Here is the rescheduled GaYee’s math club talk tomorrow about “Seven Bridges of Königsberg”. See her abstract below.
Long ago in a little town on a river in Prussia, the people wondered: can you visit every part of the city, crossing all seven bridges only once? This is called the Seven Bridges of Königsberg problem which was popular in the 18th century. In this talk I will introduce basic graph theory and Euler’s solution to this problem. Using the result, we will also explore other related puzzles and its application.
The math club offers a pleasant place to take a break in busy exam weeks. Floyd Williams gives a talk for us. For the abstract, see below:
A tractroid ( or pseudosphere ) is a surface generated by revolving a special curve ( a tractrix ) about an axis. By a clever change of variables one can find a nice realization of this surface as a certain “vaccum space”, which mathematicians call an orbifold -the latter being defined by a simple relation between points. This vaccum space is similar in nature to a 2-dimensional black hole with mass degenerating to zero. Thankfully however these objects are “not” the same (otherwise there’s no life on earth ), and thankfully no knowledge of black holes is needed for the talk-which mainly involves calculus.
We will meet in LGRT 1634 at 5 pm just as usual.
The abstract of the talk is as follows:
The Radon transform is a way of transforming one function into another which has applications in mathematics and image processing. I will define the Radon transform as well as the closely related X-ray transform. I will recall the more famous Fourier transform, and then discuss the connection between these operators (which seems to have given rise to the popularity of the Radon transform in medical imaging)
It was really unfortunate that we had to cancel the math club last week due to the snow. We will reschedule GaYee’s talk at some time this semester, so don’t miss it!
This week, we are happy to have Eric Sommers as a speaker. He will talk about “An Introduction to Representation Theory”.
Here is his abstract:
I’ll give a survey of the main ideas behind the representation theory of finite groups. Representation theory is the study of the ways in which a group can be represented by a set of matrices. Knowing some linear algebra (Math 235) is helpful, but not required. It is not necessary to know what a group is– I will give the definition. This is a beautiful subject, accessible to all math majors, but not something that shows up in our undergraduate curriculum (although our friends in chemistry do see it).
We appreciated the nice opening math club talk given by Pat Dragon. Here is his abstract.
A de Bruijn sequence is a binary string of length $2^n$ which, when viewed cyclically, contains every binary string of length $n$ exactly once as a substring. For example, 00010111 suffices for $n = 3$. Knuth refers to the lexicographically least de Bruijn sequence for each $n$ as the “Granddaddy” sequence due to its venerable origin. In 1934 Martin originally constructed these sequences and later it was shown by Fredericksen et al that they can also be constructed by concatenating the aperiodic prefixes of the binary necklaces of length $n$ in lexicographic order. In a recent publication, we proved that the Granddaddy has a lexicographic partner. The “Grandmama” sequence is constructed by concatenating the aperiodic prefixes of necklaces in co-lexicographic order. This talk will introduce de Bruijn sequences, the FKM algorithm, and some applications.
Sorry for the late announcement, but if you can, please join us tomorrow as Math club hosts its final talk of the semester. We meet Wednesday 4/26, from 5-6 pm in LGRT 1528. Dan Nichols will give what may well be his final UMass math club talk, on Finite Fields and the Mathematics of Forward Error Correction. His abstract is below.
Finite Fields and the Mathematics of Forward Error Correction
Error-correcting codes for reliably storing and transmitting data are an essential tool of the information age, and many of the most widely used algorithms are based on number theoretic concepts such as finite field arithmetic. I will give a brief overview of the mathematics of coding theory and describe several popular types of codes including Reed-Solomon codes.
There will be a final math club next week, with no talk scheduled. We’ll just enjoy pizza and some down time together to do some mathy things, perhaps play some set, or watch some math videos.
Please join us on Wednesday, April 12 when Math club will feature a talk from graduate student Tori Day titled “Hidden Figures: The African American Women Mathematicians of NASA Who
Helped Fuel America’s Space Achievements”. We meet from 5-6 pm in LGRT 1528. Pizza and soda will be provided. Tori’s abstract is below.
In this talk, we will explore the lives and times of three of the central
figures of NASA (then NACA)’s West Computing Group: Dorothy Vaughan, Mary
Jackson, and Katherine Johnson. Along the way we will discuss their
contributions to mathematics and engineering and the Space Race, as well
as the challenges they overcame and the roads they paved. We will end
with a basic and broad overview of a paper co-authored by Katherine
Johnson in 1960 entitled Determination of Azimuth Angle at Burnout for
Placing a Satellite Over a Selected Earth Position.
Please join us this Wednesday, March 29, from 5-6 pm in LGRT 1528. We will hear from graduate student Filip Dul, who will speak about the Poincaré Recurrence Theorem. His abstract is below. Pizza and soda will be provided, as usual.
The Poincaré Recurrence Theorem
When air molecules are zooming around a room, can they all return to the locations they were in earlier? Can they all wind up in one corner of the room? In this talk we’ll learn about the Poincare Recurrence Theorem and its interesting implications for those two questions, which generated a big controversy in the late 19th century between physicists and mathematicians about the meaning of the Second Law of Thermodynamics.
Wednesday, March 8th, 5-6pm in LGRT 1528 we hear from Professor Tom Braden about the “Geometry of machines”:
Configuration spaces are one way to construct very interesting geometric
spaces. A configuration space is a space whose points represent
possible states in a mechanism or other physical system. Navigating
along a path inside the space is then represented by a motion of the
mechanism. Some quite complicated and high dimensional spaces which
cannot be visualized directly can be explored very concretely in this way.
I will focus mainly on configuration spaces of planar bar-and-joint
machines, which are machines in the plane made from rigid bars, hinges,
and anchors. Amazingly, a theorem of Kapovich and Milson says roughly
that any manifold can appear as (part of) the configuration space of
such a machine.
As always, there will be pizza and soda!
This Wednesday, 3/1, please join us in LGRT 1528 from 5 to 6 pm for Math club. We will hear a talk from Angelica Simonetti on braid groups, with pizza and soda provided. Here’s Angelica’s abstract:
Braid groups: from algebra to geometry
“Who has never seen a girl with her hair gathered in a braid? Braid groups are a perfect example of how mathematics can be deep, rich, even complicated and yet intuitive at the same time. In the talk we are going to present braid groups algebraically and show some of their geometric interpretations, including how they appear in the theory of mapping class groups.”