0 ?
SIMON FRASER UNIVERSITY
OFFICE OF THE VICE-PRESIDENT, ACADEMIC?
MEMORANDUM
To:
?
Senate
From:
?
D. Gagan, Chair ?
L21
Senate Committee on Academic Planning
Subject: ?
University College of the Fraser Valley!
?
Simon Fraser University
Date: ?
October 17, 1996
Action undertaken by the Senate Committee on Undergraduate Studies and the Senate
Committee on Academic Planning gives rise to the following motion:
.
Motion:
"That Senate approve and recommend to the Board of Governors, as set forth
in S.96 -69 the following new courses to be offered at the University College of
the Fraser Valley:
Math 360 - 3 Operations Research I
Math 381 - 3 Mathematical Methods I
Math 420 - 3 Empirical and non-Parametric Statistics
Math 438 - 3 Advanced Linear Algebra
Math 445 - 3 Introduction to Graph Theory
Math 450 - 3 Statistical Distribution Theory
Math 451 - 3 Parametric Statistical Inference
Math 460 - 3 Operations Research II
Math 470 - 3 Methods of Multivariate Statistics"
SCAP 96-38
S
.
?
SIMON FRASER UNIVERSITY
?
•..
MEMORANDUM
?
.
To: A. Watt
?
.
?
From: C.H.W. Jones, Dean
Secretary to SCAP
?
Faculty of Science
Subject:
UCFV Math 360, 381, 420, 438,
?
Date: March 29, 1996
445, 450, 451, 460 and 470
At its meeting of March 26th, 1996, the Faculty of Science approved the
attached course proposals for Math 360-3, 381-3, 420-3, 438-3, 445-3, 450-3, 451-3,
460-3 and 470-3 from the University College of the Fraser Valley as detailed in the
attached document FSC 7-96.
Please include this item on the agenda of the next meeting of SCAP for
consideration and approval.
MJI&
C.H.W. Jones
C HWJ : rh : End.
SW. Welsh, Dean
Science & Technology, UCFV
M. Plischke, Chair
Faculty of Science Undergraduate Curriculum Committee
APPROVED BY SCUS AT ITS MEETING OF JULY 18, 1996
.
/
F5: 7-?,
SIMON FRASER UNIVERSITY
Memorandum
TO: C.H.W.
Jones, Dean
?
FROM: ?
M. Plischke, Chair
Faculty of Science
?
Faculty of Science
Undergraduate
Curriculum Committee
SUBJECT:
UCFV Upper Level Courses
?
DATE: ?
March 12, 1996
At its meeting of March 12th, the Faculty
of
.
Science Undergraduate
Curriculum Committee approved the attached course proposals for Math 360-3,
Math 381-3, 420-3, 438-3, 445-3, 450-3, 451-3, 460-3 and 470-3 from the University
College of the Fraser Valley.
Would you please bring these to the next Faculty of Science meeting.
ellz--lz
M. Plischke
?
S
MP:rh:Encl.
0
O ?
IFU
SIMON FRASER UNIVERSITY
MEMOR AND! TM
Dale:
?
February 27, 1996
To: ?
M. Plischke, Chair
Physics
From: ?
Katherine Heinrich, Chair
Department of Mathematics
& Statistics
Subject: ?
Fraser Valley
At the departmental meeting of February 26th, the following motion was approved.
Motion: To approve the nine courses as described in item
#5
to be
offered at the University College of the Fraser Valley.
Please take to the Faculty Undergraduate Studies Committee.
0 ?
KH:jc
cc: N. Reilly, Chair, UGSC
17
L
.
3.
For Departmental Meeting of February 23,1996- item
#5 ?
0
From the-minutes of the Undergrthuate Studies Committee Meeting of Friday, February 23,1996.
For background material, please see Judy. It will be available at the meeting.
Approval of the following courses from the University College of the Fraser Valley:
Math 360-3
Operations Research I (deterministic)
Math 381-3
Mathematical Methods I
Math 420-3
Empirical and non-Parametric Statistics
Math 438-3
Advanced Linear Algebra
Math 445-3
Introduction to Graph Theory
math
450-3
Statistical Distribution Theory
Math
45
1-3
Parametric Statistical Inference
Math 460-3
Operations Research U (stochastic)
Math 470-3
Methods of Multivariate Statistics
.
I.
Is transfer credit requested?
ION 'SR
10--
UNIVERSITY COLLEGE OF THE FRASER VALLEY
?
COURSE INFORMATION
DISCIPLINE/DEPARTMENT: Natural Science
Mathematics 381
SUBJECT/NUMBER OF COURSE
IMPLEMENTATION DATE:_________?
Revised:
Mathematical Methods I
?
3
DESCRIPTIVE TITLE
?
UCFV CREDfl
CALENDAR DESCRIPTION: This course covers a wide range of mathematical techniques: calculus problem - solving
devices; Fourier series, Fourier integrals; the gamma, beta, and error functions; Bessel functions, Legendre, Hermit; and
Laguerre polynomials, Sturm-Lioville systems; partial differential equations; and calculus of variations.
