Mathematics is patterns and logic, imagination and rigor. It is a way of seeing and a way of thinking.
Math Mornings is a series of public lectures aimed at bringing the joy and variety of mathematics to students and their families. Speakers from Yale and elsewhere will talk about aspects of mathematics that they find fascinating or useful. The talks will usually be accessible to students from 7th grade and up, although occasionally some familiarity with high-school subjects will be helpful.
Math Mornings lectures will take place on three Sundays each semester, at Davies Auditorium, 10 Hillhouse Avenue. Join us at 10:30am for snacks and math games and demonstrations -- the talks begin at 11am.
Math Mornings is partially funded by grants from the National Science Foundation. It is part of Yale's Science Outreach program. To find out more see http://onhsa.yale.edu/science-outreach-home
Fall 2016 Schedule:
The Platonic solids---the tetrahedron, cube, octahedron, dodecahedron, and icosahedron---are some of the most beautiful and symmetric geometrical objects in 3-dimensional space. Their mysteries started to be unraveled by the ancient Greeks and still fascinate us today. In 1872, the German geometer Felix Klein proposed the Erlangen program, which sought to unify the study of geometry through the study of symmetries. We will investigate instances, from crystals to wallpaper, when symmetry can lead to a more fruitful understanding of geometry and vice versa.
For every number we can name there is a bigger one, so there must be a number bigger than the total number of atoms in the observable universe. And there must be some numbers that are so incredibly large, they have more digits than the total number of atoms. That means that there is not enough matter in the universe to write one of these humongous numbers digit by digit, even if we wrote small enough that each digit was the size of an atom! Do these huge numbers have names? How do we talk about them? Why would we even want to? In this lecture we'll discuss how to think and talk about these kinds of numbers. Hopefully by the end, we'll all have a deeper appreciation for just how many numbers are out there waiting for us.
Light we observe from quasars has traveled through the intergalactic medium (IGM) to reach us, and leaves an imprint of some properties of the IGM on its spectrum. There is a particular imprint of which cosmologists are familiar, dubbed the Lyman-alpha forest. From this imprint and with help from statistics, we can construct a map of the very distant Universe. I will introduce the special data that allow us to "see" deep into the cosmos and discuss the statistical framework that provides a way to fill in the gaps between our observations.
Fall 2015 Schedule:
If you have a loopy string, how would you arrange it to capture the most area? Already in ancient times people knew that it had to be the circle but if you think about it a bit more, it is not really quite so easy to see why that is the case. We will travel through all of history starting in the ancient kingdom of Carthage (with layovers in Switzerland, the animal kingdom and the realm of computer programs) and discover step-by-step why the circle is really the nicest shape there is.
Suppose we have a line of boxes, each with two possible states, black or white. A 1-dimensional cellular automaton is a simple set of rules for determining how the states of these boxes change over time. Slight changes in the rules can lead to vastly different patterns. In this talk we will look at examples of these 1-dimensional (and possibly 2-dimensional) automata and see how mathematical artists use them in beadwork, knitting, and image processing.
Patterns are all around us! From Persian tapestries and Egyptian tombs, to honeycombs in beehives, to the wallpaper in your living room, repeating patterns appear not only throughout art and history--they're easy to find in our everyday lives. Come join in an interactive exploration of these repeating images, and learn how mathematics can be used to show how all the patterns that exist can be categorized into just 17 types.
Spring 2015 Schedule:
Tic-Tac-Toe is a game that is probably familiar to you from elementary school. Odds are that you don’t play much Tic-Tac-Toe these days. There is a great observation from the great math puzzle guru Martin Gardner: “Many players have the mistaken impression that because they are unbeatable they have nothing more to learn.” If we change the rules of Tic-Tac-Toe just a little bit we are led to interesting unsolved problems. For example, is there a winning strategy for X in the 5 x 5 x 5 version of Tic-Tac-Toe?
We will introduce several other games and problems that have to do with points and lines. For example, it is known that we can choose 16 squares on an 8 x 8 chessboard so that no three squares lie on a line. But what happens with larger boards? Can we always pick 2n points from an n x n board with no three on a line? Can you find a way to place 9 points in the plane so that there are 10 different lines containing exactly 3 points? These problems may sound like they’re just for fun, but they are actually related to important questions at the cutting-edge of mathematical research!
Fall 2014 Schedule:
In 1750 Euler described a simple relationship among the numbers of vertices, edges and faces of a polyhedron. This wonderful formula has many implications and generalizations. Join us on a guided tour of Euler's formula and and what it means for many parts of mathematics, from topographical maps to fluid flows, from geometry and symmetry to dynamical systems.
This is an elementary talk to illustrate the remarkable organizational powers of random walks on Networks. It will not require any prior knowledge beyond middle school math.
We'll describe a range of examples of Networks and their ubiquity in our life, from social networks to information , economic, political, weather and communication networks. Usually such networks can be organized as mathematical graphs, on which certain transitions,or transactions, or exposures are being quantified. We'll see that a network based computational geometric approach for the sorting and organization of data and information leads to insights, understanding and predictions for complex systems. As specific examples we'll describe the network of characters in a body of literature, the network of Congress, a network of romantic relations in a High School, and many others.
Sun, Oct 12: Roger Howe (Yale University): A dozen things about the number 12. video
Spring 2014 schedule:
Fall 2013 schedule:
I will give a friendly introduction to higher dimensional space and talk about some of the objects in it, like spheres, cubes, and other polyhedra. I'll explain some of the really weird properties of polyhedra in high dimensional space, and even convince you that these things are really true.
How many guests can come into an infinite hotel? How many ping pong balls fit into an infinite barrel? What is 1/0? What is infinity minus infinity? Is 1 = 0.999999999.....? Can anything be infinitely large or infinitely small? Are there different sizes of infinity? In a finite world, why should we even care about this?
Come find out about these and infinitely many other questions on Sunday Morning, Nov 10.
There are five ways to break down the number 4 as a sum of positive whole numbers:4 = 3 + 1 = 2+2 = 2 + 1 + 1 = 1 + 1 + 1 + 1
so we say there are five "partitions" of 4. This looks easy, right? Not so fast! Can you write down or count the partitions of 10? 100? 1000? Can you see any patterns? In this talk we'll see how this seemingly easy business of adding and counting has led to some very beautiful and very difficult problems and ideas in mathematics and number theory. Come find out how "1 + 1 = 2" has fascinated mathematicians for centuries.
In 2012-13, our speakers were: