Financial Mathematics Concentration

A concentration in Financial Mathematics is being proposed for the Applied Math BS.  Except for reducing the number of Science courses with a lab, this concentration fits into the AMA program.  For more information on this proposal, please visit

http://www.math.ncsu.edu/selfreg/proposals/

Posted at 02:55PM Dec 12, 2007 by Jeffrey Scroggs in Math Undergrad Course and Curriculum Committee  | 

Applied Math BS Curriculum

Here is an informal proposal for changing the Applied Math BS curriculum. It is a discussion document, not a formal proposal.  Michael Shearer.

B.S. Applied Mathematics Curriculum:  Proposed Changes
Discussion Document. Michael Shearer

Background

The BS in Applied Mathematics was introduced in 1995. A curriculum was formulated based on existing courses, and has remained unchanged ever since.  The purpose of this proposal is to suggest changes that will help ensure our students graduating with an Applied Mathematics BS degree have received a thorough training in Applied Mathematics, suitable for graduate work in Applied Mathematics or Multidisciplinary Studies with a major mathematics component. A further motivation is to train students for an increasingly technological work environment in which both traditional and applied mathematics skills and knowledge are valued.

The Applied and Computational Mathematics Option at Virginia Tech. has a structure that could be useful for our BS degree.  The Virginia Tech.  model has four components: area of applications; scientific computation; technical tools of applied mathematics; mathematical rigor. 

Proposal

The BS in Applied Mathematics at NC State University needs a common core  of courses in addition to a grounding in traditional mathematics.

Currently, students must take either MA 341 (Applied Differential Equations I) or MA 351 (Introduction to Discrete Mathematical Models). We propose that MA 341 be required of all students in the BS Applied Mathematics program.

The core advanced courses we propose are as follows:

1. Mathematical methods/modeling/asymptotics
This required course at the junior level includes modeling, data analysis, scaling and nondimensionalization, asymptotics. The current class MA 430 would fulfill this, but with a different syllabus from current practice. Since MA 430 and 432 are modeling courses, it might be better to introduce a new course MA 429, and retain MA 430, 432 as complementary modeling options, with students being required to take one or the other.

2. Numerical analysis and scientific computing.  The existing course MA 427 should be required, or possibly MA 428 for students more interested in discrete mathematics, combinatorics, applications of algebra.


Applied mathematics electives.  Two or more courses should be required from a list of electives such as:

MA 325 Intro to applied math
MA 351 Intro Discrete Math Models (currently alternate to MA 341)
MA 401 (or MA 534) Applied Differential Equations II (PDE)
MA 402 Computational Math, Models, Methods and Analysis
MA 421 Probability
MA 416 Combinatorics
MA 428 Introduction to Numerical Analysis II
MA 430 Mathematical Models in the Physical Sciences (if not required)
MA 432 Mathematical Models in Life and Social Sciences
MA 437 Applications of Algebra
MA 440 Game Theory
and/or graduate-level classes such as MA 573-574, MA 580.

Remarks: MA  351, MA 430 should be examined, and offered on a regular basis. Are these serving the applied mathematics majors appropriately? MA 430 taught by Ron Fulp focuses on Mathematical Physics rather than mathematical methods or models.

Bob White's Intro to Applied Math, MA 325 is positioned as a light introduction to the breadth of applied mathematics, suitable for sophomore students.

MA 402 probably should not be allowed in addition to MA 427, as there is undoubtedly a lot of overlap.

The role of a complex variables course, MA 513, in the Applied Mathematics BS curriculum should be discussed. It is generally taught from an applied perspective, with emphasis on the elegant interlocking of ideas and constructions, and some treatment of applications such as potential fluid flow and electrostatics.

Students interested in physical science or engineering applications should take a PDE course, either MA 401 or MA 534, and would not get credit for MA 501.
Can we cross-list 501 as a 400 level class, and make MA 401 a math majors class?    Suitable undergraduate texts are by: Strauss (with a new edition about to appear); Logan; Haberman. 

