Download Category II Permanent Course Request

Category II Permanent Course Request
Course Designator/Number
Select one:
MTH 463/563,
464/564, 465/565
New
Proposed Effective Term
X Change
Fall
Academic Year
2002-03
Drop
New Course/Sequence
A course syllabus and liaison must accompany this request.
Indicate Schedule type(s):
A=lecture
B=discussion
C=recitation
D=laboratory
E=seminar
F=independent studies
G=research
H=activity
I=experimental
J=internship
K=correspondence
L=tutorial
M=practicum
N=reading & conference
O=exper/co-op education
P=programmed instruction
Q=thesis
R=studio
A-F (includes I,W,R,S/U)
Select grading mode:
S=project
T=telecourse/distance learning
U=externship
W=workshop
Y=world-wide web
Z=modular
P/N
Repeat Value (for courses with variable credit, e.g., 1-16): If students are allowed to repeat this course, indicate the maximum
number of credits that students will be allowed to count toward graduation.
Does this Replace an Experimental “X” Course?
Yes
X No
Change in Existing Permanent Course
A course syllabus must accompany this request if title, credit, description, prerequisite, or corequisite is being changed.
Check all that apply:
Prefix/Designator
Number
X Title
Credit
X Description
Prerequisite
Is this an already approved Baccalaureate Core/WIC Course?
X Corequisite
Crosslisting
yes-BCC
yes-WIC
X no
Course equivalency (should the changed course be treated as equivalent to the existing course -purpose is to determine whether
students who have taken the existing course may also take the changed course for full additional credit): yes
Drop Course/Sequence
Is this an already approved Baccalaureate Core/WIC Course?
yes-BCC
yes-WIC
no
PROPOSED CATALOG LISTING: (Title: no more than 60 characters); Description: 20-25 words; include credits.)
MTH 463/MTH 563, PROBABILITY I (3) An introduction to probability theory; topics covered include: the
axioms of probability, probability spaces and models, independence, random variables; densities,
distributions, expectation, and variance; probability inequalities, the law of large numbers, and the binomial
central limit theorem. PREREQ: MTH 312 or consent of instructor.
MTH 464/MTH 564, PROBABILITY II (3) Transformations of random variables; sums of independent
random variables, generating functions, characteristic functions, the central limit theorem and other weak
limit theorems. PREREQ: MTH 463/MTH 563 and MTH 341 or consent of instructor.
MTH 465/MTH 565, INTRODUCTION TO STOCHASTIC PROCESSES (3) Foundations of stochastic
processes. Topics covered may include Markov chains, Poisson processes, renewal processes, random walk,
and financial mathematics. PREREQ: MTH 464/MTH 564 or consent of instructor.
EXISTING CATALOG LISTING:
MTH 463/563, 464/564, 465/565 THEORY OF PROBABILITY (3, 3, 3). Random variables, central limit
theorem; distributions of standard statistics; Markov chains, continuous and discontinuous stochastic
processes. PREREQ: MTH 312 and MTH 341. COREQ: MTH 313.
Last updated: 5/16/00
(Proposed Short Banner Title for Schedule of Classes and Transcripts (no more than 30 characters)
MTH 463/563 PROBABILITY I
MTH 463/563 PROBABILITY II
MTH 463/563 INTRO STOCHASTIC PROC
JUSTIFICATION:
The Mathematics Department recently completed a thorough review of the undergraduate curriculum for
mathematics majors. The result of that review is an extensively revised major that now is based on a set of
core courses that all majors take and a set of seven “breadth” elective courses that treat significant areas of
modern mathematics. Majors must take five courses from the seven areas. The revised version of MTH
463/563 is a course in the breadth category. It gives mathematics majors a modern introduction to important
techniques and theoretical results in probability theory.
4XX/5XX DISTINCTION (where relevant):
Students taking the class for graduate credit are graded on a more demanding curve. In addition, depending
on the instructor, students taking the course for graduate credit may be required to solve additional problems
on exams and/or complete more demanding assignments during the term.
