AS/SC/MATH 4000
3.0 FW and 6.0 Y Individual Project
2001/2002 Calendar copy:
A project of a pure or applied nature in mathematics or statistics
under the supervision of a faculty member. The project allows the
student to apply mathematical or statistical knowledge to problems of
current interest. A report is required at the conclusion of the
project.
The
student works under supervision of a faculty member, who is selected
by the Course Coordinator and the student. The project allows the
student to apply mathematical or statistical knowledge to problems of
current interest. A report is required at the conclusion of the
project.
Students
in the Applied Mathematics Honours Programs are particularly
encouraged to take this course. The procedure is as follows: Each
year, faculty members who are interested in supervising projects will
submit project descriptions to the Course Coordinator for Applied
Mathematics. Students will meet
with the CC for AM, and they will jointly decide on a faculty member
to supervise the project, taking into account the background and
interests of the student, as well as the availability and interests of
faculty members.
The amount
of work expected of the student is approximately ten hours per week,
that is, the equivalent of a standard fullyear (for 4000 6.0) or
halfyear (for 4000 3.0) course. The supervisor is expected to spend
about one or two hours per week with the student, averaged over the
duration of the project. In addition to the final report, regular
short progress reports will be expected at definite times during the
course. The final grade will be based upon the final report as well as
the interim progress reports.
Applied Mathematics Coordinator: Buks van Rensburg
Maths.for Commerce Coordinator: Morton Abramson
Pure Mathematics Coordinator: Morton Abramson
Statistics Coordinator:} Yuehua Wu
Prerequisites: Open to all students in
Honours programs in the Department
of Mathematics and Statistics. Permission of the Program Director is
required. Applied Mathematics students can enrol only after they have
completed the core program in Applied Mathematics.
AS/SC/AK/MATH 4010 6.0 Real
Analysis
2001/2002 Calendar copy:
Survey of the real and complex number systems, and inequalities.
Metric space topology. The RiemannStieltjes integral. Some topics of
advanced calculus, including more advanced theory of series and
interchange of limit processes. Lebesgue measure and integration.
Fourier series and Fourier integrals.
This
course provides a rigorous treatment of real analysis. All students
should have completed the introductory analysis course MATH 3210
3.0. Students contemplating graduate work in mathematics are
strongly advised to take this course.
The text
will be W.Rudin, Principles of Mathematical Analysis
(McGrawHill).
The final grade will be based on assignments
and four term tests (60%) and a final exam (40%).
Prerequisite: AS/SC/AK/MATH 3210 3.0 or
permission of the course coordinator.
Coordinator: N.Purzitsky
AS/SC/AK/MATH 4020 6.0 Algebra
II
2001/2002 Calendar copy:
Continuation of Algebra I, with applications: groups (finitely
generated Abelian groups, solvable groups, simplicity of alternating
groups, group actions, Sylow's theorems, generators and relations);
fields (splitting fields, finite fields, Galois theory, solvability of
equations); additional topics (lattices, Boolean algebras, modules).
This
course aims to broaden and deepen the student's knowledge and
understanding of modern abstract algebra by building on the material
of MATH 3020 6.0 (or a comparable course which students may have
taken). In addition
to the topics listed in the Calendar, the following will be expounded:
Group theory: Composition series.
Ring theory: General ring theory, Chinese Remainder Theorem,
factorization in domains, Noetherian rings.
Field theory: Ruler and compass constructions.
Linear algebra: The Jordan canonical form of a matrix.
Prerequisite: AS/SC/AK/MATH 3020 6.0 or
permission of the course coordinator.
Exclusion: AS/SC/MATH 4241 3.0.
Coordinator: R.G.Burns
AS/SC/AK/MATH 4080 6.0
Topology
2001/2002
Calendar copy: Topological spaces, continuity, connectedness,
compactness, nets, filters, metrization theorems, complete metric
spaces, function spaces, fundamental group, covering spaces.
Note: This course will probably NOT be
offered in FW 2002.
Unlike a
geometer, who will consider only nondistorting transformations of
geometric objects, such as reflections and rotations, a topologist
studies properties that are invariant under bending, stretching,
compressing, etc. Hence, a circle is considered topologically
equivalent not only to an ellipse, but even to a triangle or a square!