The applied electives should be retained, to encourage students to take classes outside the major.

Posted at 02:43PM Dec 11, 2007 by Michael Shearer in General  |  Comments[2]

PAMS Late Schedule Revision Policy

I have posted the new Late Schedule Revision Policy for PAMS at
http://www.math.ncsu.edu/selfreg/undergrad/Forms/LateRevisionPolicyPAMS.pdf

Nothing much has changed -- students still need a documented medical/emotional/fiscal(job) reason to make a change after the deadline.

Posted at 03:10PM Dec 07, 2007 by Jeffrey Scroggs in General  | 

MA 205 (new course)

We propose a new Matrix Algebra Course, MA 205.  Comments on this course are being solicited, both from within the Math Dept, and campus-wide.

The most recent information on the proposal is included at the web site below, especially the "Signature Page" and "Attachments".

www4.ncsu.edu/eos/users/w/white/www/white/mamac/Links.htm

Posted at 09:28PM Nov 19, 2007 by Jeffrey Scroggs in General  | 

MA 405 assessment/discussion

We are currently assessing MA 405.  Dr. Misra's email solicition for comments from faculty appears below, followed by a proposed course outline.  Several faculty responded to this solicitation, and their comments will appear here as Kailash has time to  summarize them.

-----------email soliciting comments----------------

Dear Colleagues

You are receiving this email since you either taught MA405 or taught a course which has MA405 as a prerequisite within last three years.

The MUCCC (Math. Undergraduate Course and Curricum Committee) is reassessing MA405 this year since last assessment was done more than 10 years ago (in 1989). During this period several concerns have been raised by faculty from within and outside of the Mathematics department. During the current assessment the MUCCC would like to address those concerns. Note that this is a core course for Math. majors and some graduate students outside the mathematics department take this course for credit. In the attached draft of the course content the MUCCC has agreed on the core content of this course with some flexibility (four
lessons) for the instructor to choose appropriate topic of their interest. We hope that this will help maintain the unifirmity and rigor.

MUCCC requests your comments on the attached draft on or before Nov. 9, 2007. Please email your comments to me (misra@math.ncsu.edu).

Thanks for your kind cooperation.

Best regards,
Kailash Misra
Member, MUCCC

--------------------proposed outline (attachment to email)--------

                COURSE OUTLINE- Draft-1

MA405--- Introduction to Linear Algebra and Matrices

Text Book: Linear Algebra with applications, 7th Edition, by S. Leon

Prerequisite: MA241

Co-requisite: MA242

The following schedule is for MWF sections. It should be modified appropriately for TTh sections.

LESSON    SECTIONS        TOPICS AND COMMENTS

1-3        1.1, 1.2        Linear systems of equations, elementary row
                    operations, reduction to row echelon form and
                    Gaussian eliminations.

4-6        1.3, 1.4        Definition of a matrix, addition, scalar
                    multiplication, matrix multiplication and properties,
                    special matrices, elementary matrices, inverses,
                    transpose and LU-decomposition. Also mention
                    briefly about partitioned matrices and their multi-
                    plications without too much details as in 1.5.

7                    review chapter 1

8                    Test 1

9-11        2.1-2.3            Determinants and their properties, formula for
                    inverse, Cramer?s rule.

12-14        3.1-3.3            Vector space, subspaces, spanning set, linear
                    independence

15-17        3.4-3.6            Basis, dimension, coordinate matrix, transition
                    matrix, fundamental subspaces associated with
                    a matrix such as row space, column space and null
                    space, rank and nullity of a matrix.

18                    review chapters 2 and 3

19                    Test 2



20-22        4.1-4.3            Definition and examples of linear transformations,
                    matrix representations of linear transformations
                    from Rn to Rm, similarity between two
                    nxn-matrices, (Remark: restrict this chapter to
                    only n-spaces. Mention that similar matrices
                    represent the same linear transformation and
                    motivate the concept of diagonalization.)