LIAISON (Refer to directions. List here individuals/units that received written notice of the proposed changes. If no liaison
contacts were made, state below why such contact was not needed. Be specific. Attach a copy of your liaison letter with all
responses. Attach a memo stating your position on any unfavorable responses):
This proposal simply revises an existing course that was designed primarily for undergraduate and graduate
mathematics majors and to serve certain statistics graduate students. The revisions were made with the
intention of serving well both mathematics and statistics students. MTH 463/563 is one of the seven breadth
choices in the revised mathematics major. Copies of the course descriptions have been sent to the head
advisors in the College of Science and the College of Engineering and to the Chair of Statistics. The head
advisors and ST chair were invited to send input regarding the proposals.
PREREQUISITES (This course serves as a prerequisite for the following courses):
NA
COREQUISITES (This course serves as a corequisite for the following courses):
NA
CROSSLIST (List any crosslisting equivalents. Endorsement signatures are required for each department/college.)
Endorsement Signatures
Department Chair/Head
Date
Chair, College Curriculum Committee
Date
Dean, College
Date
Contact person/Proposer
Date
Email address and phone for contact:
Date
Submit the original (additional copies are not necessary) and any attachments to the college. The college will forward the
proposal on to Undergraduate Academic Programs, Academic Affairs. Once the proposal is received in Undergraduate Academic
Programs, the process will be tracked and may be viewed on the World Wide Web. http://osu.orst.edu/dept/academic/aa/curric/
REVIEW PROCESS: For Use by Undergraduate Academic Programs/University Curriculum Council:
Tracking ID#
Received in Undergraduate Academic Programs:
Sent to Reviewer 1 (Academic Programs Coordinator)
Approved Modifications made to:
Sent to Graduate Council
Approved Modifications made to:
Sent to Reviewer 2 (liaison)
Approved Modifications made to:
Sent to Reviewer 3 (Curriculum Council Chair)
Approved Modifications made to:
Sent to Reviewer 4: (Director UAP)
Final Approval Final Modifications made to:
Notification sent to: Dept, College, Catalog Coordinator, Schedule Desk, Registrar’s Office, Admission and
Orientation, Graduate School
Sent to Catalog Coordinator
Entered into Banner and returned from Catalog Coordinator
Additional Notes:
(006) Last updated: 5/16/00
Syllabus
MTH 463/563 Probability I
Updated 11/14/01
Summary:
Topics:
This course is one of the seven breadth electives in the mathematics major.
It provides a systematic introduction to the basic concepts of probability
theory.
PREREQ: MTH 312 or consent of instructor.
1.
The axioms of probability, probability spaces, and probability as an
additive set function on sigma-fields
2.
Independence of sets and collections of sets.
3.
Conditional probability and Bayes Theorem.
4.
Random variables – discrete, continuous, and mixed.
5.
Expectation and variance. Conditional expectation.
6.
Probability inequalities: The Cauchy-Schwarz inequality and
Chebyshev’s inequality.
7.
Law of rare events and law of large numbers.
8.
The binomial central limit theorem.
Possible Texts:
Jean Jacod, Phillip Protter, Probability Essentials, SpringerVerlag, NY
Geoffry Grimmett, D. Stirzaker, Probability and Random
Processes, Oxford Publ.
LEARNING OBJECTIVES FOR
MTH 463/563 Probability I
1.
2.
3.
4.
5.
Learn the axioms for a probability space and give important examples of such spaces.
Be able to develop an appropriate probability space given an applied situation that involves randomness.
Distinguish both intuitively and analytically between dependent and independent events.
Learn and apply the notion of conditional probability and use Bayes theorem.
Be able to define and illustrate with examples random variables, their expectation, and their variance.
Explain the qualitative significance expectation and mean.
6. Learn and apply the basic inequalities of elementary probability, the law of large numbers, and the
binomial central limit theorem.
ASSESSMENT:
1. The ability to solve problems, to do proofs, and reason abstractly with probabilistic situations will be
evaluated through regular homework assignments.
2. A midterm and comprehensive final will be used to further evaluate understanding of the basic
properties of probability, conditional probability, random variables, and the student’s ability to reason
abstractly with them.
Syllabus
MTH 464/564 Probability II
Updated 11/14/01
Summary:
Topics:
This course is a continuation of Probability I. It provides a deeper
investigation of multivariate distributions and the distribution of sums of
independent random variables. More powerful mathematical tools such as
generating functions and Fourier transforms are used to develop limit
theorems, including the celebrated central limit theorem.
PREREQ: MTH 463/563 and MTH 341 or consent of instructor.
1.
Multivariate distributions and transforms of random variables.
2.
Multivariate Gaussian random variables.
3.
Generating functions associated with discrete random variables.
Weak limit theorems for sums of independent discrete random
variables.
4.
The characteristic function of a random variable. Weak limit
theorems for sums of independent random variables.
5.
The central limit theorem.
Possible Texts:
Jean Jacod, Phillip Protter, Probability Essentials, SpringerVerlag, NY
Geoffry Grimmett, D. Stirzaker, Probability and Random
Processes, Oxford Publ.
LEARNING OBJECTIVES FOR
MTH 464/564 Probability II
1. Learn the basic properties of multivariate probability distributions and multivariate random variables,
especially normal distributions.
2. Be able to develop an appropriate probability space given an applied situation that involves multivariate
distributions.
3. Be able to define the characteristic function of a distribution and use it to develop properties of the
distribution.
4. Learn and apply the weak limit theorems for sums of independent random variables.
5. Learn and apply the central limit theorem.
ASSESSMENT:
1. The ability to solve problems, to do proofs, and reason abstractly with multivariate distributions and
random variables will be evaluated through regular homework assignments.
2. A midterm and comprehensive final will be used to further evaluate understanding of characteristic
functions, generating functions, and limit theorems for random variables, and the student’s ability to
reason abstractly with them.
Syllabus
MTH 465/565 Introduction to Stochastic Processes
Updated 11/14/01
Summary:
Topics:
This course introduces students to the study of stochastic processes.
Topics covered may include Markov chains, Poisson processes, renewal
processes, random walks, martingales, and financial mathematics. The
topics covered in class may vary from year to year.
PREREQ: MTH 464/564 or consent of instructor.
1.
Definition of a stochastic process. Finite-dimensional distributions.
2.
The Markov property and Markov chains. Invariate distributions and
equilibrium. Periodicity. Absorbing states.
3.
Poisson processes. The Markov property.
4.
Renewal theory and applications.
5.
Random walks. The reflection principle. The Markov property. The
arcsine distribution.
6.
Martingales and an introduction to the stochastic processes of
financial mathematics.
Possible Texts:
R. Bhattacharya, E. Waymire, Stochastic Processes with
Applications, Wiley.
LEARNING OBJECTIVES FOR
MTH 465/565 Introduction to Stochastic Processes
1. Be able to define a stochastic process, such as a Markov process or Poisson process, and give important
examples of such processes as relates to the particular processes covered in the course.
2. Be able to develop an appropriate stochastic model given an applied situation whose description
naturally involves such models. The models developed will depend on the topics covered in the course.
ASSESSMENT:
1. The ability to solve problems, to do proofs, and reason abstractly in situations that involve stochastic
process will be evaluated through regular homework assignments.
2. A midterm and comprehensive final will be used to further evaluate understanding of stochastic
processes, Markov processes, martingales, and applications of such processes and the student’s ability to
reason abstractly with them.
LIAISON:
The letter on the following page was sent to potentially interested departments. We received no unfavorable
comments by the response deadline.