While this seems mathematically rough and disturbing, a second look
quickly reveals how fine and powerful a tool topological equivalences
(called homeomorphisms) are, since they turn out to be able to
distinguish such seemingly similar objects as open, closed and
halfopen intervals of the same length!
The main
purpose of this course is to study socalled topological spaces, and
those properties which are invariant under homeomorphisms and
isotopies. To get a feel for the latter concept, perform the following
(rather theoretical) experiment: Using both of your hands, make LINKED
rings with your thumbs and index fingers, and now assume that your
whole body is made of VERY elastic material, so that its shape may be
changed at will, by bending, stretching and compressing it as much as
you like (but tearing and gluing is forbidden). Question:
can you move your hands apart without separating the joined
fingertips? Surprisingly, the answer turns out to be positive!
Topology is an integral part of modern
mathematics, just like geometry, algebra and analysis. It has many
applications to almost all mathematical fields and is increasingly
used in other subjects, such as physics and economics. The course will
present basic constructions and concepts of general topology, such as
separation axioms, compactness, connectedness, metrizability, as well
as the fundamentals of homotopy theory.
A
text has not been chosen yet.
The
final grade will be based on assignments (20%), class tests
(40%) and a final examination (40%).
The
course can be used to fulfill the Pure Mathematics Honours
requirement.
Prerequisite:AS/SC/AK/MATH3210 3.0 or
permission of the course coordinator.
Coordinator: P.Szeptycki
AS/SC/MATH 4110N 3.0 WTopics
in Analysis: Ordinary
Differential Equations
Same as: GS/MATH 6340 3.0
2001/2002 Calendar copy:
This course is an advanced introduction to a number of topics in
ordinary differential equations. The topics are chosen from the
following: existence and uniqueness theorems, qualitative theory,
oscillation and comparison theory, stability theory, bifurcation,
dynamical systems, boundary value problems, asymptotic methods.
The last
two topics above will be omitted. The lectures will survey the others,
and students will be expected to make an indepth study of some, by
doing assignments and projects.
Students
should have passed MATH 2221 and MATH 3210, or seek permission from
the course coordinator to take this course.
The text will be Lawrence Perko, Differential
Equations and Dynamical Systems (SpringerVerlag, 1991).
Other
references include J.K.Hale and H.Kocak, Dynamics and Bifurcations
(SpringerVerlag, 1991), and M.W.Hirsch and S.Smale, Differential
Equations, Dynamical Systems and Linear Algebra (Academic Press,
1974).
The grade
will be based upon term tests and assignments (60%) and a final exam
(40%).
Prerequisite: Permission of the course
coordinator.
Coordinator: J.Wu
AS/SC/MATH 4130K 3.0 F Topics
in Probability and Statistics:
Survival Analysis
2001/2002 Calendar copy:
This course provides students with an introduction to the statistical
methods for analyzing censored data which are common in medical
research, industrial lifetesting and related fields. Topics include
accelerated life models, proportional hazards model, time dependent
covariates.
Note: It has not yet
been determined whether this course will be offered in FW 2002.
We start
with some parametric models and show how censored data can be
incorporated in the analysis. Then we proceed to nonparametric methods
and discuss KaplanMeier and Actuarial estimators. Semiparametric
models, proportional hazards model and time dependent covariates will
also be discussed. The computer will be extensively used, and
familiarity with elementary use of S+ and SAS will be assumed.
Evaluation
will be based on a combination of assignments, midterm exam, final
exam and a project.
Prerequisites: AS/SC/AK/MATH 3131 3.0; either
AS/SC/MATH 3033 3.0 or AS/SC/AK/MATH
3330 3.0.
Note: Computer/Internet use is essential for course work.
Coordinator: Stephen Chamberlin
AS/SC/MATH 4141 3.0 F Advanced
Numerical Methods
2001/2002
Calendar copy: NewtonRaphson, quasiNewton methods; optimization
problems: steepest descents, conjugate gradient methods; approximation
theory: least squares, singular value decomposition, orthogonal
polynomials, Chebyshev and Fourier approximation, Pad\'{e}
approximation; matrix eigenvalues: power method, Householder, QL and
QR algorithms.
Additional
topics will include optimization problems: simplex, conjugate
directions; fast Fourier transforms.
