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- / Math Teachers' Circle
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The CSUDH Math Teacher Circle will meet the first Tuesday of each month during the 2019-2020 academic year. All meetings are from **5:30 - 8:00 pm** and dinner will be served!

Check back here for more information on individual meetings.

**9/3/19 "Bulgarian Solitaire"**

Come learn to play Bulgarian Solitaire, a fun example of a dynamical system. Given a fixed number of beads arranged into piles, and some rules for rearranging them, will there eventually be a stable configuration of the beads, or will it cycle through different arrangements? How many arrangements are there, and how do we sort them? Made famous by Martin Gardner in the 1980’s, mathematicians have come up with numerous conjectures and proofs related to this system. Come see what has fascinated others for more than 30 years!

Click here for the flyer. Click here to sign up!

**10/1/19 "Risk in the Stock Market"**

Are there good reasons to buy stocks or other assets with negative returns? Why is diversification in the stock market important? In this session, we will use probability, statistics, and some simulation to explore these questions and see why blindly buying high-return stocks (and associated high volatility) can be catastrophic for a portfolio. We might also just learn something about the dot-com bust and the financial crisis!

Click here for the flyer. Click here to sign up!

**11/5/19 "Multiplication Madness"**

Does 3 x 4 have to be 12? Are there other ways we can multiply numbers? Do the resulting multiplication tables have any interesting properties? In this session, we find out that the answer to the first question is no! We will explore multiplications defined by looking at the intersections of lines, counting rectangles, and hosting dinner parties, and learn what these three constructions have in common.

Click here for the flyer. Click here to sign up!

**12/3/19 "Harmonic Numbers"**

Harmonic numbers get their name because they arise as ratios of musical tones. What numbers can you make as differences of harmonic numbers? How do you know when a difference cannot be made? How can we use harmonic numbers to understand the long-standing, as-yet unsolved, abc conjecture? In this session, we will learn about harmonic numbers, use them to understand the abc conjecture, and perhaps even meet up with Euler's largest lucky number!

Click here for the flyer. Click here to sign up!

**2/4/20 "Euler and Hamilton: Two Travelers"**

What do Mathematicians Euler and Hamilton have in common? It turns out more than you might realize, as they both considered questions about travelers: Can a traveler travel every road? How can a traveler visit every destination efficiently? In this session we will investigate several real world problems and the graph theory spawned by these problems.

Click here for the flyer. Click here to sign up!

**3/3/20 "Nearest Neighbor: Voronoi Diagrams"**

Have you ever wondered how Netflix is able to suggest shows or movies that you actually like? What about selecting the best location for your next business? Are you interested in creating wonderful patterns for your next DIY project? Come and learn about Voronoi Diagrams and see how this beautiful geometry can resolve these questions.

Click here for the flyer. Click here to sign up!

**4/7/20 TBD**

**5/5/20 TBD**

**9/4/18 "What I Learned About Sharing Long After Kindergarten"**

Have you ever tried sharing a dessert, like a birthday cake, with someone, and wondered how to share it fairly? What happens when you have a batch of cookies to share, some with nuts and some without--how can you share them fairly? What if you are dividing up a number of items between two people, say a jewelry collection, where the items cannot be broken apart? What does it mean to share fairly?

**10/2/18 "Winning the Lottery"**

The lottery: many will play, few will win. Have you ever played? Did you ever think about looking for a winning strategy? Would you expect to win the same amount every time you win? Is there a way to use geometry to understand the lottery? In this session, we consider all of these questions and will come up with a winning strategy!

**11/6/18 "Blokus and Polyominoes"**

Have you ever played Tetris and wondered if there could be other shapes? Or have you thought of Dominoes as geometric tiles? These are both games involving polyominoes. In this session we will investigate a different polyomino game - Blokus. Blokus is a 2 - 4 player game involving polyominoes, geometry, and tiling. Come and play and see what math we can discover in this game!

**12/4/18 "Factoring in Time for Numeracy"**

Have you been looking for a fresh math game you can use in class? Have you ever wondered how you can build numeracy (or number fluency) in a fun, interesting, and exciting way? Come see how playing Prime Climb can help! Prime Climb is a game of luck and strategy that can help build strong number fluency.

**2/5/19 "Match or No Match"**

In this session, we will explore the Match-No Match game: two players each draw one chip out of a bag – if the color of the chips match Player 1 wins, if not Player 2 wins. Is this a fair game? How do we know? How can we construct a fair game? What variations of this game are possible? How does this connect to other mathematics? Come and see how much mathematics can arise from a bag of chips!

**3/5/19 "Symmetry and Algebra"**

How can we relate ideas from geometry to those from algebra? There are many ways! If we look at a regular polygon, we can see various symmetries. How do these symmetries connect to algebra? In this session, we will explore the symmetries of a variety of shapes and ways to "operate" on the shapes to create “multiplication tables” that demonstrate an interesting underlying structure with properties from algebra.

**5/7/19 "Getting Nim-ble with Binary"**

Nim is a game played with counters arranged in piles. Each player takes turns removing counters according to certain rules, and the last player to take a counter wins. Is there a guaranteed winning strategy? Are some starting positions better or worse than others? What happens if we vary the game rules a bit? Come and see the surprising depth and connections between this game and the larger world of mathematics.

**9/5/17 "Simon Says, Four Gallons"**

Given a 5 gallon jug and a 3 gallon jug, is it possible to measure out exactly 4 gallons? That's the problem faced by John McClane and Zeus Carver in Die Hard 3. In this session, we'll not only solve this problem, but we will also look at questions such as: Is there a shorter way to do this other than trial and error? How can we use geometry to solve this problem? How is this kind of problem connected to number theory?