23-25        6.1, 6.3        Eigenvalues and eigenvectors, diagonalization
                    of a square matrix, determination of eA  for a
                    diagonalizable matrix. (Remark: Although we
                    restrict our focus to real eigenvalues, mention
                    that we can have complex eigenvalues for a matrix
                    with real entries.)

26                    Review chapter 4 and 6.1, 6.3

27                    Test 3

28 -29        5.1,5.2            Scalar product in Rn , Orhogonal subspaces.

30-33        5.4-5.6            Real Inner Product spaces, Orthogonal and
                    Orhonormal sets, Gram-Schmidt Orthogonalization
                    Process, QR-decomposition and least square
                    Problems. (Remark: Point out the difference for
                    Complex inner products, Derive the normal
                    Equation as in 5.3 and then apply QR-decompo-
                    -sition to simplify.)

34        6.4            Diagonalization of real symmetric matrices by
                    orthogonal matrices. Show that the eigenvalues
                    of a real symmetric matrix are real and its eigen-
                    vectors corresponding to distinct eigenvalues are
                    orthogonal. (Remark: Define Hermitian matrices
                    and point out that they have similar properties.)

35                    Review Chapter 5 and 6.4

36                    Test 4

37-40                    Related topics choosen by instructor.
                    (For example, 6.2, 6.5 and/or 6.6)

41-42                    Review for final exam.         

Posted at 10:38AM Nov 13, 2007 by Jeffrey Scroggs in General  |  Comments[3]

MA 405 as a pre-requisite for MA 407

The proposed minor action to add MA 405 as a pre-requiste for MA 407 passed the PAMS UAAC today (11/13/07).

Posted at 10:22AM Nov 13, 2007 by Jeffrey Scroggs in PAMS Undergraduate Academic Advisers Committee  | 

Notes from Oct 24

Notes from our meeting
Wednesday, October 24

In attendance were

John Griggs
Kailash Misra
Sandy Paur
Jeff Scroggs
Jack Silverstein
Mike Singer
Bob White

Next meeting:
Nov 28, 1:30-2:30, HA 222

The committee voted in favor of adding MA 405 as a prerequisite to MA 407.  (5 in favor, 1 abstain)

Progress on MA 205 was reviewed -- consultation with other departments has been added.  (MUCCC already voted to support this action.)

Suggestions to modify the assessment document into something appropriate for our external review were provided.  Samples from PY and CH have been provided.

John Griggs anticipates proposing a new GER class related to the mathematics of sports.

Posted at 10:33AM Nov 04, 2007 by Jeffrey Scroggs in General  | 

Notes from Sept 25

Our first meeting this semester was
9-10am
Tuesday, Sept 25
HA 222

In attendance was

Jeff Scroggs
Kailash Misra
Jack Silverstein
Mike Singer
Bob White

Action items -- reserve the next meeting date, and members that missed need to indicate how they plan to contribute to the tasks.  More information appears below.


Notes from the meeting

1. We selected Wednesday @ 1:30 to meet.

Please reserve October 24 @ 1:30 for the next meeting (if you have a conflict, suggest another Wednesday)

2. Form subgroups include
Renew MA 405, with an idea to a revised course description
Misra

      BA degree proposal (discussion and curriculum proposal)
      BS revision (discussion and curriculum change, if needed)
Misra and Singer

      review of MA GER courses
as needed, once university committees provide guidelines

      External Review preparation
Silverstein and Scroggs

Members needing to select tasks: Charlton, Griggs, and Paur

ex-officio member, Tran, only attends meetings


3. MA 205 proposal passed unanimously pending favorable comments being collected during the consultations.  A minor clarification to the Resources statement was proposed. (forms are online at www4.ncsu.edu/eos/users/w/white/www/white/mamac/Links.htm)

4. ABM for FM/AMA proposal passed unanimously.  MA 407 and MA 405 will be switched in the 10-semester display.

Posted at 10:33AM Nov 04, 2007 by Jeffrey Scroggs in Math Undergrad Course and Curriculum Committee  |