Some assignment questions will be done on
computer. Students should be familiar with either the C or Fortran
programming language.
The final
grade will be based on assignments, tests and a final examination.
Prerequisite: AS/SC/MATH 3242 3.0 or
AK/AS/SC/COSC 3122 3.0.
Coordinator: D.Liang
AS/SC/MATH 4142 3.0 W
Numerical Solutions
to Partial Differential Equations
2001/2002
Calendar copy: Review of partial differential equations, elements of
variational calculus; finite difference methods for elliptic problems,
error analysis, boundary conditions, nonCartesian variables,
PDEeigenvalue problems; hyperbolic and parabolic problems, explicit
and implicit methods, stability analysis; RayleighRitz and Galerkin
method for ODEs, finite element methods.
Prerequisites: AS/SC/AK/MATH 2270 3.0;
AS/SC/MATH 3242 3.0 or AK/AS/SC/COSC
3122 3.0.
Coordinator: H.Huang
AS/SC/MATH 4160 3.0
Combinatorial Mathematics
2001/2002 Calendar copy:
Topics from algebra of sets, permutations, combinations, occupancy
problems, partitions of integers, generating functions, combinatorial
identities, recurrence relations, inclusionexclusion principle,
Polya's theory of counting, permanents, systems of distinct
representatives, Latin rectangles, block designs, finite projective
planes, Steiner triple systems.
Note: This course will
NOT be offered in FW 2001. It
will probably be offered in FW 2002.
Prerequisites: AS/SC/AK/MATH 2022 3.0 or
AS/SC/AK/MATH 2222 3.0; six credits
from 3000level MATH
courses (without second digit 5); or
permission of the course coordinator.
AS/SC/MATH 4170 6.0 Operations
Research II
Same as: GS/MATH 6900 3.0 F plus GS/MATH 6901 3.0 W
2001/2002 Calendar copy:
Selected topics from game theory, decision theory, simulation,
reliability theory, queuing theory, nonlinear programming,
classification, patternrecognition and prediction. Each chapter
contains an optimization problem and methods and algorithms for
solving it. The course is rich in examples.
This
course deals mainly with probabilistic models based on optimization.
The following topics will be discussed: (a) Game Theory: how to find
the best strategies in a confrontation between two players with
opposite interests. (b) Decision Theory: how to act in order to
minimize the loss subject to the available data. (c) Simulation: how
to get representative samples from probability distributions and
accurately approximate multiple integrals using random numbers. (d)
Reliability Theory: how to evaluate the lifetime of a system
consisting of many interacting subsystems. (e) Queueing Theory: how to
assess what may happen in a system where the customers arrive
randomly, wait in line, and then get served. (f) Uncertainty: how to
measure uncertainty in probabilistic modelling with applications to
patternrecognition and classification.
There is
no textbook, and the lecture notes are essential. Useful books are:
(a) F.S.Hillier and G.J.Liberman, \ita{Introduction to Operations
Research (b) H.A.Taha, Operations Research.
The final
grade will be based on two tests (25% each) and a final examination
(50%).
The
following prerequisites indicate the sort of background in probability
and statistics, in calculus of several variables, and in linear
programming, needed for MATH4170. Students missing a prerequisite need
the course coordinator's permission to enrol.
Prerequisites: 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
2030 3.0; AS/SC/AK/MATH
3170 6.0; or permission of
the course coordinator.
Exclusion: AS/MATH 4570 6.0.
Coordinator: Silviu Guiasu
AS/SC/MATH 4230 3.0 W
Nonparametric Methods in Statistics
Same as: GS/MATH6639A 3.0
2001/2002 Calendar copy:
Order statistics; general rank statistics; onesample, twosample, and
ksample problems; KolmogorovSmirnov statistics; tests of
independence and relative efficiencies.
Note: It has not yet
been determined whether this course will be offered in FW 2002.
Survey of basic nonparametric test procedures
together with the related theory for permutation, rank, and related
techniques.
The
text and grading scheme have not been determined.
Prerequisite: AS/SC/AK/MATH3131 3.0.
AS/SC/AK/MATH3132 3.0 is recommended
but not required.
