will be based on assignments, two tests, a final exam plus a presentation. The text has not yet been determined. Prerequisite: AS/SC/AK/MATH 3131 3.0. Coordinator:  Y. Wu AS/SC/AK/MATH 3140 6.0 Number Theory and Theory of Equations      2001/2002 Calendar copy: 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. Note: This course will probably NOT be offered in FW 2002. MATH 3050 3.0 is expected to be offered that year instead. These two courses are normally offered in alternate years.      Number theory, "the queen of mathematics'' (as Gauss called it), is a fascinating subject in which easily stated problems, understandable to anybody who can add and multiply integer numbers, have occupied amateurs and professionals alike throughout the ages. One of the earliest problems (going back at least 4000 years) must have been that of solving the "Pythagorean'' equation x2 + y2 = z2 for integers x, y, z. Presenting the solutions in this case is not very difficult (and we shall deal with it early in the course), but it becomes a famous and very difficult problem if we replace the squares by n-th powers, with an arbitrary natural number n. The non-existence of any solutions for n > 2 is known as "Fermat's Last Theorem'', a proof of which was found only recently, after centuries of intensive research and with the use of many powerful techniques of modern mathematics.       Number theory has many modern applications, for example in cryptography. Any system to secure the flow of potentially sensitive information (encoded on credit cards, or in e-mail communication, for example) makes significant use of number theory.      The text and marking have not been determined yet. Prerequisites: AS/SC/AK/MATH 2022 3.0 or AS/SC/AK/ MATH 2222 3.0 or permission of the course coordinator. Coordinator:  A. Pietrowski AS/SC/AK/MATH 3170 6.0 Operations Research I      2001/2002 Calendar copy: 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: (a) 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. (b) Transportation Problems: the transportation algorithm with applications to network flows, assignment problems, shortest-route problems, and critical path scheduling.  (c) Integer Programming: a study of the situations leading to integer-programming problems, branch-and-bound algorithm for solving such problems. (d) 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, 1994).      The final grade will be based on two assignments (2.5% each), two tests (25% each), and a final examination (45%).             Students who have not taken the prerequisite courses need the permission of the course coordinator to enrol. Prerequisites: AS/SC/AK/MATH 1021 3.0 or AS/SC/MATH 1025 3.0 or AS/SC/MATH 2021 3.0 or AS/SC/AK/MATH 2221 3.0, plus AK/AS/SC/COSC 1520 3.0 or AK/AS/SC/COSC 1540 3.0 or AK/AS/SC/COSC1020 3.0 or equivalent. Exclusions: AK/MATH 2751 3.0, AK/MATH 3490 6.0, AK/ADMS 3351 3.0, AK/COSC 3450 6.0, AK/ECON 3120 3.0. Coordinator:  R.L.W. Brown AS/SC/AK/MATH 3210 3.0 W Principles of Mathematical Analysis      2001/2002 Calendar copy: 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. About 300 years ago, Newton and Leibniz independently created the calculus. This was used with great success, but for the most part uncritically, for about 200 years. In the last century, mathematicians began to examine the foundations of analysis, giving the concepts of function, continuity, convergence, derivative and integral the firm basis they required. These developments continue today, for example with the study of calculus on infinite dimensional spaces.      This course is a continuation of first and second year calculus. The material will be presented in a rigorous manner, putting emphasis on careful mathematical arguments, proofs and illustrative examples. The objectives of the course include improved skill at understanding and writing mathematical arguments as well as understanding of the concepts of the course.  The course will provide a useful theoretical background for a variety of higher level and graduate courses including those in analysis, probability, topology, mathematical statistics, and numerical analysis.      Text: Bartle and Sherbert, Introduction to Real Analysis. Prerequisite:  At least one of the following four courses or course combinations: (1) AS/SC/MATH 2010 3.0, (2) AS/SC/AK/MATH 3110 3.0, (3) AS/SC/AK/MATH 2310 3.0 and AS/SC/MATH 1010 3.0, (4) AS/SC/MATH 2015 3.0 and AS/SC/MATH 1010 3.0. Coordinator:  Eli Brettler AS/SC/MATH 3241 3.0 F Numerical Methods I      2001/2002 Calendar copy: 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 AK/SC/AS/COSC 3121 3.0.)      The course begins with a discussion of computer arithmetic and computational errors. Examples of ill-conditioned problems and unstable algorithms will be given. The first class of numerical methods introduced are those for nonlinear equations, i.e., the solution of a single equation in one variable. We then discuss the most basic problem of numerical linear algebra: the solution of a linear system of n equations in n unknowns. We discuss the Gauss algorithm and the concepts of error analysis, condition number and iterative refinement. We then use least squares to solve overdetermined systems of linear equations. The course emphasizes the development of numerical algorithms, the use of mathematical software, and interpretation of results obtained on some assigned problems.  