RATIONALE: This is a cross listing of Phys 381
COURSE PREREQUISITES: Math 211, 212, 213 or 310. Phys 111/112 recommended
COURSE COREQIJISITES
•
None
HOURS PER TERM
?
Lecture ?
60
FOR EACH ?
Laboratory
10
STUDENT
?
Seminar
Field Experience
MAXIMUM ENROLMENT: 35
hrs
Student Directed
hrs
Learning
?
hrs
hrs
Other - specify:
hrs
TOTAL ?
hrs
60 HRS
0U7LN95101/dd
5.
Mathematics 381 - Mathematical Methods I
?
Page 2 of.
NAME & NUMBER OF COURSE
4
SYNONYMOUS COURSES:
(a)
replaces
(course #)
(b)
cannot take Phvs 381
?
for further credit
(course #)
StJPPLIESIMATERJALS:
TEXTBOOKS, REFERENCES, MATERIALS
(List reading resources elsewhere)
?
Advanced Mathematics for En
g
ineers and Scientists. Murray R. Spigel
Integral Equations, L.G. Chambers, International Textbook
Mathematical Physics,
E. Butkov, Addison - Wesley
Mathematical Methods of Ph
ysics,
J. Mathews and RL. Walker, W.A. Benjamin Inc
OBJECTIVES:
To give students the necessary mathematical skills to tackle the most common problems they will encounter in
physics -
METHODS:
Lecture, demonstration, computer simulations.
STUDENT EVALUATION PROCEDURE:
Assignments ?
25%
Midterm Exam
?
30% ?
FinalExain
is
0
Page 3o
. ?
Mathematics 381 - Mathematical Methods I
?
NAME
&
NUMBER OF COURSE
4
COURSE CONTENT
1.
A large orientation assignment will be given covering the first six chapters of the text which covers
material students should know from the prerequisites for the course. Followed by review lectures if
needed.
Course continues with:
2.
Fourier Series
3.
Fourier Integrals
4.
Special Functions I (Gamma, Beta, Ei, Si, Erf)
5.
Special Functions II (Bessel Functions, cylindrical & spherical; Polynomials, Legendre, Hermite &
Laguerre)
S
?
6. ?
Partial differential equations, separation of variables, Laplace Transform techniques, Sturm-Liovifle
systems, elgenvalues, eigenfunctions
Complex variables, contour integrals & Cauchy's theorem, application to evaluation of integrals
Calculus of Variations (with and without constraint)
Discussion of minimum action principles in physics
Integral Equations, Green Functions and Dirac delta-function techniques
Numerical methods for quadratures and solving integral and differential equations. Richardsoriian
techniques will be discussed.
1.
UNIV
E
RSITY COLLEGE OF THE FRASER VALLEY
COURSE INFORMATION
DEPARTMENT: Mathematics
DATE:01/06/94
NAME
MATH 360&
NUMBER
?
Ooerations
OF COURSE
research
DESCRIPTIVE
I (
d
eterministic)
TITLE
??
UCFV CREDIT
3
CATALOGUE DESCRIPTION:
The application of
m
athematical methods to business problems.
Operations research was developed during and just after the last
world war, and has had amazing success in enabling organisation
to be more effective and efficient. The topics covered include:
an over-view of linear programming, duality theory and sensitivity
analysis; transportation and assignment problems, network
algorithms; dynamic and integer
p
rogramming, scheduling;
network
nonlinear
models
programming,
and
a
pplications;
optimization
PERT
with
and
and
CPM.
without constraints;
COURSE PREREQUISITES:
Math 211, 221.
COURSE COREQUISITES: None
HOURS
FOR EACH
PER
STUDENTTERM
??
LABORATORYLECTURE
??
60
?
FIRS
HRS STUDENT
LEARNINGDIRECTED
?
- HRS
SEMINAR
?
ERS OTHER - specify:
FIELD EXPERIENCE
?
HRS ?
- HRS
TOTAL GO HRS
UCFV
TRANSFERCREDIT
?
I
?
1
I ?
?
NON-TRANSFERUCFV
CREDIT ??
J ?
1
?
NON-
CREDIT
?
Li
TRANSFER STATUS (Equivalent, Unassigned, Other Details)
UPC TEA
SFU TEA
-- -.--
.-• ?
....-[ ----
?
-.
?
r-r,_--L
1JVIC TEA
-.
COURSE DESIGNER
?
J.D. Tuns tall
DEAN
S
.
0 -
Math 360 Ooeratioris research
T_(deterministic)
NAME & NUMBER OF COURSE
PAGE 2 OF 5
PREREQUISITE:
COURSES FOR WHICH
MATH 460
THIS IS A
?