Coordinator: P.Ng
AS/SC/MATH 4241 3.0 F Applied
Group Theory
2001/2002 Calendar copy:
Introduction to group theory and its applications in the physical
sciences. Finite groups. Compact Lie groups. Representation theory,
tensor representations of classical Lie groups, classification of
semisimple Lie groups.
Note: This course will probably NOT be offered in FW
2002.
Group theory is widely used in many fields
outside mathematics. This is a consequence of the fact that the
algebraic structure which definesF a group is naturally the property of
the set of symmetries of a physical system. Paying attention to this
fact, and using results from group representation theory (some of
which we will study in this course), one can often radically simplify
practical calculations in these fields.
The course will provide an introduction to
group theory, both for finite groups and continuous groups, as well as
an introduction to group representation theory. No previous knowledge
of group theory will be assumed, but a background in linear algebra is
essential. The course will begin with a review of the formal aspects
of linear algebra (vector spaces, linear transformations, dimensions,
bases, inner products for complex vector spaces, etc.) necessary for
the remainder of the course.
There is no official text. A copy of the
class notes will be available at the library, and a series of
reference texts will be on reserve at the library. In addition to the
official prerequisites, it is highly recommended that students also
have passed MATH 2015 and MATH 2270.
Prerequisites: AS/SC/MATH 2015 3.0; AS/SC/AK/MATH 2022 3.0 or AS/SC/AK/MATH
2222 3.0; AS/SC/AK/MATH 2270 3.0.
Exclusion: AS/SC/AK/MATH 4020 6.0.
Coordinator: Kim Maltman
AS/SC/AK/MATH 4271 3.0
Dynamical Systems
2001/2002 Calendar copy:
Iterations of maps and differential equations; phase portraits, flows;
fixed points, periodic solutions and homoclinic orbits; stability,
attraction, repulsion; Poincar\'{e} maps, transition to chaos.
Applications: logistic maps, interacting populations, reaction
kinetics, forced Van der Pol, damped Duffing, and Lorenz equations.
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.
Exclusion: AS/SC/MATH 3450 3.0.
AS/SC/MATH 4280 3.0 F Risk
Theory
2001/2002 Calendar copy:
Frequency and severity models in insurance, compound distributions,
compound Poisson processes, ruin theory, nonproportional reinsurance,
related topics in loss models and stochastic processes.
This
course is intended mainly for students contemplating a career in the
actuarial profession. It will cover a portion of the material on the
new Exam 3 in Actuarial Models, including the topics of Frequency and
Severity Models, Compound Distribution Models, and Ruin Models.
The
text has not yet been determined.
There will
be a final exam, two class tests, and written assignments. The exact
grading scheme will be announced during the first week of classes.
Prerequisite: AS/SC/AK/MATH 2131 3.0.
Coordinator: S.D.Promislow
AS/SC/MATH 4400 6.0 The
History of Mathematics
2001/2002
Calendar copy: Selected topics in the history of mathematics,
discussed in full technical detail but with stress on the underlying
ideas, their evolution and their context.
Note: This course will probably NOT be offered in FW
2002.
The aim of the course is to give students an
overview of some of the main currents of mathematical thought from
ancient to modern times so that they gain a better understanding of,
and acquire a broader perspective on, mathematics.
The course
will trace the evolution of various areas of mathematics, such as
algebra, analysis, geometry, and set theory. While it will involve a
great deal of technical mathematics, the course will also explore
issues closely bound up with its progress, such as the changing
standards of rigor in mathematics, the cultural context of
mathematics, the roles of problems and crises in the evolution of
mathematics, and the roles of intuition and logic in its development.
Students
will be expected to write a major paper depicting the evolution of a
given problem, general principle, concept, theory, or subfield of
mathematics; for example, function, the real numbers, the distribution
of primes among the integers, the arithmetization of analysis,
fashions in mathematics, the rise and fall of rigorous proof, or
Fermat's Last Theorem.
The course
will not follow a prescribed text, but the following book is
recommended: V.J.Katz, {\it A History of Mathematics}, 2nd Ed.
(AddisonWesley, 1998). In addition, many references on various topics
will be given. Some books will be put on reserve.
The final
grade will be based on a major paper (20%), other assignments (30%),
two tests (20%), and a final exam (30%).
