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Awards

SUMMER 2012 NSERC USRA PROJECT DESCRIPTIONS

                   _______________________________________________

Joint Supervisors: Adam Oberman and Paul Tupper

Project: nonlocal diffusions and mathematical finance (2 students)

A classic Nobel winning problem by Merton is the design of optimal portfolios.

The solution of this problem is based on the concept of stochastic control: optimizing your expected utility in a random environment.

Newer models take into account nonlocal effects, which model the fact that stock prices sometimes make unexpected large jumps.

This project will involve learning some backgrounds and performing simulations.

                     __________________________________________________

Joint Supervisors: Adam Oberman and Razvan Fetecau

Project: Flocking behaviour and nonlinear equations (2 students)

The behaviour of flocking birds and insects has been used as a model for a variety of topics, such as reputation management on the internet, political opinion forming, and controlling drone planes.   This project will involve learning background material on ODE and PDEs for modeling flocking, and performing simulations.

                     __________________________________________________

Surpervisor: Jason Bell

Project: Power series satisfying a homogeneous linear differential equation 

This project looks at the following question: If a power series with integer coefficients and finite radius of convergence is the solution to a non-trivial homogeneous linear differential equation, does it follow that it is the diagonal of a multivariate rational function?  At the moment this is known only in the case that the power series is algebraic and for some other special classes.  The background needed is some number theory and algebra.  Applicants should be able to do some programming and should also be familiar with LaTeX.

                    __________________________________________________

Supervisor: Jonathan Jedwab

Project: Combinatorial Problems Arising in Digital Communications

The project will involve the study of combinatorial problems arising in digital communications. See here for background on the general area of research, and here for examples of previous USRA projects. Students should have completed MACM 201, and preferably have some programming experience. However, the most important attributes are enthusiasm, persistence, and a willingness to learn new skills.

 
                     __________________________________________________

Supervisor: Paul Tupper

Project: What is the diversity analogue of uniform spaces?

Topologies and metric spaces are two fundamental notions of space in
mathematics. Every metric space has a standard topology associated
with it. However, it turns out that intermediate between topologies
and metric spaces there are uniform spaces (also known as
uniformities) which do not have a metric but still have the concept of
uniform convergence.

On the other hand, my colleague David Bryant and I have developed a
generalization of metric spaces called diversities. In a diversity,
any finite set of points has associated with it a measure of how
"diverse" it is. For pairs of points, this reduces to a metric.

We want to know what is the analogue to uniform spaces for
diversities. The student will work to answer this question by
familiarizing themselves with the concepts of topologies, metric
spaces, uniform spaces, and diversities, and the relations between
them. Category theory may play an important role in discovering the
correct analogue, but no prior knowledge of this is required.

The only prerequisite for this project is good performance in Math 320
or equivalent.

                __________________________________________________

Supervisor: Manfred Trummer

Project: High-order methods for differential equations

This project investigates spectral methods and radial basis function methods for solving differential equations with a focus on stability and adaptivity.  Includes theory, numerical experiments and applications. Requires basic familiarity with Matlab.

                   __________________________________________________

SUpervisors: Peter Borwein and Vahid Dabbaghian

Project: Application of Fuzzy Logic in Complex Social Systems


Human decision-making behavior is a fuzzy system. Therefore, fuzzy models, and in particular Fuzzy Cellular Automata (FCA), can be applied for better understanding the dynamic of urban transformations, such as infectious diseases, crimes, and other social disorders, among individuals in a high risk society. The models will be developed in the software package Matlab, so we expect that students have some computer programming skills.

                _________________________________________________

Supervisor: Karen Yeats

Project: c2 invariants of Feynman graphs.


The c2 invariant of a scalar Feynman graph is an arithmetic invariant which gives information about the Feynman integral but is much easier to compute.  There are many basic things which we do not know about this invariant.  This project is to compute some examples and so develop some reasonable conjectures.

The student should have a taste for discrete problems and some background either in discrete math or in number theory.  No background in quantum field theory is necessary.  The project will entail some programming.

                         __________________________________________________

Professor Michael Monagan 

Project: Computational Algebra Projects 


The Computer Algebra Group at SFU is a group of faculty and students 
interested in computer mathematics and systems like Maple and Magma. 
We presently have a MITACS project, a joint research project with the 
Maple company where we are developing algorithms and software for 
doing mathematics. For example, the Maple company asked us in 2004 
to develop a package for graph theory and now they would like us to 
develop one for computational group theory. 

We are looking for one student, a mathematics student or a computing
student, to work on one or both of the following projects. 

Project 1. Developing a Maple package for computations in finite groups. 

Students need to have taken a first course in group theory, 
e.g. MATH 341 Groups at SFU. Students need basic programming 
skills and an interest in finite groups. 

Project 2. Extending Maple's graph theory package. 


 Students need to have taken a first course in graph theory,
 e.g. MATH 345 Graph Theory at SFU, or a computing course on
 graph theory algorithms, e.g. CMPT 405 Design and Analysis of
 Computing Algorithms at SFU.  Students need basic programming
 skills and an interest in graph theory algorithms.

