AS/SC/AK/MATH 3010 3.0 F
Vector Integral Calculus
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. (AddisonWesley 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 leastsquares 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, oneway and twoway analysis of variance.
Categorical response data, twoway and threeway 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, loglinear
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
nonEuclidean 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
2000level 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
x^{2} + y^{2} = z^{2} 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 nth powers, with an
arbitrary natural number
n. The nonexistence 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 email
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,
shortestroute problems, and critical path scheduling.
(c) Integer Programming: a study of the situations leading to
integerprogramming problems, branchandbound 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 illconditioned 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 nonlinear 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
2000level (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 Ftests), 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 (PWSKent).
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 25602570. 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 highspeed 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 CauchyRiemann equations, complex
integrals, the Cauchy integral theorem, maximum modulus theorem.
Calculations of residues and applications to definite integrals,
twodimensional potential problems and conformal mappings.
Note: This course will
probably NOT be offered in FW 2002.
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 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. (PWSKent).
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 3space, 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 online 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 online discussions and a final examination.
Prerequisite: 6 credits in
universitylevel 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