RELATED COURSES: MATH 460
TEXTBOOKS, REFERENCES, MATERIALS
TEXT:
Hillier & Lieberman, Introduction to mathematical
programming. (1990) McGraw
Hill
(includes 2 3.5' disks)
COURSE
--OBJECTIVES:
1.
To introduce the students to the fundamental deterministic
models in applied operations research.
2.
To develop the students' skills in formulating and building
•
?
mathematical models.
3.
To familiarize the students with using computers to solve
operational research problems in business and industry.
STUDENT EVALUATION PROCEDURE;
Assignments
?
20
Midterm exams
?
30's
Quizzes and short tests 10
Final exam
?
40%
..
q.
PAGE 3ÔFS .
MATH 360 O
p
erations research I (deterministic)
NAME & NUMBER OF COURSE
COURSE CONTENT:
1.
Linear programming: simplex method,
p
Ost-optimality analysis.
2.
Duality theory, sensitivity analysis.
assignment
3.
Special
problems,
algorithms:
network
transportatalgorithms.
ion/transhipment problems,
4.
Dynamic programming: formulation and solution; Bellman's
principle of optimality.
control
5.
Applications
with deterministic
of dynamic
demand.
programming: scheduling,
inventory
6.
Integer programming:
bra
nch-and-bound technique, binary
integer programming, mixed integer programming.
7.
Applications of integer programming: facility layout,
assignment problems.
8.
Nonlinear programming: optimization without constraints, the
one-dimensional search procedure, the gradient search procedure.
9.
Optimization with constraints, the Karush-Kuhn-Tucker
conditions, quadratic programming.
algorithm,
10.
Separable
non-convex
programming;
p
rogramming,
convex
pSUMT.
rogramming, Frank-Wolfe
11.
Applications of nonlinear programming: financial planning and
operations management.
spanning
12.
Network
tree
models:
problem,
the
the
shortest
maximum
path
flow
problem,
problem.
the minimum
13.
The minimum cost flow problem, PERT and CR14.
E
.
10.
C
UNIVERSITY COLLEGE OF THE FRASER VALLEY
COURSE INFORMATION
4
DEPARTMENT: Mathematics
DATE: 01/06/94
Math 420
?
Empirical & non-
p
arametric statistics 3 credits
NAME & NUMBER OF COURSE DESCRIPTIVE TITLE
?
UCFV CREDIT
CATALOGUE DESCRIPTION:
Empirical and non-parametric statistics are used when either
little can be assumed about the underlying distribution or it is
very complex. These are methods based on order statistics,
rankings, or resampling; and are very useful when a relatively
quick answer is required.
COURSE PREREQUISITES:
Math 211, 270.
Reáommended: Math 221 and additional upper level statistics
courses.
COURSE COREQUIsITES: None
HOURS PER TERM
?
LECTURE ?
60 ?
HRS STUDENT DIRECTED
FOR EACH STUDENT LABORATORY
?
MRS LEARNING ?
- HRS
SEMINAR ?
MRS OTHER - specify:
- MRS
FIELD EXPERIENCE
?
MRS ?
TOTAL 60 MRS
TRANSFERUCFV
CREDIT
??
7
I ?
?
NON-TRANSFERUCFV
CREDIT
??
CREDIT
NON-
TRANSFER STATUS (Equivalent, Unassigned, Other Details)
UBC TBA
SFU TBA
t1VIC TBA
S
PAGE 2
?
0
Math 420 Em
p irical & non-
p
arametric statistics
NAME & NUMBER OF COURSE
COURSES FOR WHICH THIS IS A
?
RELATED COURSES:
PREREQUISITE: None
TEXTBOOKS, REFERENCES, MATERIALS
TEXTS:
Jean D. Gibbons & S. Chakrabortj. Nonparametrjc statistical
inference (3rd edition). Marcel Dekker (1992)
V. Choulakian, R.A.Lockhart, M.A.Stephens. Cramer-von Mises
Statistics,
statistics for
1994,
discrete
125-137.
distributions.
The Canadian Journal of
COURSE OBJECTIVES:
The course is designed to introduce the student to a range of
techniques that do not conveniently fall into one of the standard
schools of inference. It will enable the student to:
1.
develop a theoretical framework for use of order statistics
and the empirical distribution function;
2.
becorn familiar with the inference methods using these tools;
3.
meet the inference methods based on randomization and rank-
randomization;
4.
become acquainted with the bootstrap and jacknife methods of
resainpling to obtain variance estimates;
5.
meet simple standard measures of bivariate association.
STUDENT EVALUATION PROCEDURE
Assignments ?
20
Midterm exams
?
40
Finalexam ?
40'
.I.
.
PAGE 3
MATH-420 Empirical & non-parametric statistics
NAME
& NUMBER OF COURSE
COURSE CONTENT:
1.
Review of joint probability distribution theory and
transformations.
statistics.
2.
The distribution of the empirical distribution function, order
3.
Quantile point and interval estimation, tolerance limits.
and
4.