Both projects will be done in Maple. Familiarity with Maple would 
be helpful but it is not essential. However, both projects will 
involve a significant amount of programming and experimentation. 
To see what summer NSERC students have done in previous years, 
please take a look at the posters at 

http://www.cecm.sfu.ca/research/posters.shtml 

 

                        __________________________________________________

 

Project Title: Computing Flow Polynomials

Supervisors: Bojan Mohar and Jessica McDonald

 

There are many interesting open conjectures about so-called ``flow polynomials'' of graphs (see eg [1], [2], [3]).  This project will be about computing these polynomials for certain graphs, particularly graphs where all vertices have degree three. The student will look for explicit formulas for flow polynomials of graph families (eg. prisms, generalized Petersen graphs, etc.), and write a computer program based on a known recursive formula called the contraction-deletion formula (see [1]). With this project, we would hope to provide good evidence for conjectures about flow polynomials (or perhaps even disprove one).
[1] Page 563 of Graph Theory by J. A. Bondy and U.S. R. Murty (Springer, 2000)

 

            __________________________________________________

Supervisor: Mary-Catherine Kropinski

Title: Integral Equation Methods and Fluid Dynamics (2 students or 1 student who chooses 1 project) 


Integral equation methods have become increasingly popular in computational simulations involving the solution to partial differential equations (PDEs). One important advantage over finite element or finite difference methods for solving PDEs is dimension reduction: unknowns are distributed about the boundary instead of the entire domain. There are two projects involving integral equation methods and fluid dynamics: 

Project 1: Vortex Motion on the Sphere 
This project involves computing the motion of vortices on the earth's surface in the presence of multiple islands. This requires coupling the solution to an integral equation with a set of ordinary differential equations for the motion of the vortices. The work will focus on accurate time integration methods for this problem. 

Project 2: Integral Equation Formulations in Fluid Dynamics 
This project involves reformulating the Navier Stokes equations as integral equations. In addition to computing, this work will involve analysis. 

Both of these projects will require basic familiarity with matlab. 

 

             __________________________________________________

Joint: Adam Oberman and Steve Ruuth

Project: Applied math for movie special effects, video game design and image registrations (2 students)

 

Applications of variational methods and nonlinear partial differential equations to problems in image processing (image denoising, image registration) and surface and volumen deformations which are used for gaming and film special effects.

 

           __________________________________________________

 

Supervisor: D Muraki

Project: Computation of Fluid Models for Atmospheric Science

Undergraduates in the third and fourth year of their degree are invited to join a research group that investigates fluid mechanical models for atmospheric sciences. There are active projects that investigate a variety of atmospheric phenomena.  One such project would involve using a simple computational model for fluid flows on a sphere, and compating the results with stratospheric weather data.  Some background in a differential equations is essential and proficiency in a computational environment such as Matlab is preferable.  Students taking MATH 462 in Spring 2012 will be well-prepared for this type of research.

             __________________________________________________

Supervisors: Tom Brown and Veselin Jungic

Title: Double arithmetic progressions

Abstract: This project is built around the following open problem: For a given positive number r greater than 1, is there a positive number w*(r,3) such that for any r-partition of the interval [1,w*(r,3)] there is a part A={x_1<x_2<...} that contains a 3-term arithmetic progression x_i, x_j, x_k with he property that the indices i, j, k also form an arithmetic progression? Variations of this problem and its relation with the problem of the avoidability of additive squares will also be considered. The student will also become familiar with van der Waerden’s Theorem and some other fundamental theorems in Ramsey theory.

           _______________________________________


Supervisor: John Stockie and JF Williams

Project: Why don't honeybees freeze in winter?  

When a new queen honeybee is born, the colony splits in two and one queen leads half the colony off to find a new home.  Until the bees are able to find a suitable sheltered location, they first form a cluster that hangs from a tree limb in the open air.  In winter, the bees would quickly perish without some way of keeping themselves warm.  Our aim is to study the phenomenon of "thermoregulation" in which honeybee clusters generate heat by vibrating their flight muscles thereby keeping themselves, and the new queen in the centre of the cluster, from freezing to death.  This project will apply techniques from applied mathematics such as dimensional analysis, modelling with differential equations, and numerical methods.  So we are looking for a student who has taken the courses MACM 316 and MATH 310, or equivalent.

By the way, this project will also answer the equally compelling question: How do seemingly defenseless honeybees protect themselves from attacking teams of giant killer wasps? 

         _______________________________________

Supervisor: Nils Bruin

Project: Explorations in Arithmetic Geometry

Arithmetic geometry studies the interaction between geometry and number 
theory. This leads to a particularly rich theory with many deep and 
surprising results. It is also an area in which mathematical 
experimentation has turned out to be of essential importance. Once one 
assumes some deep standard results it is often possible to do meaningful 
numerical experiments with relatively elementary means. The aim of this 
project is to undertake such experimentations. The exact details will be 
established in coordination with the student.