Prerequisites: 36 credits
from MATH courses without second digit 5, including at least 12
credits at or above the 3000 level. (12 of the 36 credits may be taken
as corequisites.)
Coordinator: Israel Kleiner
AS/SC/AK/MATH 4431 3.0 W
Probability Models
2001/2002 Calendar copy:
This course introduces the theory and applications of several kinds of
probabilistic models, including renewal theory, branching processes,
and martingales. Additional topics may include stationary processes,
large deviations, or models from the sciences.
Note: This course will probably NOT be offered in FW 2002. MATH
4430 3.0 is expected to be offered that year instead. These two
courses are normally offered in alternate years.
Renewal processes are used to model an event
that occurs repeatedly at random times, such as the failure of a
machine component. The focus of study is on the longrun average
behaviour of such processes.
Branching processes are a class of simple
population growth models. One
important question is how the distribution of the number of offspring
of one parent can be used to predict the probability that the
population eventually dies out. Generating functions will be
introduced and used to derive results.
Martingales are models of "fair
games". They have been used to study stock market behaviour and
are an important theoretical tool for a wide variety of probability
problems. Important results include descriptions of how expected value
is affected if your decision of when to stop (e.g.when to sell the
stock) is determined by the behaviour of the process itself.
In
addition, we will study some probability models that arise in other
areas of science.
The
text has not been chosen yet.
The final
grade will be based on assignments (20%), two class tests (40%), and a
final exam (40%).
Prerequisite: AS/SC/AK/MATH 2030 3.0.
Corequisite: A MATH course at the 3000 level or higher, without
second digit 5 (Atkinson: second
digit 7).
Coordinator: N.Madras
AS/MATH 4570 6.0 Applied
Optimization
2001/2002 Calendar copy:
Topics chosen from decision theory, game theory, inventory control,
Markov chains, dynamic programming, queuing theory, reliability
theory, simulation, nonlinear programming.
The course
will cover several topics in optimization with an emphasis on
implementing algorithms on the computer to solve practical problems.
Of the official prerequisites (see below) the most important is MATH
3170. The text is the one used in that course: W.L.Winston, {\it
Operations Research, Applications and Algorithms}, 3rd Ed. (Wadsworth
Publishing, Duxbury Press, 1994).
The final grade
will be based on assignments (30%), four class tests (10% each), and a
final exam (30%).
Prerequisites: AS/SC/AK/MATH 3170 6.0;
AS/SC/AK/MATH 3330 3.0; AS/SC/MATH3230 3.0
or AS/SC/AK/MATH 3430 3.0.
Exclusion: AS/SC/MATH 4170 6.0.
Coordinator: R.L.W.Brown
AS/SC/MATH 4630 3.0 W
Applied Multivariate
Statistical Analysis
Same as: GS/MATH 6625 3.0
2001/2002 Calendar copy:
The course covers the basic theory of the multivariate normal
distribution and its application to multivariate inference about a
single mean, comparison of several means and multivariate linear
regression. As time and interest permit, further related topics may
also be covered.
Note: It has not yet been
determined whether this course will be offered in FW 2002.
We will study methods of analysis for data
which consist of observations on a number of variables. The primary
aim will be interpretation of the data, starting with the multivariate
normal distribution and proceeding to the standing multivariate
inference theory. Sufficient theory will be developed to facilitate an
understanding of the main ideas. This will necessitate a good
background in matrix algebra, and some knowledge of vector spaces as
well. Computers will be used extensively, and familiarity with
elementary use of SAS will be assumed. Topics covered will include
multivariate normal population, inference about means and linear
models, principal component analysis, canonical correlation analysis,
and some discussion of discriminant analysis, and factor analysis and
cluster analysis, if time permits.
Grades
will be based on a combination of class tests and final examination,
plus routine homework. The
text has not yet been determined.
Prerequisites: AS/SC/AK/MATH 3131 3.0;
AS/SC/AK/MATH 3034 3.0 or
AS/SC/AK/MATH 3230 3.0; AS/SC/AK/MATH
2022 3.0 or AS/SC/AK/MATH 2222 3.0.
Coordinator: Y.Wu
AS/SC/MATH 4730 3.0 F
Experimental Design
Same as: GS/MATH 6626 3.0
2001/2002 Calendar copy:
An examination of the statistical issues involved in ensuring that an
experiment yields relevant information. Topics include randomized
block, factorial, fractional factorial, nested, Latin square and
related designs. Further topics as time permits. The emphasis is on
applications.