K01m0A
n
d
erson-Darling
90rov-sm
j
r0 statistics,
tests of fit.
and
Durbin's
Cramer-von
method
Mises,
for allowing
Watson
statistics.
for adjustable parameters or, equivalently, components of the
5. Fisher- p
itman randomization and
ra
nk-randomization methods,
especially the Wilcoxon and Kruskall-Wallis tests.
concordance.
6.
Bivarjate association, rank correlation, Kendall's tau,
7.
Efron's bootstrap techniques.
errors.
8. The Q
u
enouille-Tukey jacknife methods for obtaining standard
S.
I.
UNIVERSITY COLLEGE OF THE FRASER VALLEY
?
.
COURSE INFORMATION
DEPARTMENT: Mathematics
DATE: 30/11/94
Mathematics 438
?
Advanced Linear Algebra 3 credits
NAME & NUMBER OF COURSE DESCRIPTIVE TITLE
?
UCFV CREDIT
CATALOGUE DESCRIPTION:
Advanced techniques and applications of linear algebra. Topics
form,
squares
include
orthogonal
general
a
pproximation,
inner
t
ransformations,
product
the spectral
spaces,
singular
theorem,
projection
value
Jordan
decomposition,
matrices,
canonical
least
applications to optimization and differential equations.
COURSE PREREQUISITES:
Math 221, and at least two upper level, math courses.
COURSE COREQUISITES: None
HOURS
FOR EACH
PER
STUDENTTERM
??
LABORATORYLECTURE
??
52 ?
HRS
MRS STUDENT
LEARNINGDIRECTED ?
MRS
SEMINAR ?
MRS OTHER - specify:
FIELD
EXPERIENCE
HRS
TOTAL 52
- HRS
MRS
TRANSFERUCFV
CREDIT
?
[ ?
1
UCFV CREDIT
r-i
NON-
NON-TRANSFER
.
CREDIT
TRANSFER STATUS (Equivalent, Unassigned, Other Details)
UBC TBA
1'4.
0 ?
PAGE 3OF5
4
Math 438 Advanced Linear Algebra
NAME & NUMBER OF COURSE
COURSES FOR WHICH THIS IS A
PREREQUISITE: None
RELATED COURSES: Math 439.
TEXTBOOKS, REFERENCES, MATERIALS
TEXT: Material selected from:
Matrix
Linear Algebra
Co
mputations
- Hoffman
- Golub
& Kunze,
& Van
Prentice-Hall.
Loan, North Oxford.
COURSE OBJECTIVES
:
Students will be introduced to central ideas
and methods of linear algebra as they are applied in modern
0 ?
employed
computation.
throughout.
A symbolic
manipulation
package (e.g. Maple) will be
Upon completion of the course, students should:
(a)
have a basic but broad knowledge of the fundamental ideas
and techniques of modern linear algebra,
(b)
Computations,
situations
be able to recognize
of
app
roximation
the many
and
guises
carry
of
out
projection
the necessary
in
(c)
be able to understand and apply the spectral theorem,
(d)
be able to employ
canonical
form decompositions,
(e)
and
linear
employ
systems.
efficient techniques of analyzing and solving
STUDENT EVALUATION PROCEDURE:
Students will be given 2 to 3 midterm exams during the semester,
as well as a final exam. They will also be expected to turn in
assignments
follows:
weekly. The
w
eighting will be as
Midterm exams 40%
Final exam
?
40%
Assignments
?
20%
i'l.
PAGE 4OF 5
0
4
MATH 438, Advanced Linear Algebra
NAME & NUMBER-OF COURSE
COURSE CONTENT: Topics covered will include:
1. Review of Matrix Algebra (matrix arithmetic over the complex
numbers.)
2. Review of Vector spaces (basis, dimension, coordinates,
subspaces.)
3. Linear transformations and linear functionals.
(a)
Kernel, range, isomorphisms.
(b)
Matrix representation
(C)
Dual spaces and dual bases.
4. Brief review of determinants.
5. Inner Product Spaces
(a)
General inner products and norms.
(b)
Generalized Gram-Schmidt process.
(c)
Orthogonal complements and projection matrices.
(d)
Least squares approximation (multiple regression,
orthogonal polynomials, finite Fourier series.)
(e)
If time permits: positive, unitary and normal operators.
6.
Canonical
forms
(a)
Eigenvalues and diagonalizability.
(b) Vie
-
spectral theorem. (Applications to optimization.)
(c)
Direct sum decompositions.
(d)
Jordan canonical form. (Applications of systems of
differential equations.)
(d) If time permits: The Cayley-Hamilton theorem.
7. Computational linear algebra
(a)
Orthogonal transformations (Householder, Givens.)
(b)
QR factorization.
(C)
Singular value decomposition.
(d) Generalized inverses.
1'.
?
•.
?
UNIVERSITY COLLEGE OF THE FRASER VALLEY
COURSE INFORMATION
DEPARTMENT: Mathematics
DATE: 05/11/94
Mathematics 445
?