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Undergraduate Awards, Bursaries and Scholarships

Carefully read the regulations that govern all university, private and endowed scholarships for continuing students over which Simon Fraser University has jurisdiction. The Financial Assistance and Awards section of the calendar lists all awards, bursaries and scholarships available at Simon Fraser University and how they are governed.


| Dean of Science AwardCanadian Federation of University Women - North Vancouver Bursary |
| Evelyn and Leigh Palmer Scholarship | Goel Memorial Scholarship |
| Margaret Lawson McTaggart-Cowan Alumni Bursary | Math Endowment Award | Putnam Awards |
| Raytheon Canada Limited Scholarship for Native Students | Rogers Sugar Ltd. Bursaries |
| Ronald Harrop Award for Excellence in Mathematical Sciences |


Title: Dean of Science Award 
Value: $250 
Awarded: Fall 
Description: Awarded on the basis of academic merit to a student in the Faculty of Science, who has completed a minimum of 90 semester hours in a major or honors degree program. The prize will be based upon the student's cumulative GPA in the previous two semesters of full-time study at Simon Fraser University (at least 12 semester hours credit in each semester) and the nominee will be nominated by the Faculty of Science undergraduate curriculum committee.
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Title: Canadian Federation of University Women - North Vancouver Bursary 
Value: $1000 
Awarded: Spring 
Description: To a female undergraduate student enrolled in the 2nd, 3rd, or 4th year in any math or science Faculty or Professional School. The recipient should be in financial need and in satisfactory academic standing. The recipient must be a resident of North Vancouver or a graduate of a North Vancouver Secondary School (School District #44).
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Title: Evelyn and Leigh Palmer Scholarship 
Value: $3000 
Awarded: Fall 
Description: The scholarships are granted in any semester based on academic merit to undergraduate students in a major or honors program in the physical sciences (Physics, Applied Physics, Mathematical Physics, Chemical Physics, Chemistry, Molecular Biology and Biochemistry, or Physics and Physiology).Applicants should have completed at least 60 SFU semester hours toward the requirements for a degree and have completed at least 30 hours in two of the last three semesters in which they were enrolled.
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Title: Goel Memorial Scholarship 
Value: $350 
Awarded: Fall 
Description: To a student who has demonstrated overall excellence in the Department of Mathematics and Statistics. Nomination required from the Chair of Mathematics. This scholarship has been established by Dr. and Mrs. D.P. Goel in memory of Mrs. Shakuntala Goel.
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Title: Margaret Lawson McTaggart-Cowan Alumni Bursary 
Value: $675 
Awarded: Fall 
Description: To a female student who is majoring in Mathematics and who has completed at least two full-time semesters at Simon Fraser University.
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Title: Math Endowment Award 
Value: $100 
Awarded: Summer 
Description: Awarded to a student in each of MATH 242, 314, 320, 332, 343 and MACM 202 for excellent achievement.
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Title: Putnam Awards 
Value: $100 
Awarded: Spring 
Description: Awarded by the Department of Mathematics and Statistics to Simon Fraser University students listed as top participants in the William Lowell Putnam Mathematical Competition. The winners will be determined according to the official list provided by the organizers of this competition. The ranking and the financial value of the award are as follows: 
P (Putnam fellow) $350 
N $300 
H $250 
I $200 
II $150 
III $100
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Title: Raytheon Canada Limited Scholarship for Native Students 
Value: $750 
Awarded: Fall 
Description: To a native undergraduate student with high academic standing at Simon Fraser University. Preference will be given to students majoring in Engineering Science, Computing Science, Mathematics, Physics or Business Administration.
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Title: Rogers Sugar Ltd. Bursaries 
Value: $1000 
Awarded: Fall 
Description: To undergraduate students, who are in their third or fourth year of study at Simon Fraser University. Two bursaries are available to students majoring in Business Administration, and three bursaries to students majoring in Economics, or the Sciences, including Mathematics and Statistics.
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Title: Ronald Harrop Award for Excellence in Mathematical Sciences 
Value: Book price and certificate 
Awarded: Summer 
Description: The Ronald Harrop Award is given to a student doing a major or honors degree in the Department of Mathematics who have completed 100 hours or more of University work, at least 60 of them being at Simon Fraser University, and who, in the semester in which they completed that 100th hour, had an upper division grade point average of at least 4 and a cumulative grade point average of at least 3.9. No student shall receive the award more than once.
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Undergraduate Awards

Mathematics Undergraduate Research Prizes (click here for citations)

         2010

  • Yuanxun (Bill) Bao
  • Michael Fry
  • Gordon Hiscott
  • Aleksandar Vlasev

        2009

  • Ryan Coghlan
  • Stephen Melczer
  • Asif Zaman

       2008

  • Aaron Chan
  • Jamie Lutley

       2007

  • Amy Wiebe

       2006

  • Denis Dmitriev
  • Al Erickson
  • Nhan Nguyen

        2005

  • Moe Ebrahimi
  • Simon Lo
  • Kayo Yoshida