Prerequisites: One of AS/SC/MATH 1010 3.0, AC/SC/MATH 1014 3.0, AS/SC/AK/MATH 1310 3.0; one of AS/SC/AK/MATH 1021 3.0, AS/SC/MATH 1025 3.0, AS/SC/ AK/MATH 2221 3.0, AS/SC/MATH 2021 3.0; one of AK/AS/SC/COSC 1540 3.0 or AK/AS/SC/COSC 2031 3.0. Exclusions: SC/AS/COSC 3121 3.0, AK/COSC 3511 3.0. Coordinator:  TBA AS/SC/MATH 3242 3.0 W Numerical Methods II      2001/2002 Calendar copy: Algorithms and computer methods for solving problems of differentiation, integration, differential equations, and an introduction to systems of non-linear equations. (Same as AK/AS/SC/COSC 3122 3.0.) Prerequisites: AS/SC/AK/MATH 2270 3.0; AS/SC/MATH 3241 3.0 or AK/AS/SC/COSC 3121 3.0. Exclusions: AK/AS/SC/COSC 3122 3.0, AK/COSC 3512 3.0. Coordinator:  J. Laframboise AS/SC/AK/MATH 3260 3.0 W Introduction to Graph Theory      2001/2002 Calendar copy: 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.      A first course in graph theory. After considering introductory material on graphs and properties of graphs, we shall look at trees, circuits and cycles. Graph embeddings, labelings and colourings, with some applications, will also be covered.      The final grade will be determined from assignments, class tests, and a final examination. Prerequisite: At least six credits from 2000-level (or higher) MATH courses (without second digit 5, or second digit 7 in the case of Atkinson), or permission of the instructor. Coordinator:  Buks van Rensburg AS/SC/MATH 3271 3.0 F Partial Differential Equations      2001/2002 Calendar copy: 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.            Other topics include orthogonal curvilinear coordinates and the grad, div, curl, and laplacian operators in these systems; the gamma function; and the cylindrical and spherical Bessel, Legendre, Laguerre, Hermite, Chebyshev, hypergeometric and confluent hypergeometric equations and functions and their properties.      The final grade will be based on assignments, two tests, and a final examination. Prerequisites: AS/SC/AK/MATH 2270 3.0; one of AS/SC/MATH 2010 3.0, AS/SC/MATH 2015 3.0, AS/SC/AK/MATH 2310 3.0; AS/SC/AK/MATH 3010 3.0 is also desirable, though not essential, as prerequisite for students presenting AS/SC/MATH 2010 3.0 or AS/SC/AK/MATH 2310 3.0. Coordinator:  H.S. Freedhoff AS/SC/MATH 3280 6.0 Actuarial Mathematics      2001/2002 Calendar copy: Deterministic and stochastic models for contingent payments. Topics include survival distributions, life tables, premiums and reserves for life insurance and annuities, multiple life contracts, multiple decrement theory.      This course is intended for students contemplating careers in the actuarial profession. It will cover the material which is now listed under the topic of "contingent payment models'' in the new actuarial examination syllabus. This topic comprises about 40% of the exam on Actuarial Models, which is exam number 3 in the new system.       The prerequisites are a sound knowledge of both interest theory and probability theory. For the probability prerequisite, students should have completed MATH 2030 3.0. For interest theory the preferred prerequisite is MATH 2280 3.0. Those who have completed MATH 2580 6.0 with a grade of B+ or better may be allowed to enrol, but such students should note that MATH 3280 6.0 is considerably more advanced, and requires much more mathematical ability, than MATH 2580 6.0.      Students will also be expected to acquire a knowledge of the Excel spreadsheet. Those who are not familiar with Excel should expect to put in some extra time in order to learn the basics. Prerequisite: AS/SC/MATH 2280 3.0. Precorequisite: AS/SC/AK/MATH 2131 3.0. Coordinator:  TBA AS/SC/AK/MATH 3330 3.0 FW Regression Analysis      2001/2002 Calendar copy: 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.      The course is intended as a thorough introduction to the use of linear models in statistical analysis, for students who have had at least two terms of statistics. We will be focussing on situations where we have one dependent variable and one or more explanatory variables. The material covered will be drawn from the textbook (see more details below), supplemented by some material from other sources. The emphasis will be on the use of the models in question for helping in the analysis of data, not on theoretical derivations.      The text has not yet been chosen, but will include coverage of multiple regression with use of matrices and vectors as an essential part. A possible text is Bowerman and O'Connell, Linear Statistical Models  (PWS-Kent).      Details of the marking scheme, assignments, etc. for section A only will be available on Prof. Denzel's web page (www.yorku.ca/lezned). Details of the method of evaluating course performance will be distributed in all sections at the beginning of the course.      