Introduction to
g rap
h theory
?
3
NAME & NUMBER OF COURSE DESCRIPTIVE TITLE
?
UCFV CREDIT
applications.
CATALOGUE DESCRIPTION: An introduction to graph theory and its
COURSE PREREQUISITES:
Math 243 or Cmpt 205
COURSE
C
OREQUISITES: None
MOORS
FOR EACH
PER
STUDENT
TERN ?
LABORATORY
LECTURE ?
52 ?
MRS STUDENT DIRECTED
?
MRS LEARNING ?
- MRS
?
/
?
SEMINAR
?
MRS OTHER - specify:
FIELD
EXPERIENCE
MRS
TOTAL
52
-
MRS
MRS
TRANSFERUCFV
CREDIT
??
IL
fl
?
J
NON-TRANSFER
UCFV
CREDIT
L_
J
?
I
NON-
CREDIT
Ll
TRANSFER'STATUS (Equivalent, Unassigned, Other Details)
tYBC TBA
SFU Math 445
UVIC TBA
0
P1
A
?
11W.
PAGE 2OF5
0
4
Math
NAME &
445
NUMBER
Introduction
OF COURSE
to
g ra p
h theory
COURSES FOR WHICH THIS IS A
PREREQUISITE: None
RELATED COURSES: upper level
math and computing courses
TEXTBOOKS, REFERENCES, MATERIALS
TEXT: Graph Theory with Applications
?
by A. Bondy and U. Murty
Elsevier Press
graph
COURSE
theory
OBJECTIVES:
and its
This
a
pplications.
course is intended
The aim
as
is
an
to
introduction
present the
to
basic material, together with a wide variety of applications,
both to other branches of mathematics and to real-world problems.
STUDENT EVALUATION PROCEDURE;
Students, will be given 2 midterm exams during the semester,
as well as a final exam. They will also be expected to turn in
assignments
follows:
approximately biweekly. The weighting will be as
Midterm exams 40%
Final exam
?
45%
Assignments
?
15%
.
L.
PAGE 3 OF 5
S
MATH
445
Introduction to cT
raDh
theory
NAME
& NUMBER OF COURSE
COURSE CONTENT: Topics covered will include:
matrix,
1.
Graphs
paths,
arnd
cycles
sibgraphs:
and vertex
Iso
m
orphism,
degrees.
subgraphs, adjacency
2.
Trees:
C
ut-vertices, cut-edges and Cay].ey's formula.
3. C
onnectivity: Blocks and applications of connectivity.
applications.
4.
Eulerian graphs:
Euler
tours, Hamiltonian cycles and
S. Matchings: Matchings, coverings and the assignment problem.
6.
Edge and vertex colorings: Chromatic number, Vizing's Theorem,
Brooks' Theorem and chromatic polynomials.
applications.
7.
Independence: Independent sets, cliques, Ramsey's Theorem and
formula
8.
Planar
and
graphs: Plane and planar graphs, dual
grahs,.
uIèr's
S
,-Y ^ ?
1q.
UNIVERSITY COLLEGE OF THE FRASER VALLEY
COURSE INFORMATION
DEPARTMENT: Mathematics
DATE: 01/06/94
Mathematics
NAME & NUMBER
450OF
?
COURSE
Statistical
DESCRIPTIVE
distribution
TITLE
?
theory
?
UCFV
3
CREDIT
credits
?
CATALOGUE DESCRIPTION:
This course provides the mathematical theory underlying
statistical inference. Illustration is given in terms of the
classical Gauss-Markov least squares the6ry. In addition, there
is extended discussion of the basic limiting distribution laws.
Contents include: Probability and distribution theory, Gauss-
Markov
samples.
least squares inference, sampling distributions in large
This course is directed towards students specialising in
either mathematics or statistics.
COURSE PREREQUISITES:
Math 211, 221, 270, and at least two upper-level courses in
mathematics or statistics.
COURSE COREQUISITES: None
HOURS
FOR EACH
PER
STUDENT
TERM
?
LABORATORY
LECTURE ?
60 ?
MRS STUDENT DIRECTED
?
HRS LEARNING ?
- MRS
SEMINAR ?
MRS OTHER - specify:
-
FIELD EXPERIENCE
?
MRS ?
MRS ?
TOTAL 60 MRS
TRANSFERUCFV
CREDIT
??
[
b. I
7
?
?
NON-TRANSFER
UCFV CREDIT ?
L ?
CREDIT
NON-
TRANSFER STATUS (Equivalent, Unassigned, Other Details)
UBC TBA
SFU TBA
• UVIC TEA
tJ ?
;o.
W
?
Math 450 Statistical distribution theory
?
PAGE 2 OF 5
NAME & NUMBER OF COURSE
PREREQUISITE:
COURSES FOR WHICH
None
THIS IS A
?
