Fall 2019 Schedule
I will in fact talk about some unsolved, or recently solved, problems in Mathematics. The main purpose of the meeting, however, will be to organize the Undergraduate Colloquium for those interested in taking it for credit (1 hour credit/no credit). For many participants this will be the first class in which they have to write a technical report. This is a complicated yet gratifying task. I will discuss some of the issues involved and also give a first introduction to the use of LaTeX.
Classifying Pythagorean Triples
Abstract: Number theory begins as the study of the natural numbers: 1, 2, 3, etc. When studying the natural numbers, one quickly arrives at the fascinating mysteries surrounding prime numbers. You might wonder: How many primes are there? How can we tell if a given number is prime? Is there a pattern to the primes? We know some things about prime numbers, for instance that there are infinitely many of them. However, there are many things which are still not understood, largely because the "pattern" of the prime numbers is unpredictable. There are many other interesting objects in mathematics that behave as erratically as the prime numbers do, and the techniques of number theory can often be used to study these objects as well. As an example, consider right triangles whose side lengths are all natural numbers. We will classify all such triangles, using techniques from arithmetic geometry and the theory of algebraic numbers. The only prerequisite for this talk is high school algebra.
The Fast Fourier Transform
Abstract: In 1965 Cooley and Tukey discovered a revolutionary algorithm: the Fast Fourier Transform (FFT). It reduces the number of operations required to do frequency analysis of a signal of length N from N2to about N log(N). We will look under the hood of this ubiquitous algorithm, and explore a few applications including noise reduction, image compression (JPEG) and sound compression (MP3).
Isoperimetric problem and the Calculus of Variations
The isoperimetric problem is one of the oldest problems in mathematics. On a plane, the problem asks for the plane region with a given perimeter that encloses the largest area. The fact that the circle is the solution to this problem appears to be intuitive and was known already in Ancient Greece, but it was not until 1879 that Karl Weierstrass gave the first rigorous proof of this statement. This leads to the development of an emerging field in modern mathematics known as the Calculus of Variations. Besides its links with other branches of mathematics such as differential equations and functional analysis, it finds its diverse applications in physics, engineering, economics, and biology. In this talk, we will introduce several classical problems in the field and discuss the classical techniques for solving these problems explicitly.
University of Utah Mathematics Alumni
Please join us for the September 25 Undergraduate Colloquium where four University of Utah alumni will share the career paths taken from a mathematics degree to their current jobs, followed by Q&A. This is a great opportunity to engage with professionals in a range of STEM careers.
The Department of Mathematics Undergraduate Colloquium welcomes;
Evan Dudley, VP Credit Risk Technology, Goldman Sachs
Jeremiah Perry, VP Liquidity Risk, Goldman Sachs
Dan Eardley, Director, Mathnasium
Jonathan Bown, Quantitative Modeling Analyst, Zions Bank
Math 3000 (Receive Credit for Attending)
The Undergraduate Colloquium is open to anyone to attend; however, if students would
like to receive credit, you may register for Math 3000.
This is a 1 credit hour CR/NC course. To receive credit:
- You may not miss more than 2 of the colloquia
- You will need to write a short paper on one of the topics presented during the semester. (Report Specifications)
|Peter Alfeld||Lisa Penfold|
|Course Instructor||Administrative Coordinator|