Prerequisites: All students will be assumed to be familiar with elementary statistical concepts, such as are covered in MATH 2560-2570. Familiarity with the basic concepts of vectors and matrices is also assumed.      Computing: Students will be expected to use available computing resources, primarily the Gauss Lab (S110 Ross), or the labs in the Steacie Science Building. Accounts for these labs and the phoenix and Gauss servers can be obtained through MAYA. For those students who have computers available elsewhere, and need to dial in through a modem, an account on York's high-speed modem pool should also be obtained. (There is a small monthly charge for use of this service.)  Printing services are available in the Gauss Lab or in Steacie. There are many statistical programs which could be used for much of the work in this course. We will mostly present sample programs and solutions using SAS. Prerequisites: One of AS/SC/AK/MATH 2131 3.0, AS/SC/AK/MATH 2570 3.0, AS/SC/PSYC 2020 6.0, or equivalent; some acquaintance with matrix algebra (such as is provided in AS/SC/AK/MATH 1021 3.0, AS/SC/MATH 1025 3.0, AS/SC/MATH 1505 6.0, AS/AK/MATH 1550 6.0, AS/SC/MATH 2021 3.0, or AS/SC/AK/MATH 2221 3.0). Exclusions: AS/SC/MATH 3033 3.0, AS/SC/GEOG 3421 3.0, AS/SC/PSYC 3030 6.0, AS/ECON 4210 3.0, AK/PSYC 3110 3.0.  Coordinators:  Fall: G.E.\ Denzel  Winter: TBA AS/SC/AK/MATH 3410 3.0 F Complex Variables      2001/2002 Calendar copy: Analytic functions, the Cauchy-Riemann equations, complex integrals, the Cauchy integral theorem, maximum modulus theorem. Calculations of residues and applications to definite integrals, two-dimensional potential problems and conformal mappings. Note: This course will probably NOT be offered in FW 2002.      Some polynomials, such as x2+ 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 i2= -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 x2 + 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 ei p + 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.       Further topics 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's theorem; Cauchy's integral formula and its applications; complex power series; the residue theorem and its applications. Prerequisite: AS/SC/MATH 2010 3.0 or AS/SC/MATH 2015 3.0 or AS/SC/AK/MATH 2310 3.0. (AS/SC/AK/MATH 3010 3.0 is also recommended as a prerequisite for students who have taken AS/SC/MATH 2010 3.0.) Coordinator:  Allan Trojan   AS/SC/AK/MATH 3430 3.0 W Sample Survey Design      2001/2002 Calendar copy: 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 (5%), class tests (40%) and a final examination (55%). Prerequisite: AS/SC/AK/MATH 2131 3.0 or AS/SC/AK/MATH 3330 3.0. Exclusions: These courses may not be taken for credit after taking MATH 3430: AK/MATH 2752 3.0, AK/ADMS 3352 3.0, AK/ECON 3130 3.0. Coordinator:  P. Peskun AS/SC/MATH 3450 3.0 Introduction to Differential Geometry      2001/2002 Calendar copy: Curves and surfaces in 3-space, tangent vectors, normal vectors, curvature, introduction to topology and to manifolds. Note: This course will not be offered in FW 2001. In recent years it has run fairly frequently. It has not been determined whether it will be offered in FW 2002. Prerequisites: AS/SC/AK/MATH 3010 3.0; AS/SC/AK/MATH 2022 3.0 or AS/SC/AK/MATH 2222 3.0; or permission of the course coordinator. Exclusions: AS/SC/AK/MATH 4250 6.0.  AS/MATH 3500 6.0 Mathematics in the History of Culture Same as: AS/HUMA 3990A 6.0      2001/2002 Calendar copy: An introduction to the history of mathematical ideas from antiquity to the present, with emphasis on the role of these ideas in other areas of culture such as philosophy, science and the arts. Note: This course is a Major course for ITEC and STCS students.       Rather than focusing on "mathematical ideas from antiquity to the present'', this course will examine ideas from other areas of human enquiry which have been influenced by mathematical thinking. This will be accomplished through readings from the popular literature about mathematics, philosophy, linguistics and cognitive studies. Students will be required to read assigned material and prepare written reports on it as well as participate in on-line seminar discussions. Students considering taking this course should note that there will be only a few scheduled lectures; the bulk of the course will be organized through the internet. Those who do not have access to the internet at home or are not willing to devote time to accessing the internet on campus are discouraged from taking this course.      The text will consist of a compilation of readings from various sources.      The course web page (www.math.yorku.ca/Info/course_home.html) contains a bibliography which should give a good indication of the sort of works which will be examined.       The final mark will be based on written work, participation in on-line discussions and a final examination. Prerequisite: 6 credits in university-level mathematics (other than AS/SC/MATH 1500 3.0, AS/SC/MATH 1510 6.0, or AS/SC/MATH 1515 3.0) is strongly recommended. Exclusion: AS/HUMA 3990A 6.0. Coordinator:  Juris Steprans