RELATED COURSES:
TEXTBOOKS, REFERENCES, MATERIALS
TEXTS Probability and Statistical Infernce, Volumes 1 & 2:
Statistical inference. Kalbflejsch, J.G. (Springer-Verlag, 1985)
Introduction to the Theory of Statistics. Mood, Graybill & Boes.
(McGraw-Hill)
Introduction to Probability and Statistics, from a Bayesian
viewpoint. Parts 1 & 2: Inference. D.V. Lindley (Cambridge
Un-iversity Press)
COURSE OBJECTIVES:
This course is designed to give the basic mathematical. background
underlying standard statistical theory. The formal approach given
here is motivated by applications in the the second and third
year statistical courses to which the students have hopefully
been exposed.
1.
The students should be sufficiently confident in probability
and diseribution theory to set up their own probabilistic
models in real situations.
2.
The student should be knowlegable with the classical least
squares theory used extensively in science and be able to justify
and derive the classical inference distributions.
3.
The student should be able to understand the notion of the
asymptotic distributions of the sample mean and proportion, and
of the maximum likelihood estimators, and the relevance to finite
sample size estimation procedures.
STUDENT EVALUATION PROCEDURE;
Assignments ?
10%
Midterm exams
?
30%
Final exam
?
60%
01
.
PAGE 3 PF 5
MATH 450 Statistical distribution theory
NAME & NUMBER OF COURSE
COURSE CONTENT:
I. The axioms of probability, conditional probability,
independence, Bayes' theorem. Random variables and distribution
functions. Joint, marginal and conditional distributions.
2 Mathematical expectation, moments, conditional expectation,
means
functions.
and variances of linear
combinations,
moment generating
3.
Special univariate distributions. The raultinoinial, bivariate
normal and multivariate normal distributions. Transformations of
random variables. The sum of squares of normal variables, joint
distribution of sample mean and variance, the chi-square, Student
't', and 'F' distributions.
Conditional
mean or regression with
the Tnultinom j
al and multivariate normal.
4.
The Gauss-Markov model, least squares estimators and the
normal equations, estimation of the residual variance, variance
and covariance of l.s. estimators, the analysis of variance
table. Adjustments for weights and correlation. Least squares
theory with
constraints.
S. Asymptotic distributions. The convergence of a sequence of
random variables, the laws of large numbers, the Central Limit
theorem.
6. The notion of the asymptotic distribution of an estimator.
C
UNIVERSITY COLLEGE OF
THE
FRASER VALLEY
COURSE INFORMATION
DEPARTMENT: Mathematics
DATE:01/06/94
NAME
Mathematics
& NuMBER
451OF
?
COURSE
Parametric
DESCRIPTIVE
statistical
TITLE
inference
?
UCFV
?
3
CREDIT
credits
CATALOGUE DESCRIPTION:
A course on the ideas, nomenclature and techniques of the main
schools of parametric statistical inference, namely, likelihood,
Neyman-Pearson, Bayesian. The general similarities of the
situations
inferences made
which
by
are
each
co
ntroversial
school will
will
be emphasised,
also be discussed.
but inference
This course is directed towards students specialising in either
mathematics or statistics.
COURSE PREREQUISITES:
Math 450
COURSE
COREQIJISITES:
None
•
FOR
HOURS
EACH
PER
STUDENT
TERM
?
LABORATORY
LECTURE
?
60 ?
HRS STUDENT DIRECTED
?
HRS LEARNING ?
-
MRS
SEMINAR
?
HRS OTHER - specify:
- HRS
FIELD EXPERIENCE
?
MRS
?
TOTAL 60 MRS
TRANSFERUCFV
CREDIT
?
h
I
??
1 ?
NON-TRANSFER
UCFV CREDIT ?
I ?
L I
?
NON-
CREDIT
TRANSFER STATUS (Equivalent, Unassigned, Other Details)
UBC TBA
SFTJ TBA
U
I
/IC TBA
PAGE ? OF 5
S
Math 451 Parametric statistical inference
NAME & NUMBER OF COURSE
PREREQUISITE:
COURSES FOR WHICH
None
THIS IS A
?
RELATED COURSES:
TEXTBOOKS, REFERENCES, MATERIALS
TEXTS: Probability and Statistical Inferencè, Volume 2:
Statistical inference. Kalbfleisch, J. G. (
S
pringer-Verlag, 1985)
Introduction to the Theory of Statistics. Mood, Graybill & Boes.
(McGraw-Hill)
Introduction to Probability and Statistics, from a Bayesian
viewpoint. Part 2: Inference. D.V. Lindley (Cambridge University
Press)
This
COURSE
course
OBJECTIVES:is
designed
?
to enable students to be familiar, in a
0
straightforward manner, with the standard tools of parametric
statistical inference. These will include:
1.
The method of likelihood.
2.
The frequency or Newman-Pearson approach. Where possible, the
sampling'distributjon approach will be illustrated by simulation,
3.
Bayesian inference.
In addition, there will be discussion about special problems and
techniques, such as: conditional and marginal likelihoods,
conditional tests, exact tests, the problem of the relevant
reference set.
