Fri. Nov. 26
12:00--12:50
Room C674 |
Laura Faber
BSc/BEd student, Math
Chinook award 2010
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Explicit bounds for the number of primes up to a large number.
Summer Research Project 2010 - Supervisor: Habiba Kadiri
In 1859, Riemann presented a paper on the Number of Primes Less than a Given Magnitude to the Berlin Academy of Sciences.
It is within his memoir that the Riemann Hypothesis was first conjectured.
It states that the zeta function zeta(s) has infinitely many nontrivial roots (nontrivial zeros) all most likely on the line Re(s)=1/2.
These zeros are intricately related to the location of the primes.
We have a number of prime counting functions such as pi(x), psi(x), and theta(x);
all of which depend on our knowledge of the zeros of zeta(s).
However, direct computation of these functions for large values of x is dependent on the computers computational power.
We therefore need a proof to go beyond the computational range.
The paper I worked on this summer is devoted to obtaining improved estimates for psi(x) when x is large.
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Fri. Nov. 19
12:00--12:50
Room C674 |
The music of the Primes (III)
produced by BBC and the Open University
Written and presented by
Marcus Du Sautoy (Oxford)
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From Turing to tomorrow
This last episode gives an account of Alan Turing's unresolved zeta function research, the tragic conclusion of his life, and his legacy in the mathematical community. Interviews with some of today's prominent mathematicians reveal tantalizing notions about the future of the Riemann hypothesis.
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Wed. Nov. 17
12:00--12:50
Room C674 |
BSc Students:
Darcy Best, Hugh Ramp, Keilan Scholten
and their coach:
Howard Cheng
ACM Programming Contest in Lethbridge
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ACM Rocky Mountain Regional Contest
This year our top team ranked second in the ACM Rocky Mountain Regional Contest,
beating many of the larger universities in Canada and the United States.
The top team will describe their experiences with the training and the actual competition.
They will describe some of the problems that they were given, and give some hints on how to improve for those who want to participate in future contests.
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Fri. Nov. 05
12:00--12:50
Room C674 |
The music of the Primes (II)
produced by BBC and the Open University
Written and presented by
Marcus Du Sautoy (Oxford)
with an introduction by Tim Trudgian
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From Riemann to Ramanujan
This episode focuses on the numerical landscape which Bernhard Riemann's calculations opened up and examines the work of subsequent mathematicians who challenged the notion of a finite set of prime numbers.
It guides viewers through the zero-punctuated pattern that Riemann unveiled.
It also describes the friendship between G. H. Hardy and Srinivasa Ramanujan and the difficulties both men experienced as they confronted problems in number theory.
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Fri. Oct. 22
12:00--12:50
Room C674 |
The music of the Primes (I)
produced by BBC and the Open University
Written and presented by
Marcus Du Sautoy (Oxford)
with an introduction by Habiba Kadiri
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From the Greeks to Gauss
Prime numbers are the atoms of arithmetic - the hydrogen and oxygen of the world of numbers. Despite their fundamental importance to mathematics, they represent one of the most tantalising enigmas in the pursuit of human knowledge.
This first episode details the early history of prime number theory, beginning with discoveries that took place in the Hellenistic world. \\
It illustrates how the torch of Euclid's work passed to 18th- and 19th-century Europeans, exploring Carl Friedrich Gauss' groundbreaking work in the prediction of prime numbers and introducing Bernhard Riemann's revolutionary zeta function.
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Friday Oct. 08
12:00--12:50
Room C674 |
Keilan Scholten
BSc student, Mathematics
NSERC award 2010
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Artin Prime Producing Polynomials
This talk will be discussing the results and motivation of a research project conducted during the Summer of 2010 under the supervision of Dr. Amir Akbary.
An Artin prime for an integer g is a prime such that g is a primitive root
modulo that prime.
In 1957 Raymond Griffin studied Artin primes and his work led to the question of whether or not there is a quadratic polynomial and fixed integer such that all primes produced by the quadratic are Artin primes for that integer.
I will discuss a similar problem; that of finding a polynomial and fixed integer such that the polynomial produces a very large number of consecutive Artin primes.
I will discuss the results of Pieter Moree’s 2007 paper on Artin prime producing quadratics as well as my results for cubic polynomials including a generalization of Moree's method for finding these polynomials.
Finally I will present the current records for Artin prime producing polynomials.
The majority of the talk will not require more than a basic background in mathematics. Undergraduate students are welcome.
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Friday Sept. 24
12:00--12:50
Room C674 |
Darcy Best
BSc student, Mathematics
NSERC award 2010
Hugh Ramp
BSc student, Physics
Chinook award 2010
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Mutually Unbiased Complex Weighing Matrices
This talk is about a research project that was conducted this Summer 2010, under the supervision of Dr. Hadi Kharaghani.
In a major 1997 paper Calderbank, Cameron, Kantor and Seidel studied the following problem:
A family of lines through the origin in R^n, such that any two are either perpendicular or at an angle theta.
Our research has focused mainly on a model of lines pertaining to the above study and in doing so, we only consider matrices over the complex roots of unity.
By studying the class of Mutually Unbiased Complex Weighing matrices, we will show the existence of some very interesting set of lines for certain small values of n and p. We also show some nonexistence results for certain values of n and p.
There will be a short introduction to complex numbers, so no prior knowledge of this topic is necessary.
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