to return to the Graduate Student Seminar Page.
Reference Librarians from the Science and Math Libraries will cover several electronic databases and library services important to Mathematics research. Come and learn about Pegasus, a fast self-service electronic ordering service for documents not held in the UBC Library; learn how to effectively search for articles on Mathscinet, and hear about our new subscriptions to Math electronic journals.
The sex of hatchling crocodilians is determined by the incubation temperature of eggs in the laboratory as well as in nature. The talk consists of two parts. The first part gives a review of the biological problem. Two experimental observations are used: that male fitness depends more strongly on the quality of the incubation environment than female fitness, and that females lay eggs at a temperature close to the temperature at which they themselves were incubated. In the second part, we derive a population genetics model based on the above mentioned biological concepts. A method for finding the optimal sex ratio as a function of temperature is developed and applied under different assumptions. Numerical solutions are given and compared with available experimental data.
Integrating factors provide a way of reducing the order of an ODE by giving its conservation laws, i.e., a relationship between the lower order derivatives which is constant.
In the first part of the talk I will define what an integrating factor is, and discuss the connection between them and the Euler-Lagrange operator. By exploring this connection, we find that all of the integrating factors of an n-th order ODE are given as solutions to a certain system of linear PDEs of n variables.
I will then explain how the conservation laws can be systematically obtained from the integrating factors, i.e., how to find a first integral of an exact n-th order ODE.
Time permitting, I will discuss an algorithm that can be used to reduce an (overdetermined) linear system of PDEs, and its computer implementation.
Among many interesting discoveries on conic sections recorded in Blaise Pascal's manuscript (dates 1640), one intriguing theorem states: the three intersection points of three pairs of opposite sides of an arbitrary hexagon inscribed in a conic section will always be collinear. This is Pascal's famous mystic hexagram theorem. It has been proven in diverse ways -- although, strangely, none by Pascal himself. His actual proof, unfortunately, will never be known but how he might have arrived at his result is suggested by Germinal Dandelin's elegant illustration of Pascal's Theorem.
In this presentation, we will explain Dandelin's reasoning with the help of a sequence of pictures drawn in PostScript. We hope these pictures will clearly demonstrate Dandelin's ideas which proves Pascal's theorem requiring neither analytic geometry nor messy calculations.
A pilot project to update the curriculum of Math 100/101 started last September. During the colloquium I will present some of the work of myself and others involved in one aspect of the project, namely to include the use of computers in the course. This use comes in three main forms: in-class demonstrations, interactive computer labs, and an on-line text.
During the talk I will present several examples of each of these three areas. However, I will particularly emphasize the topic that I have spent most of my effort on: the interactive laboratories. Rather than use computers as a computational tool, we use Java applets in web pages to create a mixture of text and interactive diagrams for the students read and use. The labs are set up as an exploratory environment wherein broad ideas are explained.
Although I am optimistic about our work, there are some potentially serious technological and pedagogic drawbacks to our approach. I will also discuss these problems and possible remedies.
In the past interdisciplinary research between mathematics and theology has led to many important results, e.g. the discovery of transcendental numbers, a priori estimates (=precognition) or Homo-Morphisms.
In my talk I want to give an introduction to the new and exciting field of Pope matrices, an area of linear algebra with applications in ecumenicalism.
A linear form which gives the Pope Number of a square matrix with an odd number of rows can be used to decompose Mat(2k+1,K) into catholic and protestant subspaces. I want to present results about the interplay between these spaces, in particular between Pope and Lutheran Matrices, and attempt a proof of the famous Vatican Lemma.
In our talk, we would like to focus on the mathematical side of two games developed by E-GEMS - Phoenix Quest, an adventure game, and Super Tangrams, a game based on the classic puzzle. The level of mathematics involved in these games are suitable for grades 4-10; so viewer discretion is advised. ;)
Giving high school students illustrative and interactive math problems that are intersting, historical, and fun to solve is a possible solution.
Giving high school students illustrative and interactive math problems that are intersting, historical, and fun to solve is a possible solution. Examples of these math problems will be given at the talk. Some of these problems should involve proving some mathematical fact. High school students should see proofs so that they don't think math is just about computing and manipulating symbols. Also, they should see proofs at the high school level so that they will not be so intimidated by proofs when they encounter them in their university math courses.
Hopefully, at the seminar, a discussion of how math can be made fun, easy, interesting and useful for math high school students will take place.
The class number one problem - that h(-d) =1 for d=3,4, 7,8,11,19,43,67,163 and for no other d greater than 163 - was fully solved by Kurt Heegner in 1952 and the general Gauss class number problem was solved (up to a finite amount of computation) in 1983 in a theorem by Goldfeld, Gross, and Zagier.
I will define the class number and discuss the class number problem in terms of binary quadratic forms, imaginary quadratic fields and, time permitting, complex multiplication on elliptic curves.
I will attempt to give an introduction to the field of mathematical electrophysiology suitable to a general audience with no background in this field. I am interested in a general class of cells, called excitable cells, which include neurons, cardiac cells, and pancreatic beta cells. The flow of ions across the cell membrane of these cells leads to a voltage difference across the membrane. A sudden spike in this membrane potential results in a nerve impulse which may cause your toes to wiggle or your heart cells may contract. Using some rather complicated systems of ordinary differential equations, we keep track of the ions flowing across the cell membrane and the resulting membrane potential. We can simulate the electrical behaviour of the cell and also apply dynamical systems theory to analyze these systems.
I will mainly focus on issues related to getting your system up and running and why it's worthwhile. (and just a little bit about why you should dump windows).
What I will do is discuss a few ways in which both the storage requirements and the computation time for a direct method may be reduced. These methods will be illustrated with some examples drawn from standard test problems.
Click this button to return to the Graduate Student Seminar Page.