In particular, the general similarities of the inferences made by
each school of thought will be emphasised, but inference
situations which are controversial will also be discussed.
STUDENT EVALUATION PROCEDUPE;
Assignmnts
?
10%
Midterm
exams ?
30%
Final exam
?
60%
s
oll
ILkTH 451 Parametric statistical inference
?
PAGE 3 OF 5
NAME & NUMBER OF COURSE
COURSE CONTENT:
1.
Likelihood methods: likelihood, method of maximum likelihood,
score and information functions, relative likelihood and contour
maps, likelihood regions and intervals, continuous models,
censoring, invariance, transformations, normal approximations,
numerical methods.
2.
Frequency or Heyman-Pearson methods: sampling distributions
(use of computer where possible), expected (or Fisher)
information, the likelihood ratio statistic, Pearson's chisquare
approximation, confidence intervals, tests of significance,
power, unbiasedness, uniformly most powerful tests. The
sequential probability ratio test. Sample size estimation.
3.
Special cases: nuisance parameters, the problem of the number
of parameters increasing with the sample size, conditional and
marginal likelihoods, residual maximum likelihood estimation,
sufficient and ancillary statistics, the exponential family,
conditional tests, exact tests, the reference set. (Fiducial
•
?
inference, if time allows.)
4.
Bayesian inference: prior and posterior distributions,
posterior intervals, Bayesian significance testing - the Bayes'
factor, predictive distributions and intervals, setting the prior
distribution - simple priors, invariance priors, conjugate
priors, quantification of prior knowledge, priors for multi-
parameter situations, exchangeability; the Gibbs sampler;
empirical Bayes. Sequential experimentation. Sample size
estimatibri with prior information and costs.
5.
Discussion of competing inferences in common situations.
.
UNIVERSITY COLLEGE OF THE FRASER VALLEY
?
COURSE INFORMATION
4
DEPARTMENT: Mathematics
DATE: 01/06/94
MATH 460 ?
Ooeratjons research II (stochastic)
?
3
NAME & NUMBER OF COURSE DESCRIPTIVE TITLE
?
UCFV CREDIT
CATALOGUE DESCRIPTION;
The application of mathematical methods problems in industry and
business, allowing for random occurrence. Topics covered include:
decisions under uncertainty; renewal theory,. stochastic inventory
control; Markov chains; queueing models, networks of queues;
Markov decision processes, waiting lines; simulations;
reliability.
COURSE PREREQUISITES:
Math 270, Math 360
COURSE COREQUISITES: None
FOR
HOURS
EACH
PER
STUDENTTERM
??
LABORATORYLECTURE
??
60 ?
HRS
HRS STUDENT
LEARNINGDIRECTED ?
- HRS
SEMINAR ?
HRS OTHER - specify:
- HRS
FIELD EXPERIENCE ?
HRS ?
TOTAL 60 HRS
TRANSFERUCFV
CREDIT
??
NON-TRANSFER
UCFV CREDIT ?
_____
?
NON-CREDIT
TRANSFER STATUS (Equivalent, Unassigned, Other Details)
UBC TEA
SFU TEA
UVIC TEA
Math
COURSE
Curr.
DESIGNER
Corn.
??
DEAN
J .D. Tunstall
.
-
PAGE 2 OF S
Math 460 Ocerations research II (stochastic)
NAME & NUNBER OF COURSE
COURSES FOR WHICH THIS IS A
?
RELATED COURSES: MATH 360
PREREQUISITE:
NONE
TEXTBOOKS, REFERENCES, MATERIALS
TEXT: Hillier & Lieberman, Introduction to stocahstic models in
operations research. (1990) McGraw Hill (includes 2 3.5" disks)
Reference: S.Ross, introduction to probability models, 4th
edition, (1991), Academic Press.
COURSE OBJECTIVES:
1.
To introduce the students to the fundamental probabilistic
models in applied operations research.
2.
To develop the students' skills in formulating stochastic
models in a business and industrial context.
3.
To familiarize the students with using com
puters
to solve
operational research problems in business and industry.
STUDENT
EVALUATION
PROCEDURE;
Assignments
?
20
Midterm exams
?
30?
Quizzes and short tests 10'
Final exam ?
40;
0
PAGE 3bFS
MATH 460 O
perations
research II (stochastic)
NAME & NUMBER OF COURSE
COURSE CONTENT:
1.
Review of probability theory.
2.
Decisions under uncertainty, decision trees, utility theory,
Bayesian analysis.
3.
Random variables, discrete and Continuous variables, moment
generating functions, limit theorems, stochastic processes.
4.
Renewal theory: renewal and renewal-reward processes,
regenerative processes.
5.
Applications of renewal processes: stochastic inventory
control, machine maintenance problems.
6.
Markov chains: Chapman-Kolmogorov equations, limiting
probabilities.
7.
