This page includes descriptions, slides, videos, and related handouts from all the past talks of the Monthly Math Hour at the University of Washington. You can also find information about previous UW Math Hour Olympiads.
June 10, 2012
Location: Room 260, Savery Hall
Math Hour Olympiad
May 13, 2012
Location: Room 260, Savery Hall
Speaker: Eric Brechner, Principal Development Manager, Xbox Engineering Fundamentals
Title:"Rainbow Mathematics"
Video available here
Slides available here
Abstract: What time of day is best to see a rainbow? Why is a rainbow shaped like an arch? Which color is on top? Are there ever two rainbows at once?
Rainbows are uncommonly beautiful. Most people have seen them, especially here in Seattle. Yet, most people don't know a rainbow's secrets. A little optics, some math, and your imagination are all you need to unlock rainbows and reveal things few people know. You'll uncover them all for yourself in this engaging talk that turns Snell's law, water, sunlight, and reflection into a beautiful sight.
April 15, 2012
Location: Room 260, Savery Hall
Speaker: Steven Klee from the UC Davis Department of Mathematics
Title: "The Mathemagic of Magic Squares"
--Video available here--
--Slides available here--
Abstract: A magic square is a filling of the squares of an n x n grid with the
numbers 1, 2, 3, ..., n2 so that the numbers in all rows and columns
have the same sum. In this talk, we will explore the history of magic
squares, from ancient mathematicians in China, India, and Persia, to
Benjamin Franklin's fascination with constructing magic squares and modern
mathematical problems. We will explore the underlying mathematics of magic
squares. We will end by taking the magic out of magic squares and using
them to understand a mathematical game.
March 11, 2012
Location: Room 260, Savery Hall
Speaker: Professor Jonathan Brundan from the University of Oregon Department of Mathematics
Title: "Domino Tilings and Determinants"
--Video available here--
--Handout available here--
Abstract:
There are two ways to tile a 2x2 board with 2x1 tiles (= or ||).
There are thirty six ways to tile a 4x4 board with 2x1 tiles (you can
check this by listing all the possibilities!).
Question: How many ways are there to tile an 8x8 board with 2x1 tiles?
I'll explain a neat way to work this out using some techniques from graph theory and linear algebra --- though no knowledge of that will be assumed in advance. If there's time I'll talk about some other related combinatorial/counting problems.
June 5, 2011
Location: First Floor, Savery Hall
Time: 9:30am - 3:00pm
Math Hour Open Olympiad
Olympiad Poster
--Photos available here--
The Olympiad is intended for students in grades 6-9.
May 15, 2011
Location: Room 260, Savery Hall
Speaker: Professor Sara Billey from the University of Washington Department of Mathematics
Title: "Computer proofs in Algebra, Combinatorics and Geometry"
--Slides available here--
--Video available here--
Abstract: Have you ever tried to prove a theorem using a computer?
If not, this talk might give you some ideas to help you get started. If so,
this talk will hopefully encourage you to think about the next
questions -- what types of problems are amenable to computer proofs
and how should one publish a computer proof?
We will survey some famous and some not so famous theorems with computer assisted proofs but no known human-only proof. For example, the 4-color theorem and Kepler's conjecture are known to be true only because of computer assisted proofs. In addition, we will discuss some current research where the proof is not reduced to a finite check but instead depends on reaching a halting condition.
Some useful references:
April 17, 2011
Location: Room 264, Savery Hall
Speaker: Dr. Daniel Finkel, Mathematician, Math for Love
Title: "Billiard Balls and Laser Beams"
--Video available here--
Abstract: Imagine standing in a room made entirely of mirrors, with a light bulb in a particular spot. The light is on. You would imagine that the room would be totally illuminated. And yet, you are in complete darkness. How is this possible?
Welcome to the geometry of reflection, where our thoughts turn to laser beams bouncing off mirrors, or billiard balls ricocheting off the sides of a pool table. In this talk, we'll explore the extraordinary reflective properties of geometric shapes like rectangles, triangles, circles, ellipses, parabolas, and hyperbolas. In fact, it's possible to understand many of these shapes almost entirely in terms of their reflective properties.
There are tremendous applications in the real world for reflective geometry, from satellite dishes to solar power, engineering to art to architecture. Reflective geometry is also a great source of purely mathematical questions, including a number of unsolved problems. We'll see the gamut in this lively talk on a unique topic.
March 13, 2011
Location: Room 260, Savery Hall
Speaker: Professor Sándor Kovács from the University of Washington Department of Mathematics
Title: "A glimpse into the sixth dimension"
Abstract: Higher dimensional geometry is used in more places than most people realize. Anyone who uses a mobile phone (is there anyone who does not?) takes advantage of higher dimensional geometry during every call. Higher dimensional geometry is used in robotics and cryptography. If you ever bought something on the internet, you were able to do that safely because of higher dimensional geometry.
The main purpose of this talk is to discuss higher dimensions from a practical angle. This is usually an intriguing topic if for nothing else but because it is so out-of-this-world. My hope is that at the end of this discussion the idea of higher dimensions will seem perhaps less romantic and exotic, but more approachable and useful and definitely at least as intriguing as it had been before.
Many people have heard about time being considered the fourth dimension and perhaps even figured out ways to think about the fifth. In this talk we will go beyond both of that and as the main example of the usefulness of higher dimensions I will explain how the geometry of a six dimensional space can tell us about interesting questions regarding plane curves. The cell phone, robotics, and cryptography applications would require a semester long course at least, but I will say a few words about those as well and depending on time we will probably go up to working with 10 dimensions and say at least one word about the true dimension of the space we live in.
June 6, 2010
Speaker: Dr. Noble Hendrix, Biometrician, R2 Resource Consultants, Inc.
Title: "One Fish, Two Fish, False Fish, True Fish"
Abstract: Why do we count fish? The short answer isto eat them. A slightly longer winded explanation is, so that we can harvest fish at a rate such that the population can continue to replace itself. This scientific explanation makes several assumptions, though. Those assumptions are: we understand how fish populations increase and decrease naturally, we understand how fishing affects the population, and we know how accurate our counts of the population are.
I will talk about all three of these topics but mostly concentrate on the final one, because people (Homo sapiens) in general are not very good at counting. As an extreme example of this trait, members of the Pirahc tribe use a "one-two-many" system of counting, and lack a linguistic mechanism for numerals. Although we do not have the same linguistic constraints of the Pirahc, our counts of fish are inaccurate. To quantify the errors in counting, we can use probability models. For example, if I observed 10 fish what is the probability that there were actually 12?
There have been many technological improvements to counting fish. Each new approach has its own set of problems, though. Therefore, building probability models to understand the error in each successive technological breakthrough becomes a recurring process. We will look at some of the more interesting approaches to fish detection, such as video and acoustic imagery. The fundamental approach of using probability models to understand errors in measurement is, of course, not limited to counting fish. Probability models are applied in economics, medicine, and politics among other fields. Application in fisheries does have its unique benefits, however, and eating fish is certainly one of them.
May 16, 2010
Speaker: Professor Jennifer Quinn from the University of Washington at Tacoma Department of Mathematics
Title: "Fibonacci Fascination"
Abstract: Behold, the Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... , a number sequence which has long fascinated scholars because of its frequent occurrence in art, architecture, music, magic, and nature. You may have seen them in Dan Brown's novel The DaVinci Code or perhaps a FoxTrot cartoon. The next number of the sequence is generated by adding the two preceding. This talk will exhibit many natural examples of Fibonacci numbers while exploring the unusual (and aesthetically pleasing) patterns of the sequence itself. History and popular culture weave together with beautiful mathematics, plus a Fibonacci trick for good measure!
May 2, 2010
Speaker: Professor Jack Lee from the University of Washington Department of Mathematics
Title: "The Curvature of Space"
Abstract: Do you think that everything there is to know about geometry was already discovered ages ago? Think again. Since the time of Euclid, the history of geometry has been a dramatic saga that your middle school teachers probably won't tell you about. It led, more than a century ago, to the mind-bending mathematical discovery that the three-dimensional space we live in might be "curved," in much the same way as the two-dimensional surface of the earth is curved.
In this talk you'll have a chance to learn what it could possibly mean mathematically for space to be curved, how we can detect it, and the fascinating story of how we got from Euclid to here. Along the way, you'll find out about "proofs" by professional mathematicians that turned out to be wrong, bitter personal battles over who was right and who was wrong, a million-dollar prize for solving a mathematical problem, and a mysterious modern-day Russian mathematician who earned it but isn't sure he wants it.
The Monthly Math Hour at the University of Washington is partially supported by the NSF award DMS-095-3011.