**10/3/17 "Estimathon"**

How many airline passengers are there in a year? How many miles long is the Mississippi River? In this session, we will play a game called Estimathon, where the questions involve giving a range in which you think the correct answer lies. You and your team will have to select your ranges carefully to maximize your score in the game. We will also look at how to use what we learn from one estimate to make estimates of related values and explore estimation tasks you can use with your students. Come and hone your skills at estimation!

**11/7/2017 "Candy Sharing"**

In this session we will play a game called Candy Sharing. Can you create a game that results in an infinite loop? Can you predict how long the game will last? When is the game over before it begins? In this session, we will investigate these and other questions and see the mathematics of dynamical systems in action. Come get a taste of candy sharing--the sweetest math!

**12/5/2017 "Is Santa Secretly Deranged?"**

Have you ever been part of a Secret Santa gift exchange? Did anyone ever draw their own name and have to re-draw? How often does that happen? What happens as the size of the group of participants grows? In this Math Teacher Circle, we look at the mathematics of these exchanges, called derangements. A derangement is a one-way assignment of each person in a group to another person. As the group grows bigger, what happens may surprise you.

**2/6/2018 "Pick Connects the Dots"**

When it comes to measuring the area of a simple polygon all you have to do is take out a measuring tape and your area formula, right? But what do you do if your simple polygon is not so simple? Is there some way to find the area without measuring all the edges? In this Math Teacher Circle, we take a look at how the connect the dots grid game helps us calculate the area of any simple polygon. Pick’s Theorem will help us do the rest.

**3/6/2018 "The Game of Hex"**

In this session, we will investigate the game of Hex - a two player “grid” game that seems to always have a winner. Does Hex really always have a winner? Can you discover a winning strategy? Or can your opponent always keep you from winning, as in Tic-Tac-Toe? Come and see what you can find out.

**4/3/2018 "Length Spectrum of Numbers"**

This session begins with the question, ‘Which natural numbers can be written as sums of (more than one) consecutive natural number’?

Note that a number may be written as such a sum in more than one way, e.g. 9 = 4+5 = 2+3+4. We call the collection of the lengths of these sums the length spectrum of the number, so the lspec(9) = {1,2,3}. In this session we will explore some natural questions that one may ask about these spectra. Along the way, we will have some fun in playing a guessing game. Be prepared for some surprises!

**5/1/2018 "Knot Mosaics"**

Knot theory is an area of mathematics concerned with, well, knots, loops of string crossed over and around each other in different ways. How can you tell two knots apart, or if two knots are really the same? This is the core of knot theory. In 2008, a new perspective on this theory, knot mosaics, took hold. These mosaics enable a knot to be represented using tiles. In this session, we explore basics of knots and questions such as, What tiles are required to make knot mosaics? How can knots created using mosaics be classified? Come and get tangled up in learning some new mathematics!

See the links below for more information about each session.

**9/6/16 “Pancake Sorting and Recursion”**

Have you ever wondered how and where mathematics and computer programming overlap? In this session, we will see that one example of the overlap comes in a very surprising place: pancakes. We will be exploring ideas related to sorting and recursion, and use them to flip our flapjacks into a nicely ordered stack.

**10/4/16 "Rational Tangle Dance"**

In 1967, mathematician John H. Conway presented seminal results on the classification of knots through a study of “rational tangles.” In order to explain some of the key ideas behind the theory, he developed an activity, the “rational tangle dance,” that four people holding the ends of two lengths of rope, and a fifth person looking on, can perform. The magic of this activity has captivated many over the decades, and the rational tangle dance is now considered a favorite in many math circle groups.*Description by James Tanton*

**11/1/16 "The Mad Veterinarian: The Mathematics of Mad Science”**

In this session, we will explore a situation from science fiction, in which a scientist can transform one animal into others. What mad configurations are possible with an initial set of animals? When can we undo the transformations and get the original animals back? More importantly, what kind of mathematical structures are involved? We will examine these questions and the underlying mathematics involved. White lab coat not required!

**12/6/16 "Pirates, Prisoners and Chicken: An Introduction to Game Theory"**

How should a pirate share the loot with fellow cutthroats? Should two captured prisoners each confess to a lesser crime? Did President Kennedy play Chicken with Russia? In this session, we will explore answers to these questions. We will see how these three life-or-death situations are part of a larger mathematical landscape known as game theory, and discuss how game theory can be used in an array of situations to decide on a course of action.

**2/7/17 "SET: The Mathematics Behind the Game"**

Set is a fascinating card game developed by Marsha Falco in 1974. The rules specify how certain groups of three cards can be formed to make a "SET". While the rules are fairly straightforward, beneath the surface lurks some deep mathematics. The game leads to questions such as: "How many cards do you need to guarantee a SET?", "How many SETs are possible?", "How is this game like doing geometry?" In this session, we will learn and play SET, and explore some answers to these questions.

**3/7/17 "KenKen"**

**4/4/17 "Liar's Bingo"**

Do Bingo cards have patterns? Can you lie about what’s on your card and get away with it? Do mathematicians know something special about how to find the truth? In this session, you get to put your tall-tale skills to the test. In the process, we will learn some of the mathematics of information transmission, and how to use mathematics to find the truth.

**5/2/17 "Spot-It!"**

The rules of Spot it are simple: match a symbol on your card to a symbol on a card drawn from the top of the deck. Could this simple children’s game give rise to interesting mathematics? Is there a deeper structure to this game? In this session, we will discover how the Spot it! game is constructed and explore some of the mathematics involved.

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