Queuing models: M/M/i, M/G/1 systems. Variations on single
server systems.
8.
Multisex-ver queues: M/M/k, M/G/k systems. Network of queues.
9.
Applications of queuing models: assembly line problems,
telecommunications problems, traffic control problems.
10.
Markov decision processes, policy improvement algorithm,
value iteration algorithm.
11.
Applications of Markov decision processes: inventory control
and scheduling problems, optimization problems in waiting lines.
12.
Simulations: techniques for simulating random variables,
reducing variance and determining the number of runs.
13.
Reliability theory: systems with independent components,
systems with repair.
40
UNIVERSITY COLLEGE OF THE FRASER VALLEY
- ?
COURSE INFORMATION
DEPARTMENT: Mathematics
DATE:01/06/94
MATH 470 ?
Methods of multivariate statistics
?
3
NAME & NUMBER OF COURSE DESCRIPTIVE TITLE
?
UCFV CREDIT
CATALOGUE DESCRIPTION:
This course consists of the extension of the linear model methods
developed in Math 302 to the multivariate situation. The emphasis
of the course is on a range of widely used multivariate
statistical techniques, their relationship with familiar
univariate methods and the solution to practical problems. Topics
will include: Hotelling's 1'
2
, the analysis of dispersion,
repeated measures, discriminant analysis, canonical correlations,
principal components, factor analysis.
COURSE PREREQUISITES:
Math 211, 221, 270, 302 and at least two upper level courses.
COURSE COREQTJISITES: None
HOURS PER TERM
?
LECTURE ?
60 ?
HRS STUDENT DIRECTED
FOR EACH STUDENT LABORATORY
?
HRS LEARNING
?
- HRS
SEMINAR ?
HRS OTHER - specify:
- HRS
FIELD EXPERIENCE ?
HRS ?
TOTAL 60 HRS -
TRANSFERUCFV
CREDIT
?
h ?
7
I ??
NON-TRANSFERUCFV
CREDIT ??
1
I
?
?
NON-
CREDIT
TRANSFER STATUS (Equivalent, Unassigned, Other Details)
UBC TEA
SFU TBA
UVIC TEA
Math Curr. Corn.
?
J.D. Tunstall
COURSE DESIGNER ?
DEAN
act.
PAGE 2OFS
0
Math 470 Methods of multivariate statistics
NAME & NUMBER OF COURSE
COURSES FOR WHICH THIS IS A
?
RELATED COURSES:
PREREQUISITE: None
TEXTBOOKS, REFERENCES, MATERIALS
TEXT: TBA
Basic references:
Rao, C.R. (1973) Linear statistical models (chapter 8). John
Wiley & Sons.
Timm, Neil H : 'Multivariate analysis of variance of repeated
measures'. In P.R.Krishnaiah (ed), Handbook of Statistics:
Analysis of variance; Volume 1, pages 41-87, Amsterdam, North-
Holland (1980)
Berhard Flury and Hans Riedwyl (1985), 'T
2
tests, the linear
- ?
group discrimination function and their computation by linear
regression', The American Statistician, 39, 20-25.
COURSE OBJECTIVES:
1.
Understand how asound grasp of the univariate linear model
can be simply developed into an intuitive understanding of the
commonly used multi-normal statistical techniques.
2.
Be conversant with the commonly used rnultivatite statistical
methods and how to apply them to data sets using statistical
software.
3.
Become acquainted with the major multivariate criteria for the
comparison of competitive hypotheses, and inter-relationships of
these criteria.
STUDENT EVALUATION PROCEDURE;
Assignments ?
20
Midterm exams
?
4011;
Final exam ?
400;
.
S
30.
0 ?
PAGE
3ÔFS
MATH 470 Methods of multivariate statistics
NAME
.& NUMBER OF
COURSE
COURSE CONTENT:
1.
Expectation, dispersion and covariance of vector random
variables.
2.
The general multivariate normal distribution, its marginal and
conditional distributions and properties.
3.
Estimation of ji and E; the sums of squares and cross-products
matrices. Sampling and the use of the basic results on the
Wishart distribution, the distribution of special cases of Wilks'
lambda criterion and of Hotelling's T2.
4.
Tests for assigned mean values, for a given structure of mean
values, for differences between (vector) mean values of two
populations. Fisher's linear discriminant. Relationship between
linear discriminant analysis and linear regression. Mahalanobis'.
D2.
5.
The analysis of dispersion, test of linear hypotheses, test
for additional information. Test for differences in mean values
between several populations.
6.
Multivariate regression. Repeated measures, growth curves.
7.
Discussion of criteria and their interrelationships: Wilks'
lambda, Hotelling-Lawley trace, Roy-Pillai largest root.
8.
Discriminant analysis, the equivalent
discrimination
score.
9.
Canonical correlations.
Canonical
discriminant functions.
10.
Principal components.
11.
The ideas underlying factor analysis; the principal factor
method. Modern methods illustrated by use of software.
.
11