Experimental
design is the process of planning an experiment so that appropriate
data will be collected which may be analysed by statistical methods,
resulting in valid and meaningful conclusions. This includes the
choice of treatments, the required sample size, the random allocation
of experimental units to treatments, the method of estimation, and a
consideration of how the data will be analysed once collected.
We will
study various experimental situations in this course, considering how
the principles of design can be applied to each to create a design
that is appropriate to the objectives of the experiment. We will
examine appropriate procedures for the analysis of the resulting data,
including the underlying assumptions and limitations of the
procedures.
Students
will use the statistical software SAS for data analysis. The final
grade will be based on assignments, a midterm test, and a final exam.
The text will be Dean and Voss, Design and Analysis of Experiments
(Springer, 1999).
Prerequisites: AS/SC/AK/MATH 3034 3.0
or permission of the course
coordinator.
Coordinator: A.Gibbs
AS/SC/MATH 4830 3.0 F Time
Series and Spectral Analysis
2001/2002 Calendar copy:
Treatment of discrete sampled data by linear optimum Wiener filtering,
minimum error energy deconvolution, autocorrelation and spectral
density estimation, discrete Fourier transforms and frequency domain
filtering and the Fast Fourier Transform algorithm. (Same as SC/EATS
4020 3.0 and SC/PHYS 4060 3.0.)
Ed. note: In the absence of any input from Smylie, we provide
no supplementary course description here.
Prerequisites: AK/AS/SC/COSC 1540 3.0 or equivalent FORTRAN
programming experience; AS/SC/AK/MATH 2270 3.0; AS/SC/MATH
2015 3.0 or AS/SC/AK/MATH 3010 3.0.
Exclusions: AK/AS/SC/COSC 4242 3.0, AK/AS/SC/COSC
4451 3.0, SC/EATS 4020
3.0, AS/SC/MATH\4130B 3.0, AS/SC/MATH
4930C 3.0, SC/PHYS 4060 3.0.
Coordinator: D.Smylie
AS/SC/MATH 4930A 3.0 W
Topics in Applied Statistics: Statistical
Quality Control
2001/2002 Calendar copy:
This course provides a comprehensive coverage of the modern practice
of statistical quality control from basic principles to
stateoftheart concepts and applications.
Note: This course will probably NOT be offered in FW
2002.
This course presents the modern approach to
quality through the use of statistical methods. The primary focus will
be on the control chart whose use in modernday business and industry
is of tremendous value. Various control charts will be discussed,
including EWMA and CUSUM charts. Time permitting, the important
interrelationship between statistical process control and experimental
design for process improvement will be discussed.
The text
will be D.C.Montgomery, Introduction to Statistical Quality Control,
4th Ed. (Wiley).
The final
grade may be based on assignments (15%), a class test (35%), and a
final examination (50%).
Prerequisites: AS/SC/AK/MATH 3330
3.0; AS/SC/AK/MATH
3034 3.0 or AS/SC/AK/MATH 3230 3.0 or
AS/SC/AK/MATH 3430 3.0.
Corequisite: AS/SC/MATH 4730 3.0.
Coordinator: P.Peskun
AS/SC/MATH 4930B 3.0
Topics in Applied Statistics: Simulation
and the Monte Carlo Method
Same as: GS/MATH 6003V 3.0
2001/2002 Calendar copy:
Introduction to systems, models, simulation, and Monte Carlo methods.
Random number generation. Random variate generation. Monte Carlo
integration and variance reduction techniques. Applications to queuing
systems and networks.
Note: This course will
NOT be offered in FW 2001. It
will probably be offered in FW 2002.
Prerequisite:
In addition to the official prerequisites below, a 3000level
course in statistics, preferably mathematical statistics, such as
AS/SC/AK/MATH/3131 3.0, is recommended.
Prerequisites: AS/SC/AK/MATH 3330
3.0;AS/SC/AK/MATH 3034 3.0 or AS/SC/AK/MATH 3230 3.0or AS/SC/AK/MATH
3430 3.0.
Exclusion: AK/AS/SC/COSC 3408 3.0.
